diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..6a9f562 --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2021 MIT Probabilistic Computing Project + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/Manifest.toml b/Manifest.toml new file mode 100644 index 0000000..db37b78 --- /dev/null +++ b/Manifest.toml @@ -0,0 +1,552 @@ +# This file is machine-generated - editing it directly is not advised + +[[AbstractFFTs]] +deps = ["ChainRulesCore", "LinearAlgebra"] +git-tree-sha1 = "6f1d9bc1c08f9f4a8fa92e3ea3cb50153a1b40d4" +uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" +version = "1.1.0" + +[[Adapt]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "af92965fb30777147966f58acb05da51c5616b5f" +uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" +version = "3.3.3" + +[[ArgParse]] +deps = ["Logging", "TextWrap"] +git-tree-sha1 = "3102bce13da501c9104df33549f511cd25264d7d" +uuid = "c7e460c6-2fb9-53a9-8c5b-16f535851c63" +version = 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"4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5" + +[[Wavelets]] +deps = ["DSP", "FFTW", "LinearAlgebra", "Reexport", "SpecialFunctions", "Statistics"] +git-tree-sha1 = "e5903fb2bf93697a79d01383618ea0855256a337" +uuid = "29a6e085-ba6d-5f35-a997-948ac2efa89a" +version = "0.9.3" + +[[Zlib_jll]] +deps = ["Libdl"] +uuid = "83775a58-1f1d-513f-b197-d71354ab007a" + +[[nghttp2_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" + +[[p7zip_jll]] +deps = ["Artifacts", "Libdl"] +uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" diff --git a/Project.toml b/Project.toml new file mode 100644 index 0000000..01e7cb6 --- /dev/null +++ b/Project.toml @@ -0,0 +1,9 @@ +[deps] +ArgParse = "c7e460c6-2fb9-53a9-8c5b-16f535851c63" +Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa" +DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab" +Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f" +Entropies = "ed8fcbec-b94c-44b6-89df-898894ad9591" +FunctionalCollections = "de31a74c-ac4f-5751-b3fd-e18cd04993ca" +Gen = "ea4f424c-a589-11e8-07c0-fd5c91b9da4a" +TimerOutputs = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f" diff --git a/README.md b/README.md new file mode 100644 index 0000000..bc5b167 --- /dev/null +++ b/README.md @@ -0,0 +1,44 @@ +# Estimators of Entropy and Information via Inference in Probabilistic Models + +This repository contains experiment code for + +_Estimators of Entropy and Information via Inference in Probabilistic Models__. +Feras A. Saad, Marco Cusumano Towner, Vikash K. Mansinghka. +Proceedings of The 25th International Conference on Artificial Intelligence +and Statistics, PMLR 151:5604-5621, 2022. +https://proceedings.mlr.press/v151/saad22a.html + +## Getting started + +1. Install julia v1.6.2 from + + https://github.com/JuliaLang/julia/releases/tag/v1.6.2 + +2. Set current directory to the Julia project using + + export JULIA_PROJECT=. + +3. Instantiate the package dependencies using + + julia -e 'using Pkg; Pkg.instantiate()' + + The main dependency is the Gen.jl package, + +## Running experiments + +Please navigate to [./examples](./examples) and follow the README. + +These experiments show how to estimate the entropy of random variables or +the (conditional) mutual information between groups of random variables in +a probabilistic program written in [Gen.jl](https://www.gen.dev/). The two +applications in [./examples](./examples) directory are based on Gen +probabilistic programs that encode models for blood glucose monitoring and +the HEPAR expert system for liver disease. + +A further reference of the program analysis implementation in Gen can be +found in Section 8.6 of the following dissertation: + +_Scalable Structure Learning, Inference, and Analysis with Probabilistic +Programs_. Feras A. K. Saad. PhD Thesis, Massachusetts Institute of +Technology, 2022. Pages 178–182. +https://dspace.mit.edu/handle/1721.1/147226 diff --git a/entropy.jl b/entropy.jl new file mode 100644 index 0000000..94bc55a --- /dev/null +++ b/entropy.jl @@ -0,0 +1,177 @@ +import Gen + +using Statistics: mean + +using Gen: + assess, + complement, + project, + generate, + GenerativeFunction, + get_choices, + get_score, + get_selected, + Selection, + simulate + +function logmeanexp(arr::AbstractArray{T}) where {T <: Real} + return Gen.logsumexp(arr) - log(length(arr)) +end + +"""Entropy lower bound using custom proposal.""" +function entropy_lower_bound( + model::GenerativeFunction, + model_args::Tuple, + proposal::GenerativeFunction, + proposal_args::Tuple, + targets::Selection, + N::Integer, + M::Integer; + model_traces::Vector{Gen.Trace}=Gen.Trace[]) + wi_list = [] + for i=1:N + # Sample observations from model. + tr_p = isempty(model_traces) ? simulate(model, model_args) : model_traces[i] + observations = get_selected(get_choices(tr_p), targets) + wj_list = [] + for j=1:M + # Sample latents from proposal and compute score. + tr_q = simulate(proposal, (proposal_args..., observations,)) + log_q = get_score(tr_q) + # Compute score of latents + observations under model. + choices = merge(observations, get_choices(tr_q)) + _, log_p = generate(model, model_args, choices) + # Compute importance weight. + log_w = log_p - log_q + push!(wj_list, log_w) + end + wj_avg = mean(wj_list) + push!(wi_list, wj_avg) + end + return mean(wi_list) +end + +"""Entropy upper bound using custom proposal.""" +function entropy_upper_bound( + model::GenerativeFunction, + model_args::Tuple, + proposal::GenerativeFunction, + proposal_args::Tuple, + targets::Selection, + N::Integer, + M::Integer; + model_traces::Vector{Gen.Trace}=Gen.Trace[]) + @assert(M == 1) + wi_list = [] + for i=1:N + # Sample latents + observations from model and compute score. + tr_p = isempty(model_traces) ? simulate(model, model_args) : model_traces[i] + wj_list = [] + for j=1:M + # Compute score of latents + observations under model. + log_p = get_score(tr_p) + # Compute score of latents under proposal. + observations = get_selected(get_choices(tr_p), targets) + latents = get_selected(get_choices(tr_p), complement(targets)) + _, log_q = generate(proposal, (proposal_args..., observations,), latents) + # Compute importance weight. + log_w = log_q - log_p + push!(wj_list, log_w) + # TODO: MCMC step iterating the latents in tr_p + # if j < M + # tr_p = metropolis_hastings(tr_p, complement(targets); + # check=true, observations=observations) + # end + end + wj_avg = -mean(wj_list) + push!(wi_list, wj_avg) + end + return mean(wi_list) +end + +"""Entropy lower bound using default proposal.""" +function entropy_lower_bound( + model::GenerativeFunction, + model_args::Tuple, + targets::Selection, + N::Integer, + M::Integer, + K::Integer; + model_traces::Vector{Gen.Trace}=Gen.Trace[], + return_weights::Bool=false) + wi_list = [] + for i=1:N + # Sample observations from model. + tr_p = isempty(model_traces) ? simulate(model, model_args) : model_traces[i] + observations = get_selected(get_choices(tr_p), targets) + wj_list = [] + for j=1:M + wk_list::Vector{Float64} = [] + for k=1:K + # Sample latents (particle k) from default proposal + # and retrieve weight w_k, + # which is p(observations | latents) + tr_q, log_w = generate(model, model_args, observations) + push!(wk_list, log_w) + end + # Compute overall log importance weight, + # which is log [1/K sum w_k] + wk_avg = logmeanexp(wk_list) + !isinf(wk_avg) || throw("Invalid proposal (infinite log weight)") + push!(wj_list, wk_avg) + end + wj_avg = mean(wj_list) + push!(wi_list, wj_avg) + end + return return_weights ? wi_list : mean(wi_list) +end + +"""Entropy upper bound using default proposal.""" +function entropy_upper_bound( + model::GenerativeFunction, + model_args::Tuple, + targets::Selection, + N::Integer, + M::Integer, + K::Integer; + model_traces::Vector{Gen.Trace}=Gen.Trace[], + return_weights::Bool=false) + @assert(M == 1) + wi_list = [] + for i=1:N + # Sample latents + observations from model. + tr_p = isempty(model_traces) ? simulate(model, model_args) : model_traces[i] + observations = get_selected(get_choices(tr_p), targets) + wj_list = [] + for j=1:M + tr_pk = tr_p + wk_list::Vector{Float64} = [] + # Retrieve weight of exact posterior sample (particle 1) + # using default proposal, which is + # p(observations | latents) + log_w = Gen.project(tr_pk, targets) + push!(wk_list, log_w) + for k=2:K + # Sample latents (particle k) from default proposal + # and retrieve weight w_k, + # which is p(observations | latents) + tr_pk, log_w = generate(model, model_args, observations) + push!(wk_list, log_w) + end + # Compute overall log importance weight, which is + # log [1 / (1/K sum w_k)] + # = - log [1/K sum w_k] + wk_avg = -logmeanexp(wk_list) + @assert !isinf(wk_avg) + push!(wj_list, wk_avg) + # TODO: MCMC step iterating the latents in tr_p + # if j < M + # tr_p = metropolis_hastings(tr_p, complement(targets); + # check=true, observations=observations) + # end + end + wj_avg = -mean(wj_list) + push!(wi_list, wj_avg) + end + return return_weights ? wi_list : mean(wi_list) +end diff --git a/examples/1-mvn/README b/examples/1-mvn/README new file mode 100644 index 0000000..71d1c9b --- /dev/null +++ b/examples/1-mvn/README @@ -0,0 +1,6 @@ +The main runner script is in mvn_entropy.sh + + $ ./mvn_entropy.sh results/ results/cov.dim@4.txt + $ ./mvn_entropy.sh results/ results/cov.dim@20.txt + $ ./mvn_entropy.sh results/ results/cov.dim@50.txt + $ ./mvn_entropy.sh results/ results/cov.dim@100.txt diff --git a/examples/1-mvn/mvn.jl b/examples/1-mvn/mvn.jl new file mode 100644 index 0000000..9436592 --- /dev/null +++ b/examples/1-mvn/mvn.jl @@ -0,0 +1,206 @@ +import Gen + +using Gen: ChoiceMap, GenerativeFunction, Selection, Trace +using Gen: categorical, choicemap, generate, propose, simulate +using Gen: @gen + +import LinearAlgebra +import Distributions + +# Trace for Multivariate Normal GenerativeFunction +struct MvnTrace{U <: Real} <: Gen.Trace + gen_fn::GenerativeFunction + mu::AbstractVector{U} + cov::AbstractMatrix{U} + constrained::Set{Int} + choices::ChoiceMap + retval::AbstractVector{U} + score::Float64 +end + +# Multivariate Normal GenerativeFunction +abstract type MvnGF{U <: Real} <: GenerativeFunction{AbstractVector{U}, MvnTrace} end +struct MvnGFLW{U} <: MvnGF{U} end # Likelihood weighting +struct MvnGFExact{U} <: MvnGF{U} end # Exact inference + +# Singleton types. +const mvnorm_lw = MvnGFLW{Real}() +const mvnorm_exact = MvnGFExact{Real}() + +# Trace API. +Gen.get_gen_fn(trace::MvnTrace) = trace.gen_fn +Gen.get_args(trace::MvnTrace) = (trace.mu, trace.cov) +Gen.get_score(trace::MvnTrace) = trace.score +Gen.get_retval(trace::MvnTrace) = trace.retval +Base.getindex(trace::MvnTrace, addr::Integer) = trace.choices[addr] +Gen.get_choices(trace::MvnTrace) = trace.choices + +# SIMULATE +function Gen.simulate(gen_fn::MvnGF{U}, args::Tuple) where {U} + (mu, cov) = args + dist = Distributions.MvNormal(mu, cov) + constrained = Set{Int}() + retval = rand(dist) + choices = choicemap(((i, x) for (i, x) in enumerate(retval))...) + score = Distributions.logpdf(dist, retval) + trace = MvnTrace(gen_fn, mu, cov, constrained, choices, retval, score) + return trace +end + +# PROJECT +function Gen.project(trace::MvnTrace, selection::Selection) + if isempty(selection) + return 0. + end + # No type annotations causes StackOverflowError? + (mu::Vector{Float64}, cov::Matrix{Float64}) = Gen.get_args(trace) + ndim = length(mu) + constrained = Set{Int}(keys(Gen.get_subselections(selection))) + @assert all((1 <= i <= ndim for i in constrained)) + retval = Gen.get_retval(trace) + # All constrained. + if length(constrained) == ndim + dist = Distributions.MvNormal(mu, cov) + score = Distributions.logpdf(dist, retval) + return score + end + # Partial constraints. + gen_fn::MvnGF = Gen.get_gen_fn(trace) + return project_mvn_partial(gen_fn, mu, cov, retval, constrained) +end + +function project_mvn_partial(::MvnGFLW, + mu::AbstractVector, + cov::AbstractMatrix, + retval::AbstractVector, + constrained::Set{Int}) + # p(x,y) / p(x), where x is the unconstrained part. + ndim = length(mu) + unconstrained = [i for i=1:ndim if !(i in constrained)] + dist_sim = Distributions.MvNormal(mu[unconstrained], cov[unconstrained,unconstrained]) + logp_sim = Distributions.logpdf(dist_sim, retval[unconstrained]) + dist = Distributions.MvNormal(mu, cov) + logp = Distributions.logpdf(dist, retval) + score = logp - logp_sim + return score +end + +function project_mvn_partial(::MvnGFExact, + mu::AbstractVector, + cov::AbstractMatrix, + retval::AbstractVector, + constrained::Set{Int}) + # p(x,y) / p(x|y) = p(y), where x is the unconstrained part. + ndim = length(mu) + idx = [i for i=1:ndim if (i in constrained)] + dist = Distributions.MvNormal(mu[idx], cov[idx,idx]) + return Distributions.logpdf(dist, retval[idx]) +end + +# GENERATE +function Gen.generate(gen_fn::MvnGF{U}, args::Tuple, constraints::ChoiceMap) where {U} + # No constraints. + if isempty(constraints) + trace = Gen.simulate(gen_fn, args) + score = 0. + return (trace, score) + end + # Extract arguments. + (mu, cov) = args + ndim = length(mu) + constrained = Set{Int}(keys(Gen.get_values_shallow(constraints))) + # All constrained. + if length(constrained) == ndim + dist = Distributions.MvNormal(mu, cov) + retval = [constraints[i] for i=1:ndim] + choices = choicemap(((i, retval[i]) for i=1:ndim)...) + score = Distributions.logpdf(dist, retval) + trace = MvnTrace{U}(gen_fn, mu, cov, constrained, choices, retval, score) + return (trace, score) + end + # Partial constraints. + return generate_mvn_partial(gen_fn, mu, cov, constrained, constraints) +end + +function generate_mvn_partial( + gen_fn::MvnGFLW{U}, + mu::AbstractVector, + cov::AbstractMatrix, + constrained::Set{Int}, + constraints::ChoiceMap) where {U} + # Partial constraints (likelihood weighting). + ndim = length(mu) + unconstrained = [i for i=1:ndim if !(i in constrained)] + dist_sim = Distributions.MvNormal(mu[unconstrained], cov[unconstrained, unconstrained]) + retval_sim = rand(dist_sim) + logp_sim = Distributions.logpdf(dist_sim, retval_sim) + retval = Vector{U}(undef, ndim) + for (i, j) in enumerate(unconstrained) + retval[j] = retval_sim[i] + end + for i in constrained + retval[i] = constraints[i] + end + choices = choicemap(((i, retval[i]) for i=1:ndim)...) + dist = Distributions.MvNormal(mu, cov) + logp = Distributions.logpdf(dist, retval) + score = logp - logp_sim + trace = MvnTrace{U}(gen_fn, mu, cov, constrained, choices, retval, score) + return trace, score +end + +function generate_mvn_partial( + gen_fn::MvnGFExact{U}, + mu::AbstractVector, + cov::AbstractMatrix, + constrained::Set{Int}, + constraints::ChoiceMap) where {U} + # Partial constraints (exact inference). + # p(x|y) with weight p(x,y) / p(x|y) = p(y) + ndim = length(mu) + unconstrained = [i for i=1:ndim if !(i in constrained)] + mu_sim, cov_sim = mvn_condition(mu, cov, constraints) + dist_sim = Distributions.MvNormal(mu_sim, cov_sim) + retval_sim = rand(dist_sim) + retval = Vector{U}(undef, ndim) + for (i, j) in enumerate(unconstrained) + retval[j] = retval_sim[i] + end + for i in constrained + retval[i] = constraints[i] + end + choices = choicemap(((i, retval[i]) for i=1:ndim)...) + score = project_mvn_partial(gen_fn, mu, cov, retval, constrained) + trace = MvnTrace{U}(gen_fn, mu, cov, constrained, choices, retval, score) + return trace, score +end + +function mvn_condition(mu::AbstractVector, cov::AbstractMatrix, constraints::ChoiceMap) + # Partition indexes. + ndim = length(mu) + idx_obs_set = keys(Gen.get_values_shallow(constraints)) + idx_obs = [i for i=1:(ndim) if i in idx_obs_set] + idx_new = [i for i=1:(ndim) if !(i in idx_obs_set)] + ys = [constraints[i] for i in idx_obs] + # Extract mean and covariance submatrices. + mu1 = mu[idx_obs] + mu2 = mu[idx_new] + cov_11 = cov[idx_obs, idx_obs] + cov_22 = cov[idx_new, idx_new] + cov_12 = cov[idx_obs, idx_new] + cov_21 = cov[idx_new, idx_obs] + @assert cov_12 == cov_21' + # Make condition + conditional_mu = mu2 + cov_21 * (cov_11 \ (ys - mu1)) + conditional_cov = cov_22 - cov_21 * (cov_11 \ cov_12) + conditional_cov = .5 * conditional_cov + .5 * conditional_cov' + return (conditional_mu, conditional_cov) +end + +# JULIA + +# Allows calling MvnGF as a regular function. +function (gen_fn::MvnGF)(args...) + trace = simulate(gen_fn, args) + return Gen.get_retval(trace) +end diff --git a/examples/1-mvn/mvn.py b/examples/1-mvn/mvn.py new file mode 100644 index 0000000..aca9004 --- /dev/null +++ b/examples/1-mvn/mvn.py @@ -0,0 +1,173 @@ +#!/usr/bin/env python + +import math + +import numpy as np + +from scipy.special import logsumexp +from scipy.stats import multivariate_normal +from scipy.stats import wishart +from npeet import entropy_estimators + +prng = np.random.RandomState(1) + +def logmeanexp(x): + return logsumexp(x) - math.log(len(x)) + +def merge_sample(ix, iy, vx, vy): + n = len(ix) + len(iy) + L = [None] * n + for i, v in zip(ix, vx): + L[i] = v + for i, v in zip(iy, vy): + L[i] = v + return L + +def is_pos_def(x): + return np.all(0 < np.linalg.eigvals(x)) + +def get_mvn(mu, cov, ix): + assert is_pos_def(cov) + return multivariate_normal(mu[ix], cov[np.ix_(ix, ix)]) + +def entropy_theoretical(cov, ix): + """Exact MVN entropy.""" + assert is_pos_def(cov) + assert 0 < len(ix) + n = len(ix) + det = np.linalg.det(cov[np.ix_(ix, ix)]) + return (n/2.) * (1 + np.log(2*np.pi)) + .5 * np.log(det) + +def neg_entropy_theoretical(cov, ix): + return -entropy_theoretical(cov, ix) + +def entropy_unbiased(mu, cov, ix, N): + dist_x = get_mvn(mu, cov, ix) + samples_x = dist_x.rvs(N) + logp_x = dist_x.logpdf(samples_x) + return -np.mean(logp_x) + +def weights_py_prior(mu, cov, iy, y_obs, M): + """Return list of importance weights using prior as proposal.""" + n = len(mu) + ixy = range(n) + # Sample and assess from proposal q(x; y) = p(x). + ix = [i for i in ixy if i not in iy] + dist_x = get_mvn(mu, cov, ix) + samples_x = np.atleast_2d(dist_x.rvs(M, random_state=prng)) + p_x = dist_x.logpdf(samples_x) + # Compute probabilities under target p(x, y) + n = len(mu) + ixy = list(range(n)) + dist_xy = get_mvn(mu, cov, ixy) + samples_xy = [merge_sample(ix, iy, sample, y_obs) for sample in samples_x] + p_xy = dist_xy.logpdf(samples_xy) + # Return list of importance weights. + p_y_approx = p_xy - p_x + return np.atleast_1d(p_y_approx) + +def weights_py_iwae(mu, cov, iy, y_obs, M, K): + """Return list of importance weights using k-IWAE as proposal.""" + weights = [] + for j in range(M): + w_j = weights_py_prior(mu, cov, iy, y_obs, K) + weights.append(logmeanexp(w_j)) + return weights + +def weights_py_inv_prior(mu, cov, iy, y_obs, ix, x_obs): + """Return single importance weight using posterior sample and targeting the prior.""" + n = len(mu) + ixy = range(n) + # No need to sample from the proposal, we are importance sampling + # the proposal using one exact posterior sample. + ix = [i for i in ixy if i not in iy] + dist_x = get_mvn(mu, cov, ix) + p_x = dist_x.logpdf(x_obs) + # Compute probability under target p(x, y) + dist_xy = get_mvn(mu, cov, ixy) + sample = merge_sample(ix, iy, x_obs, y_obs) + p_xy = dist_xy.logpdf(sample) + # Return single importance weight. + return [p_x - p_xy] + +def weights_py_inv_iwae(mu, cov, iy, y_obs, ix, x_obs, M, K): + """Return single importance weight using posterior sample and target k-IWAE.""" + assert M == 1 + weights = [] + for j in range(M): + w_exact = weights_py_inv_prior(mu, cov, iy, y_obs, ix, x_obs)[0] + w_unbiased = weights_py_prior(mu, cov, iy, y_obs, K-1) if K > 1 else [] + w_list = np.append(w_unbiased, -w_exact) + w_j = -logmeanexp(w_list) + weights.append(w_j) + return weights + +def entropy_lower_bound(mu, cov, iy, N, M, K): + dist_y = get_mvn(mu, cov, iy) + dist_xy = get_mvn(mu, cov, range(len(mu))) + samples_xy = dist_xy.rvs(N, random_state=prng) + log_py_approx = [] + for sample in samples_xy: + y_obs = sample[iy] + p_y_approx_weights = weights_py_iwae(mu, cov, iy, y_obs, M, K) + # p_y_approx = np.mean(p_y_approx_weights) + # weight = math.log(p_y_approx) + # Compute overall log importance weight, + # which is log [1/K sum w_k] + weight = np.mean(p_y_approx_weights) + log_py_approx.append(weight) + # Check. + # p_y = dist_y.pdf(y_obs) + # print('%1.4f %1.4f' % (p_y, p_y_approx,)) + return np.mean(log_py_approx) + +def entropy_upper_bound(mu, cov, iy, N, M, K): + assert M == 1 + indexes = np.arange(len(mu)) + ix = [i for i in indexes if i not in iy] + dist_y = get_mvn(mu, cov, iy) + dist_xy = get_mvn(mu, cov, indexes) + samples_xy = dist_xy.rvs(N, random_state=prng) + log_py_inv_approx = [] + for sample in samples_xy: + y_obs = sample[iy] + x_obs = sample[ix] + p_y_inv_approx_weights = weights_py_inv_iwae(mu, cov, iy, y_obs, ix, x_obs, M, K) + weight = -np.mean(p_y_inv_approx_weights) + log_py_inv_approx.append(weight) + return np.mean(log_py_inv_approx) + +def experiment_is(mu, cov, iy, N=200, M=1, K=1): + # mu = np.asarray([0, 0, 0, 0]) + # cov = np.asarray([ + # [3 , 2 , 1 , 1] , # 0 + # [2 , 3 , 1 , 2] , # 1 + # [1 , 1 , 3 , 1] , # 2 + # [1 , 2 , 1 , 3] , # 3 + # ]) + # iy = [2,3] + start = time.time() + H_lo = entropy_lower_bound(mu, cov, iy, N, M, K) + H_hi = entropy_upper_bound(mu, cov, iy, N, 1, K) + elapsed = time.time() - start + print((H_lo, H_hi, elapsed)) + +import time +def experiment_kraskov(mu, cov, iy, N=200): + start = time.time() + dist_y = get_mvn(mu, cov, iy) + samples = dist_y.rvs(N, random_state=prng) + H_est = -entropy_estimators.entropy(samples, k=5, base=np.e) + elapsed = time.time() - start + return H_est, elapsed + +fnames = ['results/cov.dim@4.txt', 'results/cov.dim@20.txt', 'results/cov.dim@50.txt'] +for fname in fnames: + cov = np.loadtxt(fname, delimiter=',') + dim = len(cov) + mu = np.zeros(dim) + dim = len(cov) + iy = np.arange(dim/2, dtype=int) + H_ex = neg_entropy_theoretical(cov, iy) + H_est, elapsed = experiment_kraskov(mu, cov, iy, N=100) + print(fname, H_ex, H_est, elapsed) diff --git a/examples/1-mvn/mvn_entropy.jl b/examples/1-mvn/mvn_entropy.jl new file mode 100644 index 0000000..01c2e21 --- /dev/null +++ b/examples/1-mvn/mvn_entropy.jl @@ -0,0 +1,182 @@ +include("mvn.jl") +include("../../entropy.jl") +include("../../sir.jl") + +import LinearAlgebra +import Random +import ArgParse +import DelimitedFiles + +using Gen: @gen, @trace + +function entropy_theoretical(cov::AbstractMatrix{U}, ix::Vector{Int}) where {U<:Real} + @assert LinearAlgebra.isposdef(cov) + @assert 0 < length(ix) + n = length(ix) + subcov = view(cov, ix, ix) + det = LinearAlgebra.det(subcov) + return (n/2.) * (1 + log(2*pi)) + .5 * log(det) +end + +function neg_entropy_theoretical(cov::AbstractMatrix{U}, ix::Vector{Int}) where {U <: Real} + return -entropy_theoretical(cov, ix) +end + +@gen function mvn_proposal_indep(mu::AbstractVector, cov::AbstractMatrix, + baseaddr, constraints::ChoiceMap) + ndim = length(mu) + idx_obs_set = Gen.get_values_shallow(constraints) + idx_obs = [i for i=1:(ndim) if i in keys(idx_obs_set)] + idx_new = [i for i=1:(ndim) if !(i in keys(idx_obs_set))] + mu_sim, cov_sim = mvn_condition(mu, cov, constraints) + make_addr = (i) -> isnothing(baseaddr) ? i : baseaddr => i + retval = Vector{Float64}(undef, length(idx_new)) + for (i, j) in enumerate(idx_new) + mu_i = mu_sim[i] + std_i = sqrt(cov_sim[i, i]) + retval[i] = @trace(Gen.normal(mu_i, std_i), make_addr(j)) + end + return retval +end + +# Small case. +function test_crash() + mu = [0., 0., 0., 0.] + cov = hcat( + [3., 2., 1., 1.], + [2., 3., 1., 2.], + [1., 1., 3., 1.], + [1., 2., 1., 3.]) + + N = 1000 + M = 1 + K = 10 + targets = [3, 4] + H_ex = neg_entropy_theoretical(cov, targets) + H_lo = entropy_lower_bound(mvnorm_lw, (mu, cov), Gen.select(targets...), N, M, K) + H_hi = entropy_upper_bound(mvnorm_lw, (mu, cov), Gen.select(targets...), N, 1, K) +end +test_crash() + +function make_random_cov(ndim::Int, seed::Int64) + @assert ndim % 2 == 0 + cov = rand(Distributions.Wishart(ndim, Matrix(LinearAlgebra.I(ndim)))) + return cov +end + +# Exact inference. +function experiment_exact_inference( + mu::AbstractVector, cov::AbstractMatrix, targets::AbstractVector, + N::Integer, M::Integer, K::Integer) + H_lo = entropy_lower_bound(mvnorm_exact, (mu, cov), Gen.select(targets...), N, 1, 1) + H_hi = entropy_upper_bound(mvnorm_exact, (mu, cov), Gen.select(targets...), N, 1, 1) + return (H_lo, H_hi) +end + +# Independent proposal. +function experiment_independent_proposal( + mu::AbstractVector, cov::AbstractMatrix, targets::AbstractVector, + N::Integer, M::Integer, K::Integer) + proposal = K == 1 ? mvn_proposal_indep : + SIRGF(mvnorm_exact, mvn_proposal_indep, (mu, cov), K) + H_lo = entropy_lower_bound( + mvnorm_exact, (mu, cov), + proposal, (mu, cov, nothing), + Gen.select(targets...), + N, M) + H_hi = entropy_upper_bound( + mvnorm_exact, (mu, cov), + proposal, (mu, cov, nothing), + Gen.select(targets...), + N, 1) + return (H_lo, H_hi) +end + +function experiment_likelihood_weighting( + mu::AbstractVector, cov::AbstractMatrix, targets::AbstractVector, + N::Integer, M::Integer, K::Integer) + H_lo = entropy_lower_bound(mvnorm_lw, (mu, cov), Gen.select(targets...), N, M, K) + H_hi = entropy_upper_bound(mvnorm_lw, (mu, cov), Gen.select(targets...), N, 1, K) + return (H_lo, H_hi) +end + +# experiment_independent_proposal(200, 10, 1) +# experiment_independent_proposal(200, 10, 10) +# experiment_likelihood_weighting(200, 10, 1) +# experiment_likelihood_weighting(200, 10, 10) + +settings = ArgParse.ArgParseSettings() +ArgParse.@add_arg_table settings begin + "--outdir" + arg_type = String + help = "output directory" + required = false + default = "." + "cov_path" + arg_type = String + help = "path to target covariance matrix" + required = true + "experiment" + help = "name of experiment to run" + required = true + arg_type = String + "Nrep" + arg_type = Int64 + help = "number of repetitions" + required = true + default = 2 + "N" + help = "number of outer samples" + required = true + arg_type = Int64 + "M" + help = "number of inner samples" + required = true + arg_type = Int64 + "K" + help = "number of SIR samples" + required = true + arg_type = Int64 +end +args = ArgParse.parse_args(ARGS, settings) + +experiments = Dict( + "exact_inference" => experiment_exact_inference, + "independent_proposal" => experiment_independent_proposal, + "likelihood_weighting" => experiment_likelihood_weighting, +) + +# Prepare experiment. +cov = DelimitedFiles.readdlm(args["cov_path"], ',') +ndim = size(cov)[1] +mu = zeros(ndim) +targets = Vector{Int}(1:ndim/2) +func = experiments[args["experiment"]] + +# Prepare output file. +fkeys = ["experiment", "N", "M", "K"] +fname = join([join((k, args[k]), "@") for k in fkeys], ".") +pathname = joinpath(args["outdir"], fname) +rm(pathname, force=true) + +# Run warm-up. +H_ex = neg_entropy_theoretical(cov, targets) +println(H_ex) +func(mu, cov, targets, 1, 1, 1) + +for i=1:args["Nrep"] + seed = i + Random.seed!(seed) + # Run timed code. + runtime = @elapsed begin + (H_lo, H_hi) = func(mu, cov, targets, args["N"], args["M"], args["K"]) + end + # Save to disk. + data = join([seed, runtime, H_lo, H_hi, ], ",") + open(pathname, "a") do io + write(io, data) + write(io, "\n") + end + println(seed, " ", H_lo, " ", H_hi) +end +println(pathname) diff --git a/examples/1-mvn/mvn_entropy.sh b/examples/1-mvn/mvn_entropy.sh new file mode 100755 index 0000000..6ad1cff --- /dev/null +++ b/examples/1-mvn/mvn_entropy.sh @@ -0,0 +1,25 @@ +#!/bin/sh + +set -Ceux + +experiments="likelihood_weighting independent_proposal" + +outdir=${1} +cov_file=${2} + +test -d ${outdir} || (echo no such ${outdir} && exit 1) + +K_max=4 +K_list=$(python -c "print(' '.join([str(2**i) for i in range(${K_max})]))") +N=100 +M=1 +N_rep=10 + +for experiment in ${experiments}; do + echo ${K_list} | xargs -I% -d' ' -n1 -P4 \ + julia mvn_entropy.jl \ + --outdir=${outdir} \ + ${cov_file} \ + ${experiment} \ + ${N_rep} ${N} ${M} % +done diff --git a/examples/1-mvn/mvn_test.jl b/examples/1-mvn/mvn_test.jl new file mode 100644 index 0000000..f2b3ee8 --- /dev/null +++ b/examples/1-mvn/mvn_test.jl @@ -0,0 +1,55 @@ +include("mvn.jl") + +import Distributions +import Gen +import Random + +using Gen: @gen, @trace + +Random.seed!(1) + +mu = [0., 0.] +cov = [[1., .5] [.5, 1.]] +dist = Distributions.MvNormal(mu, cov) + +@gen function model() + xs = @trace(mvnorm_lw(mu, cov), :ys) + return xs +end + +trace = Gen.simulate(mvnorm_lw, (mu, cov)) +trace, score = Gen.generate(mvnorm_lw, (mu, cov)) +trace, score = Gen.generate(mvnorm_lw, (mu, cov), Gen.choicemap((1, 0.))) + +weights = Vector{Float64}() +for i=1:1000 + tr, sc = Gen.generate(mvnorm_lw, (mu, cov), choicemap((1, 0))) + push!(weights, sc) + sc2 = Gen.project(tr, Gen.select(1)) + @assert isapprox(sc, sc2) +end +logp_est = Gen.logsumexp(weights) - Gen.log(length(weights)) +dist_exact = Distributions.MvNormal(mu[1:1], cov[1:1, 1:1]) +@assert abs(logp_est - Distributions.logpdf(dist_exact, [0.])) < 0.1 + +ys = model() +@assert length(ys) == length(mu) + +trace = Gen.simulate(mvnorm_lw, (mu, cov)) +@assert isapprox( + Distributions.logpdf(dist, Gen.get_retval(trace)), + Gen.get_score(trace)) +@assert isapprox(0, Gen.project(trace, Gen.select())) +@assert isapprox(Gen.get_score(trace), Gen.project(trace, Gen.select(1, 2))) + +tr, w = Gen.generate(model, (), choicemap((:ys => 1, 0))) +@assert Gen.get_choices(tr)[:ys=>1] == 0 +@assert Gen.get_choices(tr)[:ys=>2] != 0 + +tr, w = Gen.generate(model, (), choicemap((:ys => 2, 0))) +@assert Gen.get_choices(tr)[:ys=>1] != 0 +@assert Gen.get_choices(tr)[:ys=>2] == 0 + +tr, w = Gen.generate(model, (), choicemap((:ys => 1, 0), (:ys => 2, 0))) +@assert Gen.get_choices(tr)[:ys=>1] == 0 +@assert Gen.get_choices(tr)[:ys=>2] == 0 diff --git a/examples/1-mvn/results/cov.dim@100.txt b/examples/1-mvn/results/cov.dim@100.txt new file mode 100644 index 0000000..0b740c7 --- /dev/null +++ b/examples/1-mvn/results/cov.dim@100.txt @@ -0,0 +1,100 @@ 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b/examples/2-hepar2/README new file mode 100644 index 0000000..66bfd18 --- /dev/null +++ b/examples/2-hepar2/README @@ -0,0 +1,6 @@ +The main runner script is in hepar2_entropy.jl + + $ julia hepar2_entropy.jl + +This script will produce the estimator runtime, ranking of tests for +different diseases, and the variance of the weights. diff --git a/examples/2-hepar2/hepar2.jl b/examples/2-hepar2/hepar2.jl new file mode 100644 index 0000000..ae0f5b5 --- /dev/null +++ b/examples/2-hepar2/hepar2.jl @@ -0,0 +1,1622 @@ +using Gen: + @gen, + categorical + +@gen function model() + hepatotoxic ~ categorical([0.08154506, 0.91845494]) + + alcoholism ~ categorical([0.1359084, 0.8640916]) + + gallstones ~ categorical([0.1530758, 0.8469242]) + + hospital ~ categorical([0.5350501, 0.4649499]) + + surgery ~ categorical([0.4234621, 0.5765379]) + + vh_amn ~ categorical([0.1731044, 0.8268956]) + + sex ~ categorical([0.5979971, 0.4020029]) + + age ~ categorical([0.07725322, 0.38769671, 0.39771102, 0.13733906]) + + diabetes ~ categorical([0.03576538, 0.96423462]) + + if ((hepatotoxic == 1)) + RHepatitis ~ categorical([0.01754386, 0.98245614]) + elseif ((hepatotoxic == 2)) + RHepatitis ~ categorical([0.02492212, 0.97507788]) + else + @assert false + end + + if ((hepatotoxic == 1) && (alcoholism == 1)) + THepatitis ~ categorical([0.2, 0.8]) + elseif ((hepatotoxic == 1) && (alcoholism == 2)) + THepatitis ~ categorical([0.00191939, 0.99808061]) + elseif ((hepatotoxic == 2) && (alcoholism == 1)) + THepatitis ~ categorical([0.08888889, 0.91111111]) + elseif ((hepatotoxic == 2) && (alcoholism == 2)) + THepatitis ~ categorical([0.0326087, 0.9673913]) + else + @assert false + end + + if ((gallstones == 1)) + choledocholithotomy ~ categorical([0.7102804, 0.2897196]) + elseif ((gallstones == 2)) + choledocholithotomy ~ categorical([0.03716216, 0.96283784]) + else + @assert false + end + + if ((gallstones == 1)) + upper_pain ~ categorical([0.411215, 0.588785]) + elseif ((gallstones == 2)) + upper_pain ~ categorical([0.3868243, 0.6131757]) + else + @assert false + end + + if ((gallstones == 1)) + fat ~ categorical([0.1775701, 0.8224299]) + elseif ((gallstones == 2)) + fat ~ categorical([0.2804054, 0.7195946]) + else + @assert false + end + + if ((gallstones == 1)) + flatulence ~ categorical([0.3925234, 0.6074766]) + elseif ((gallstones == 2)) + flatulence ~ categorical([0.4307432, 0.5692568]) + else + @assert false + end + + if ((gallstones == 1)) + amylase ~ categorical([0.01869159, 0.04672897, 0.93457944]) + elseif ((gallstones == 2)) + amylase ~ categorical([0.01013514, 0.01689189, 0.97297297]) + else + @assert false + end + + if ((sex == 1) && (age == 1)) + PBC ~ categorical([0.6571429, 0.3428571]) + elseif ((sex == 1) && (age == 2)) + PBC ~ categorical([0.700565, 0.299435]) + elseif ((sex == 1) && (age == 3)) + PBC ~ categorical([0.6149425, 0.3850575]) + elseif ((sex == 1) && (age == 4)) + PBC ~ categorical([0.125, 0.875]) + elseif ((sex == 2) && (age == 1)) + PBC ~ categorical([0.3684211, 0.6315789]) + elseif ((sex == 2) && (age == 2)) + PBC ~ categorical([0.08510638, 0.91489362]) + elseif ((sex == 2) && (age == 3)) + PBC ~ categorical([0.06730769, 0.93269231]) + elseif ((sex == 2) && (age == 4)) + PBC ~ categorical([0.00156006, 0.99843994]) + else + @assert false + end + + if ((age == 1) && (sex == 1)) + Hyperbilirubinemia ~ categorical([0.002849, 0.997151]) + elseif ((age == 1) && (sex == 2)) + Hyperbilirubinemia ~ categorical([0.0052356, 0.9947644]) + elseif ((age == 2) && (sex == 1)) + Hyperbilirubinemia ~ categorical([0.01129944, 0.98870056]) + elseif ((age == 2) && (sex == 2)) + Hyperbilirubinemia ~ categorical([0.0212766, 0.9787234]) + elseif ((age == 3) && (sex == 1)) + Hyperbilirubinemia ~ categorical([0.04597701, 0.95402299]) + elseif ((age == 3) && (sex == 2)) + Hyperbilirubinemia ~ categorical([0.07692308, 0.92307692]) + elseif ((age == 4) && (sex == 1)) + Hyperbilirubinemia ~ categorical([0.21875, 0.78125]) + elseif ((age == 4) && (sex == 2)) + Hyperbilirubinemia ~ categorical([0.453125, 0.546875]) + else + @assert false + end + + if ((diabetes == 1)) + obesity ~ categorical([0.24, 0.76]) + elseif ((diabetes == 2)) + obesity ~ categorical([0.06231454, 0.93768546]) + else + @assert false + end + + if ((RHepatitis == 1) && (THepatitis == 1)) + anorexia ~ categorical([0.1818182, 0.8181818]) + elseif ((RHepatitis == 1) && (THepatitis == 2)) + anorexia ~ categorical([0.1176471, 0.8823529]) + elseif ((RHepatitis == 2) && (THepatitis == 1)) + anorexia ~ categorical([0.2222222, 0.7777778]) + elseif ((RHepatitis == 2) && (THepatitis == 2)) + anorexia ~ categorical([0.280916, 0.719084]) + else + @assert false + end + + if ((RHepatitis == 1) && (THepatitis == 1)) + nausea ~ categorical([0.3636364, 0.6363636]) + elseif ((RHepatitis == 1) && (THepatitis == 2)) + nausea ~ categorical([0.3529412, 0.6470588]) + elseif ((RHepatitis == 2) && (THepatitis == 1)) + nausea ~ categorical([0.3703704, 0.6296296]) + elseif ((RHepatitis == 2) && (THepatitis == 2)) + nausea ~ categorical([0.2854962, 0.7145038]) + else + @assert false + end + + if ((hospital == 1) && (surgery == 1) && (choledocholithotomy == 1)) + injections ~ categorical([0.8, 0.2]) + elseif ((hospital == 1) && (surgery == 1) && (choledocholithotomy == 2)) + injections ~ categorical([0.715847, 0.284153]) + elseif ((hospital == 1) && (surgery == 2) && (choledocholithotomy == 1)) + injections ~ categorical([0.8333333, 0.1666667]) + elseif ((hospital == 1) && (surgery == 2) && (choledocholithotomy == 2)) + injections ~ categorical([0.4818182, 0.5181818]) + elseif ((hospital == 2) && (surgery == 1) && (choledocholithotomy == 1)) + injections ~ categorical([0.375, 0.625]) + elseif ((hospital == 2) && (surgery == 1) && (choledocholithotomy == 2)) + injections ~ categorical([0.2333333, 0.7666667]) + elseif ((hospital == 2) && (surgery == 2) && (choledocholithotomy == 1)) + injections ~ categorical([0.01098901, 0.98901099]) + elseif ((hospital == 2) && (surgery == 2) && (choledocholithotomy == 2)) + injections ~ categorical([0.0647482, 0.9352518]) + else + @assert false + end + + if ((hospital == 1) && (surgery == 1) && (choledocholithotomy == 1)) + transfusion ~ categorical([0.3333333, 0.6666667]) + elseif ((hospital == 1) && (surgery == 1) && (choledocholithotomy == 2)) + transfusion ~ categorical([0.2896175, 0.7103825]) + elseif ((hospital == 1) && (surgery == 2) && (choledocholithotomy == 1)) + transfusion ~ categorical([0.1666667, 0.8333333]) + elseif ((hospital == 1) && (surgery == 2) && (choledocholithotomy == 2)) + transfusion ~ categorical([0.1181818, 0.8818182]) + elseif ((hospital == 2) && (surgery == 1) && (choledocholithotomy == 1)) + transfusion ~ categorical([0.125, 0.875]) + elseif ((hospital == 2) && (surgery == 1) && (choledocholithotomy == 2)) + transfusion ~ categorical([0.3, 0.7]) + elseif ((hospital == 2) && (surgery == 2) && (choledocholithotomy == 1)) + transfusion ~ categorical([0.01098901, 0.98901099]) + elseif ((hospital == 2) && (surgery == 2) && (choledocholithotomy == 2)) + transfusion ~ categorical([0.01079137, 0.98920863]) + else + @assert false + end + + if ((PBC == 1)) + ama ~ categorical([0.5678571, 0.4321429]) + elseif ((PBC == 2)) + ama ~ categorical([0.01193317, 0.98806683]) + else + @assert false + end + + if ((PBC == 1)) + le_cells ~ categorical([0.1214286, 0.8785714]) + elseif ((PBC == 2)) + le_cells ~ categorical([0.04057279, 0.95942721]) + else + @assert false + end + + if ((PBC == 1)) + joints ~ categorical([0.1285714, 0.8714286]) + elseif ((PBC == 2)) + joints ~ categorical([0.1002387, 0.8997613]) + else + @assert false + end + + if ((obesity == 1) && (alcoholism == 1)) + Steatosis ~ categorical([0.3636364, 0.6363636]) + elseif ((obesity == 1) && (alcoholism == 2)) + Steatosis ~ categorical([0.1891892, 0.8108108]) + elseif ((obesity == 2) && (alcoholism == 1)) + Steatosis ~ categorical([0.2380952, 0.7619048]) + elseif ((obesity == 2) && (alcoholism == 2)) + Steatosis ~ categorical([0.06349206, 0.93650794]) + else + @assert false + end + + if ((transfusion == 1) && (vh_amn == 1) && (injections == 1)) + ChHepatitis ~ categorical([0.2094241, 0.0052356, 0.7853403]) + elseif ((transfusion == 1) && (vh_amn == 1) && (injections == 2)) + ChHepatitis ~ categorical([0.4615385, 0.3076923, 0.2307692]) + elseif ((transfusion == 1) && (vh_amn == 2) && (injections == 1)) + ChHepatitis ~ categorical([0.06, 0.06, 0.88]) + elseif ((transfusion == 1) && (vh_amn == 2) && (injections == 2)) + ChHepatitis ~ categorical([0.13043478, 0.04347826, 0.82608696]) + elseif ((transfusion == 2) && (vh_amn == 1) && (injections == 1)) + ChHepatitis ~ categorical([0.15384615, 0.05128205, 0.7948718]) + elseif ((transfusion == 2) && (vh_amn == 1) && (injections == 2)) + ChHepatitis ~ categorical([0.24, 0.14, 0.62]) + elseif ((transfusion == 2) && (vh_amn == 2) && (injections == 1)) + ChHepatitis ~ categorical([0.07692308, 0.00591716, 0.91715976]) + elseif ((transfusion == 2) && (vh_amn == 2) && (injections == 2)) + ChHepatitis ~ categorical([0.13095238, 0.05357143, 0.81547619]) + else + @assert false + end + + if ((PBC == 1) && (joints == 1)) + pain ~ categorical([0.3888889, 0.6111111]) + elseif ((PBC == 1) && (joints == 2)) + pain ~ categorical([0.147541, 0.852459]) + elseif ((PBC == 2) && (joints == 1)) + pain ~ categorical([0.8095238, 0.1904762]) + elseif ((PBC == 2) && (joints == 2)) + pain ~ categorical([0.1830239, 0.8169761]) + else + @assert false + end + + if ((Steatosis == 1)) + triglycerides ~ categorical([0.1791045, 0.1641791, 0.6567164]) + elseif ((Steatosis == 2)) + triglycerides ~ categorical([0.02373418, 0.03164557, 0.94462025]) + else + @assert false + end + + if ((Steatosis == 1) && (Hyperbilirubinemia == 1)) + pain_ruq ~ categorical([0.3934426, 0.6065574]) + elseif ((Steatosis == 1) && (Hyperbilirubinemia == 2)) + pain_ruq ~ categorical([0.4776119, 0.5223881]) + elseif ((Steatosis == 2) && (Hyperbilirubinemia == 1)) + pain_ruq ~ categorical([0.2857143, 0.7142857]) + elseif ((Steatosis == 2) && (Hyperbilirubinemia == 2)) + pain_ruq ~ categorical([0.421875, 0.578125]) + else + @assert false + end + + if ((RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Hyperbilirubinemia == 1)) + hepatomegaly ~ categorical([0.6097561, 0.3902439]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Hyperbilirubinemia == 2)) + hepatomegaly ~ categorical([0.68, 0.32]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Hyperbilirubinemia == 1)) + hepatomegaly ~ categorical([0.5918367, 0.4081633]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Hyperbilirubinemia == 2)) + hepatomegaly ~ categorical([0.673913, 0.326087]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Hyperbilirubinemia == 1)) + hepatomegaly ~ categorical([0.5901639, 0.4098361]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Hyperbilirubinemia == 2)) + hepatomegaly ~ categorical([0.6527778, 0.3472222]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Hyperbilirubinemia == 1)) + hepatomegaly ~ categorical([0.5555556, 0.4444444]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Hyperbilirubinemia == 2)) + hepatomegaly ~ categorical([0.7058823, 0.2941177]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Hyperbilirubinemia == 1)) + hepatomegaly ~ categorical([0.6, 0.4]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Hyperbilirubinemia == 2)) + hepatomegaly ~ categorical([0.6756757, 0.3243243]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Hyperbilirubinemia == 1)) + hepatomegaly ~ categorical([0.5897436, 0.4102564]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Hyperbilirubinemia == 2)) + hepatomegaly ~ categorical([0.7777778, 0.2222222]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Hyperbilirubinemia == 1)) + hepatomegaly ~ categorical([0.5866667, 0.4133333]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Hyperbilirubinemia == 2)) + hepatomegaly ~ categorical([0.6865672, 0.3134328]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Hyperbilirubinemia == 1)) + hepatomegaly ~ categorical([0.375, 0.625]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Hyperbilirubinemia == 2)) + hepatomegaly ~ categorical([0.6973684, 0.3026316]) + else + @assert false + end + + if ((ChHepatitis == 1)) + fibrosis ~ categorical([0.3, 0.7]) + elseif ((ChHepatitis == 2)) + fibrosis ~ categorical([0.05, 0.95]) + elseif ((ChHepatitis == 3)) + fibrosis ~ categorical([0.001, 0.999]) + else + @assert false + end + + if ((ChHepatitis == 1) && (THepatitis == 1) && (RHepatitis == 1)) + fatigue ~ categorical([0.6363636, 0.3636364]) + elseif ((ChHepatitis == 1) && (THepatitis == 1) && (RHepatitis == 2)) + fatigue ~ categorical([0.625, 0.375]) + elseif ((ChHepatitis == 1) && (THepatitis == 2) && (RHepatitis == 1)) + fatigue ~ categorical([0.6236559, 0.3763441]) + elseif ((ChHepatitis == 1) && (THepatitis == 2) && (RHepatitis == 2)) + fatigue ~ categorical([0.6043956, 0.3956044]) + elseif ((ChHepatitis == 2) && (THepatitis == 1) && (RHepatitis == 1)) + fatigue ~ categorical([0.6071429, 0.3928571]) + elseif ((ChHepatitis == 2) && (THepatitis == 1) && (RHepatitis == 2)) + fatigue ~ categorical([0.5932203, 0.4067797]) + elseif ((ChHepatitis == 2) && (THepatitis == 2) && (RHepatitis == 1)) + fatigue ~ categorical([0.5892857, 0.4107143]) + elseif ((ChHepatitis == 2) && (THepatitis == 2) && (RHepatitis == 2)) + fatigue ~ categorical([0.5277778, 0.4722222]) + elseif ((ChHepatitis == 3) && (THepatitis == 1) && (RHepatitis == 1)) + fatigue ~ categorical([0.6153846, 0.3846154]) + elseif ((ChHepatitis == 3) && (THepatitis == 1) && (RHepatitis == 2)) + fatigue ~ categorical([0.6666667, 0.3333333]) + elseif ((ChHepatitis == 3) && (THepatitis == 2) && (RHepatitis == 1)) + fatigue ~ categorical([0.7058823, 0.2941177]) + elseif ((ChHepatitis == 3) && (THepatitis == 2) && (RHepatitis == 2)) + fatigue ~ categorical([0.5359849, 0.4640151]) + else + @assert false + end + + if ((gallstones == 1) && (PBC == 1) && (ChHepatitis == 1)) + pressure_ruq ~ categorical([0.3333333, 0.6666667]) + elseif ((gallstones == 1) && (PBC == 1) && (ChHepatitis == 2)) + pressure_ruq ~ categorical([0.328125, 0.671875]) + elseif ((gallstones == 1) && (PBC == 1) && (ChHepatitis == 3)) + pressure_ruq ~ categorical([0.3292683, 0.6707317]) + elseif ((gallstones == 1) && (PBC == 2) && (ChHepatitis == 1)) + pressure_ruq ~ categorical([0.4, 0.6]) + elseif ((gallstones == 1) && (PBC == 2) && (ChHepatitis == 2)) + pressure_ruq ~ categorical([0.09090909, 0.90909091]) + elseif ((gallstones == 1) && (PBC == 2) && (ChHepatitis == 3)) + pressure_ruq ~ categorical([0.2857143, 0.7142857]) + elseif ((gallstones == 2) && (PBC == 1) && (ChHepatitis == 1)) + pressure_ruq ~ categorical([0.3424658, 0.6575342]) + elseif ((gallstones == 2) && (PBC == 1) && (ChHepatitis == 2)) + pressure_ruq ~ categorical([0.3227513, 0.6772487]) + elseif ((gallstones == 2) && (PBC == 1) && (ChHepatitis == 3)) + pressure_ruq ~ categorical([0.2929293, 0.7070707]) + elseif ((gallstones == 2) && (PBC == 2) && (ChHepatitis == 1)) + pressure_ruq ~ categorical([0.4691358, 0.5308642]) + elseif ((gallstones == 2) && (PBC == 2) && (ChHepatitis == 2)) + pressure_ruq ~ categorical([0.4285714, 0.5714286]) + elseif ((gallstones == 2) && (PBC == 2) && (ChHepatitis == 3)) + pressure_ruq ~ categorical([0.4532374, 0.5467626]) + else + @assert false + end + + if ((PBC == 1) && (ChHepatitis == 1) && (Steatosis == 1) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.2704918, 0.1721312, 0.557377]) + elseif ((PBC == 1) && (ChHepatitis == 1) && (Steatosis == 1) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.2972973, 0.1837838, 0.5189189]) + elseif ((PBC == 1) && (ChHepatitis == 1) && (Steatosis == 2) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.2941177, 0.1911765, 0.5147058]) + elseif ((PBC == 1) && (ChHepatitis == 1) && (Steatosis == 2) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.3205575, 0.2055749, 0.4738676]) + elseif ((PBC == 1) && (ChHepatitis == 2) && (Steatosis == 1) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.3093923, 0.1767956, 0.5138121]) + elseif ((PBC == 1) && (ChHepatitis == 2) && (Steatosis == 1) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.3315508, 0.171123, 0.4973262]) + elseif ((PBC == 1) && (ChHepatitis == 2) && (Steatosis == 2) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.3333333, 0.172043, 0.4946237]) + elseif ((PBC == 1) && (ChHepatitis == 2) && (Steatosis == 2) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.368, 0.184, 0.448]) + elseif ((PBC == 1) && (ChHepatitis == 3) && (Steatosis == 1) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.3425926, 0.1712963, 0.4861111]) + elseif ((PBC == 1) && (ChHepatitis == 3) && (Steatosis == 1) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.36298933629893365, 0.1779359177935918, 0.4590747459074746]) + elseif ((PBC == 1) && (ChHepatitis == 3) && (Steatosis == 2) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.36363636363636365, 0.18181818181818182, 0.45454545454545453]) + elseif ((PBC == 1) && (ChHepatitis == 3) && (Steatosis == 2) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.4321428567857143, 0.21071427892857209, 0.3571428642857135]) + elseif ((PBC == 2) && (ChHepatitis == 1) && (Steatosis == 1) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.2682927, 0.1768293, 0.554878]) + elseif ((PBC == 2) && (ChHepatitis == 1) && (Steatosis == 1) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.175, 0.1625, 0.6625]) + elseif ((PBC == 2) && (ChHepatitis == 1) && (Steatosis == 2) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.1045752, 0.1633987, 0.7320261]) + elseif ((PBC == 2) && (ChHepatitis == 1) && (Steatosis == 2) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.03296703, 0.21978022, 0.74725275]) + elseif ((PBC == 2) && (ChHepatitis == 2) && (Steatosis == 1) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.06024096, 0.12048193, 0.81927711]) + elseif ((PBC == 2) && (ChHepatitis == 2) && (Steatosis == 1) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.08602151, 0.08602151, 0.82795698]) + elseif ((PBC == 2) && (ChHepatitis == 2) && (Steatosis == 2) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.05434783, 0.07608696, 0.86956521]) + elseif ((PBC == 2) && (ChHepatitis == 2) && (Steatosis == 2) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.05555556, 0.05555556, 0.88888888]) + elseif ((PBC == 2) && (ChHepatitis == 3) && (Steatosis == 1) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.07594937, 0.06329114, 0.86075949]) + elseif ((PBC == 2) && (ChHepatitis == 3) && (Steatosis == 1) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.13432836, 0.05970149, 0.80597015]) + elseif ((PBC == 2) && (ChHepatitis == 3) && (Steatosis == 2) && (Hyperbilirubinemia == 1)) + ESR ~ categorical([0.01785714, 0.07142857, 0.91071429]) + elseif ((PBC == 2) && (ChHepatitis == 3) && (Steatosis == 2) && (Hyperbilirubinemia == 2)) + ESR ~ categorical([0.04733728, 0.05325444, 0.89940828]) + else + @assert false + end + + if ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1590909, 0.1477273, 0.1136364, 0.5795454]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1696429, 0.1607143, 0.125, 0.5446428]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1546392, 0.1443299, 0.1134021, 0.5876288]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1730769, 0.1538462, 0.125, 0.5480769]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1666667, 0.1481482, 0.1111111, 0.574074]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1854839, 0.1612903, 0.1209677, 0.5322581]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1694915, 0.1610169, 0.1186441, 0.5508475]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1832061, 0.1755725, 0.129771, 0.5114504]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1759259, 0.1574074, 0.1111111, 0.5555556]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1913044, 0.173913, 0.1217391, 0.5130435]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1885246, 0.1639344, 0.1065574, 0.5409836]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.2108843, 0.1836735, 0.1156463, 0.4897959]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1666667, 0.1590909, 0.1212121, 0.5530303]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1768707, 0.1632653, 0.1292517, 0.5306123]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1652893, 0.1487603, 0.1157025, 0.5702479]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1742424, 0.1590909, 0.1287879, 0.5378788]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1726619, 0.1510791, 0.1151079, 0.5611511]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1893491, 0.1656805, 0.1242604, 0.52071]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1741935, 0.1677419, 0.1225806, 0.535484]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.18579231857923187, 0.18579231857923187, 0.1311475131147513, 0.497267849726785]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1748252, 0.1678322, 0.1188811, 0.5384615]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.19375, 0.18125, 0.125, 0.5]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1918605, 0.1744186, 0.1104651, 0.5232558]) + elseif ((PBC == 1) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.2142857, 0.1932773, 0.1176471, 0.4747899]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1756757, 0.1621622, 0.1216216, 0.5405405]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.18, 0.1666667, 0.1333333, 0.52]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1666667, 0.15, 0.125, 0.5583333]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1782946, 0.1627907, 0.131783, 0.5271317]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1764706, 0.1544118, 0.1176471, 0.5514705]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1939394, 0.169697, 0.1272727, 0.5090909]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1776316, 0.1710526, 0.125, 0.5263158]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.18994411899441188, 0.18994411899441188, 0.13407821340782133, 0.48603354860335485]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1785714, 0.1714286, 0.1214286, 0.5285714]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.198717919871792, 0.18589741858974185, 0.12820511282051128, 0.4871795487179549]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1964286, 0.1785714, 0.1130952, 0.5119048]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.2207792, 0.1991342, 0.1212121, 0.4588745]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.178771, 0.1731844, 0.122905, 0.5251396]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1804878, 0.1756098, 0.1365854, 0.507317]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1698113, 0.1572327, 0.1257862, 0.5471698]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.1843575, 0.1675978, 0.1340782, 0.5139665]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1822917, 0.1614583, 0.1197917, 0.5364583]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.197761180223882, 0.17910448208955182, 0.12686568731343129, 0.49626865037313506]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1826087, 0.1782609, 0.126087, 0.5130434]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.19397991939799195, 0.19397991939799195, 0.13712371371237136, 0.47491644749164474]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1846847, 0.1846847, 0.1261261, 0.5045045]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.2007435, 0.197026, 0.133829, 0.4684015]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.19867548013245198, 0.1920529807947019, 0.12251658774834122, 0.48675495132450486]) + elseif ((PBC == 1) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.2392857, 0.225, 0.1321429, 0.4035714]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.1509434, 0.1415094, 0.1226415, 0.5849057]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.10526316, 0.09210526, 0.13157895, 0.67105263]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.05555556, 0.03703704, 0.09259259, 0.81481481]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.06122449, 0.02040816, 0.10204082, 0.81632653]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.05649718, 0.00188324, 0.07532957, 0.86629001]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.07393715, 0.00184843, 0.09242144, 0.83179298]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.06557377, 0.04918033, 0.09836066, 0.78688524]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.078125, 0.078125, 0.125, 0.71875]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.04166667, 0.02083333, 0.08333333, 0.85416667]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.04761905, 0.02380952, 0.0952381, 0.83333333]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.04338395, 0.0021692, 0.04338395, 0.9110629]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.06651885, 0.00221729, 0.0443459, 0.88691796]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.05714286, 0.04285714, 0.1, 0.8]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.07142857, 0.07142857, 0.13095238, 0.72619048]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.04545455, 0.03030303, 0.10606061, 0.81818181]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.04615385, 0.03076923, 0.12307692, 0.8]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.04285714, 0.01428571, 0.08571429, 0.85714286]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.0617284, 0.01234568, 0.09876543, 0.82716049]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.06024096, 0.04819277, 0.09638554, 0.79518073]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.07070707, 0.08080808, 0.12121212, 0.72727273]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.04166667, 0.04166667, 0.09722222, 0.81944444]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.03030303, 0.03030303, 0.10606061, 0.83333333]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.02702703, 0.01351351, 0.05405405, 0.90540541]) + elseif ((PBC == 2) && (THepatitis == 1) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.07380074, 0.00369004, 0.03690037, 0.88560885]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.06349206, 0.04761905, 0.11111111, 0.77777778]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.07594937, 0.07594937, 0.13924051, 0.70886075]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.0483871, 0.03225806, 0.11290323, 0.80645161]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.05, 0.03333333, 0.13333333, 0.78333334]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.04615385, 0.01538462, 0.09230769, 0.84615384]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.06756757, 0.01351351, 0.10810811, 0.81081081]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.06410256, 0.05128205, 0.1025641, 0.78205129]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.07692308, 0.08791209, 0.13186813, 0.7032967]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.04545455, 0.04545455, 0.10606061, 0.80303029]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.03448276, 0.03448276, 0.12068966, 0.81034482]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.03076923, 0.01538462, 0.06153846, 0.89230769]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 1) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.11695906, 0.00584795, 0.05847953, 0.81871346]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.06493506, 0.06493506, 0.11688312, 0.75324676]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.07692308, 0.08547009, 0.14529915, 0.69230768]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.04444444, 0.04444444, 0.12222222, 0.7888889]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.04210526, 0.04210526, 0.13684211, 0.77894737]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.03703704, 0.02777778, 0.10185185, 0.83333333]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 1) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.07462687, 0.02985075, 0.13432836, 0.76119402]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.05660377, 0.06603774, 0.12264151, 0.75471698]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 1) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.08791209, 0.14285714, 0.17582418, 0.59340659]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.04395604, 0.07692308, 0.13186813, 0.74725275]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 2) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.00277008, 0.05540166, 0.19390582, 0.74792244]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 1)) + ggtp ~ categorical([0.00177936, 0.00177936, 0.01779359, 0.97864769]) + elseif ((PBC == 2) && (THepatitis == 2) && (RHepatitis == 2) && (Steatosis == 2) && (ChHepatitis == 3) && (Hyperbilirubinemia == 2)) + ggtp ~ categorical([0.08, 0.096, 0.144, 0.68]) + else + @assert false + end + + if ((PBC == 1) && (Steatosis == 1) && (ChHepatitis == 1)) + cholesterol ~ categorical([0.08965517, 0.28275862, 0.62758621]) + elseif ((PBC == 1) && (Steatosis == 1) && (ChHepatitis == 2)) + cholesterol ~ categorical([0.09659091, 0.30113636, 0.60227273]) + elseif ((PBC == 1) && (Steatosis == 1) && (ChHepatitis == 3)) + cholesterol ~ categorical([0.1034483, 0.3256705, 0.5708812]) + elseif ((PBC == 1) && (Steatosis == 2) && (ChHepatitis == 1)) + cholesterol ~ categorical([0.1015873, 0.3047619, 0.5936508]) + elseif ((PBC == 1) && (Steatosis == 2) && (ChHepatitis == 2)) + cholesterol ~ categorical([0.1050955, 0.3152866, 0.5796179]) + elseif ((PBC == 1) && (Steatosis == 2) && (ChHepatitis == 3)) + cholesterol ~ categorical([0.125, 0.3642857, 0.5107143]) + elseif ((PBC == 2) && (Steatosis == 1) && (ChHepatitis == 1)) + cholesterol ~ categorical([0.09174312, 0.27981651, 0.62844037]) + elseif ((PBC == 2) && (Steatosis == 1) && (ChHepatitis == 2)) + cholesterol ~ categorical([0.06918239, 0.23899371, 0.6918239]) + elseif ((PBC == 2) && (Steatosis == 1) && (ChHepatitis == 3)) + cholesterol ~ categorical([0.04477612, 0.2238806, 0.73134328]) + elseif ((PBC == 2) && (Steatosis == 2) && (ChHepatitis == 1)) + cholesterol ~ categorical([0.03296703, 0.06593407, 0.9010989]) + elseif ((PBC == 2) && (Steatosis == 2) && (ChHepatitis == 2)) + cholesterol ~ categorical([0.00277008, 0.02770083, 0.96952909]) + elseif ((PBC == 2) && (Steatosis == 2) && (ChHepatitis == 3)) + cholesterol ~ categorical([0.00044425, 0.09773434, 0.90182141]) + else + @assert false + end + + if ((vh_amn == 1) && (ChHepatitis == 1)) + hbsag ~ categorical([0.5, 0.5]) + elseif ((vh_amn == 1) && (ChHepatitis == 2)) + hbsag ~ categorical([0.4615385, 0.5384615]) + elseif ((vh_amn == 1) && (ChHepatitis == 3)) + hbsag ~ categorical([0.1125, 0.8875]) + elseif ((vh_amn == 2) && (ChHepatitis == 1)) + hbsag ~ categorical([0.1904762, 0.8095238]) + elseif ((vh_amn == 2) && (ChHepatitis == 2)) + hbsag ~ categorical([0.04347826, 0.95652174]) + elseif ((vh_amn == 2) && (ChHepatitis == 3)) + hbsag ~ categorical([0.04674797, 0.95325203]) + else + @assert false + end + + if ((vh_amn == 1) && (ChHepatitis == 1)) + hbc_anti ~ categorical([0.00355872, 0.99644128]) + elseif ((vh_amn == 1) && (ChHepatitis == 2)) + hbc_anti ~ categorical([0.00763359, 0.99236641]) + elseif ((vh_amn == 1) && (ChHepatitis == 3)) + hbc_anti ~ categorical([0.0875, 0.9125]) + elseif ((vh_amn == 2) && (ChHepatitis == 1)) + hbc_anti ~ categorical([0.07936508, 0.92063492]) + elseif ((vh_amn == 2) && (ChHepatitis == 2)) + hbc_anti ~ categorical([0.1304348, 0.8695652]) + elseif ((vh_amn == 2) && (ChHepatitis == 3)) + hbc_anti ~ categorical([0.101626, 0.898374]) + else + @assert false + end + + if ((vh_amn == 1) && (ChHepatitis == 1)) + hcv_anti ~ categorical([0.00355872, 0.99644128]) + elseif ((vh_amn == 1) && (ChHepatitis == 2)) + hcv_anti ~ categorical([0.00763359, 0.99236641]) + elseif ((vh_amn == 1) && (ChHepatitis == 3)) + hcv_anti ~ categorical([0.00124844, 0.99875156]) + elseif ((vh_amn == 2) && (ChHepatitis == 1)) + hcv_anti ~ categorical([0.00158479, 0.99841521]) + elseif ((vh_amn == 2) && (ChHepatitis == 2)) + hcv_anti ~ categorical([0.004329, 0.995671]) + elseif ((vh_amn == 2) && (ChHepatitis == 3)) + hcv_anti ~ categorical([0.00203252, 0.99796748]) + else + @assert false + end + + if ((vh_amn == 1) && (ChHepatitis == 1)) + hbeag ~ categorical([0.00355872, 0.99644128]) + elseif ((vh_amn == 1) && (ChHepatitis == 2)) + hbeag ~ categorical([0.00763359, 0.99236641]) + elseif ((vh_amn == 1) && (ChHepatitis == 3)) + hbeag ~ categorical([0.00124844, 0.99875156]) + elseif ((vh_amn == 2) && (ChHepatitis == 1)) + hbeag ~ categorical([0.00158479, 0.99841521]) + elseif ((vh_amn == 2) && (ChHepatitis == 2)) + hbeag ~ categorical([0.04347826, 0.95652174]) + elseif ((vh_amn == 2) && (ChHepatitis == 3)) + hbeag ~ categorical([0.00203252, 0.99796748]) + else + @assert false + end + + if ((hepatomegaly == 1)) + hepatalgia ~ categorical([0.3142251, 0.6857749]) + elseif ((hepatomegaly == 2)) + hepatalgia ~ categorical([0.03070175, 0.96929825]) + else + @assert false + end + + if ((fibrosis == 1) && (Steatosis == 1)) + Cirrhosis ~ categorical([0.56, 0.24, 0.2]) + elseif ((fibrosis == 1) && (Steatosis == 2)) + Cirrhosis ~ categorical([0.49, 0.21, 0.3]) + elseif ((fibrosis == 2) && (Steatosis == 1)) + Cirrhosis ~ categorical([0.35, 0.15, 0.5]) + elseif ((fibrosis == 2) && (Steatosis == 2)) + Cirrhosis ~ categorical([0.001, 0.001, 0.998]) + else + @assert false + end + + if ((vh_amn == 1) && (ChHepatitis == 1) && (hbsag == 1)) + hbsag_anti ~ categorical([0.0070922, 0.9929078]) + elseif ((vh_amn == 1) && (ChHepatitis == 1) && (hbsag == 2)) + hbsag_anti ~ categorical([0.07142857, 0.92857143]) + elseif ((vh_amn == 1) && (ChHepatitis == 2) && (hbsag == 1)) + hbsag_anti ~ categorical([0.01639344, 0.98360656]) + elseif ((vh_amn == 1) && (ChHepatitis == 2) && (hbsag == 2)) + hbsag_anti ~ categorical([0.01408451, 0.98591549]) + elseif ((vh_amn == 1) && (ChHepatitis == 3) && (hbsag == 1)) + hbsag_anti ~ categorical([0.01098901, 0.98901099]) + elseif ((vh_amn == 1) && (ChHepatitis == 3) && (hbsag == 2)) + hbsag_anti ~ categorical([0.04225352, 0.95774648]) + elseif ((vh_amn == 2) && (ChHepatitis == 1) && (hbsag == 1)) + hbsag_anti ~ categorical([0.08333333, 0.91666667]) + elseif ((vh_amn == 2) && (ChHepatitis == 1) && (hbsag == 2)) + hbsag_anti ~ categorical([0.00195695, 0.99804305]) + elseif ((vh_amn == 2) && (ChHepatitis == 2) && (hbsag == 1)) + hbsag_anti ~ categorical([0.09090909, 0.90909091]) + elseif ((vh_amn == 2) && (ChHepatitis == 2) && (hbsag == 2)) + hbsag_anti ~ categorical([0.00452489, 0.99547511]) + elseif ((vh_amn == 2) && (ChHepatitis == 3) && (hbsag == 1)) + hbsag_anti ~ categorical([0.004329, 0.995671]) + elseif ((vh_amn == 2) && (ChHepatitis == 3) && (hbsag == 2)) + hbsag_anti ~ categorical([0.01492537, 0.98507463]) + else + @assert false + end + + if ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.04347826, 0.2173913, 0.34782609, 0.39130435]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.07407407074074071, 0.2222222222222222, 0.3333333333333333, 0.37037037370370374]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.07894737, 0.23684211, 0.34210526, 0.34210526]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.019230769807692304, 0.11538461884615381, 0.3653846163461539, 0.4999999950000001]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.01818182, 0.11818182, 0.38181818, 0.48181818]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.021897810218978103, 0.12408759124087591, 0.416058394160584, 0.43795620437956206]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.03571428964285711, 0.16071428839285715, 0.39285713607142864, 0.41071428589285713]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.05882353, 0.20588235, 0.38235294, 0.35294118]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.07692308000000002, 0.23076923000000002, 0.35897436000000005, 0.33333333000000004]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.02020202, 0.11111111, 0.34343434, 0.52525253]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.01941748, 0.10679612, 0.34951456, 0.52427184]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.023622049763779504, 0.11811023881889762, 0.3779527562204725, 0.48031495519685047]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.04225352, 0.15492958, 0.36619718, 0.43661972]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.06, 0.2, 0.36, 0.38]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.07575758, 0.22727273, 0.36363636, 0.33333333]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.03030303, 0.12121212, 0.35606061, 0.49242424]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.021582730215827302, 0.1151079111510791, 0.3741007237410072, 0.48920863489208627]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.02061856, 0.12371134, 0.40721649, 0.44845361]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.01449275, 0.11594203, 0.39130435, 0.47826087]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.00398406, 0.11952191, 0.35856574, 0.51792829]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.00662252, 0.13245033, 0.26490066, 0.59602649]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.00151286, 0.04538578, 0.34795764, 0.60514372]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.00144718, 0.04341534, 0.37626628, 0.5788712]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.00114811, 0.05740528, 0.44776119, 0.49368542]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.00311526, 0.03115265, 0.43613707, 0.52959502]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.00892857, 0.00892857, 0.44642857, 0.53571429]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.01388889, 0.01388889, 0.41666667, 0.55555555]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.00178253, 0.01782531, 0.28520499, 0.69518717]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.00174825, 0.00174825, 0.2972028, 0.6993007]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.00144509, 0.00144509, 0.36127168, 0.63583814]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.00255102, 0.00255102, 0.33163265, 0.66326531]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.0049505, 0.0049505, 0.2970297, 0.6930693]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.07692308, 0.07692308, 0.07692308, 0.76923076]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.00146843, 0.01468429, 0.30837004, 0.67547724]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.00127877, 0.00127877, 0.33248082, 0.66496164]) + elseif ((Hyperbilirubinemia == 1) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.00181159, 0.00181159, 0.54347827, 0.45289855]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.0408163295918367, 0.14285713857142862, 0.4081632659183674, 0.4081632659183674]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.06818182068181822, 0.20454545204545452, 0.36363636363636365, 0.36363636363636365]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.07692308, 0.23076923, 0.35384615, 0.33846154]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.030303030303030304, 0.1439393914393939, 0.3409090934090909, 0.48484848484848486]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.02173913, 0.13768116, 0.35507246, 0.48550725]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.025906739740932605, 0.15025906849740933, 0.38341968616580313, 0.44041450559585493]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.0425531895744681, 0.17021276829787235, 0.37234042627659575, 0.4148936158510639]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.05084745949152541, 0.20338982796610172, 0.37288135627118646, 0.37288135627118646]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.07042254, 0.22535211, 0.36619718, 0.33802817]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.032, 0.136, 0.312, 0.52]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.0234375, 0.1328125, 0.3125, 0.53125]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.02824859, 0.14124294, 0.33898305, 0.49152542]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.044776120447761206, 0.164179101641791, 0.34328358343283577, 0.44776119447761187]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.05555556, 0.19444444, 0.35185185, 0.39814815]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.08536585, 0.24390244, 0.36585366, 0.30487805]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.039106149608938504, 0.15083798849162014, 0.32960893670391067, 0.4804469251955308]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.02926829, 0.14634146, 0.33658537, 0.48780488]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 1) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.03030303, 0.16666667, 0.38888889, 0.41414141]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.028301889716981103, 0.1603773583962264, 0.3679245263207548, 0.44339622556603775]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.01818182, 0.16363636, 0.34545455, 0.47272727]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.01923077, 0.19230769, 0.01923077, 0.76923077]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.01449275, 0.07246377, 0.24637681, 0.66666667]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.01282051, 0.07692308, 0.26923077, 0.64102564]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 1) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.0188679201886792, 0.1320754713207547, 0.4339622643396226, 0.41509434415094343]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.0032154300321543, 0.0964630209646302, 0.4180064341800643, 0.4823151148231511]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.00621118, 0.0621118, 0.43478261, 0.49689441]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.04545455, 0.04545455, 0.45454545, 0.45454545]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.01818182, 0.01818182, 0.14545455, 0.81818181]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.01694915, 0.01694915, 0.10169492, 0.86440678]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 2) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.03448276, 0.03448276, 0.10344828, 0.8275862]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.00980392, 0.00980392, 0.19607843, 0.78431373]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.07692308, 0.07692308, 0.07692308, 0.76923076]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 1) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.01587302, 0.01587302, 0.01587302, 0.95238094]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 1)) + bilirubin ~ categorical([0.01234568, 0.02469136, 0.14814815, 0.81481481]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 2)) + bilirubin ~ categorical([0.00284091, 0.00284091, 0.05681818, 0.9375]) + elseif ((Hyperbilirubinemia == 2) && (PBC == 2) && (Cirrhosis == 3) && (gallstones == 2) && (ChHepatitis == 3)) + bilirubin ~ categorical([0.00070872, 0.02126152, 0.13465627, 0.84337349]) + else + @assert false + end + + if ((RHepatitis == 1) && (THepatitis == 1) && (Cirrhosis == 1) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.04166667, 0.29166667, 0.66666666]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Cirrhosis == 1) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.04347826, 0.30434783, 0.65217391]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Cirrhosis == 1) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.04166667, 0.33333333, 0.625]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Cirrhosis == 2) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.03773585, 0.26415094, 0.69811321]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Cirrhosis == 2) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.025, 0.25, 0.725]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Cirrhosis == 2) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.02702703, 0.27027027, 0.7027027]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Cirrhosis == 3) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.03571429, 0.21428571, 0.75]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Cirrhosis == 3) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.02272727, 0.20454545, 0.77272728]) + elseif ((RHepatitis == 1) && (THepatitis == 1) && (Cirrhosis == 3) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.02325581, 0.18604651, 0.79069768]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Cirrhosis == 1) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.02898551, 0.28985507, 0.68115942]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Cirrhosis == 1) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.03389831, 0.3220339, 0.64406779]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Cirrhosis == 1) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.04545455, 0.37878788, 0.57575757]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Cirrhosis == 2) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.02985075, 0.29850746, 0.67164179]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Cirrhosis == 2) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.02040816, 0.28571429, 0.69387755]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Cirrhosis == 2) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.02083333, 0.3125, 0.66666667]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Cirrhosis == 3) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.02597403, 0.24675325, 0.72727272]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Cirrhosis == 3) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.015625, 0.234375, 0.75]) + elseif ((RHepatitis == 1) && (THepatitis == 2) && (Cirrhosis == 3) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.00584795, 0.23391813, 0.76023392]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Cirrhosis == 1) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.04761905, 0.28571429, 0.66666666]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Cirrhosis == 1) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.04918033, 0.31147541, 0.63934426]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Cirrhosis == 1) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.05555556, 0.34722222, 0.59722222]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Cirrhosis == 2) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.04166667, 0.27777778, 0.68055555]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Cirrhosis == 2) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.03703704, 0.25925926, 0.7037037]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Cirrhosis == 2) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.05357143, 0.26785714, 0.67857143]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Cirrhosis == 3) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.04651163, 0.22093023, 0.73255814]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Cirrhosis == 3) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.04054054, 0.2027027, 0.75675676]) + elseif ((RHepatitis == 2) && (THepatitis == 1) && (Cirrhosis == 3) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.07407407, 0.14814815, 0.77777778]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Cirrhosis == 1) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.04597701, 0.29885057, 0.65517242]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Cirrhosis == 1) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.04494382, 0.33707865, 0.61797753]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Cirrhosis == 1) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.06896552, 0.48275862, 0.44827586]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Cirrhosis == 2) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.04494382, 0.33707865, 0.61797753]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Cirrhosis == 2) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.03896104, 0.31168831, 0.64935065]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Cirrhosis == 2) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.06451613, 0.38709677, 0.5483871]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Cirrhosis == 3) && (ChHepatitis == 1)) + phosphatase ~ categorical([0.03296703, 0.21978022, 0.74725275]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Cirrhosis == 3) && (ChHepatitis == 2)) + phosphatase ~ categorical([0.02777778, 0.19444444, 0.77777778]) + elseif ((RHepatitis == 2) && (THepatitis == 2) && (Cirrhosis == 3) && (ChHepatitis == 3)) + phosphatase ~ categorical([0.2118451, 0.3394077, 0.4487472]) + else + @assert false + end + + if ((Cirrhosis == 1)) + proteins ~ categorical([0.99827883, 0.00172117]) + elseif ((Cirrhosis == 2)) + proteins ~ categorical([0.99678457, 0.00321543]) + elseif ((Cirrhosis == 3)) + proteins ~ categorical([0.98032787, 0.01967213]) + else + @assert false + end + + if ((Cirrhosis == 1)) + edema ~ categorical([0.3448276, 0.6551724]) + elseif ((Cirrhosis == 2)) + edema ~ categorical([0.06451613, 0.93548387]) + elseif ((Cirrhosis == 3)) + edema ~ categorical([0.1311475, 0.8688525]) + else + @assert false + end + + if ((Cirrhosis == 1) && (PBC == 1)) + platelet ~ categorical([0.06547619, 0.63690476, 0.17857143, 0.11904762]) + elseif ((Cirrhosis == 1) && (PBC == 2)) + platelet ~ categorical([0.06896552, 0.46551724, 0.27586207, 0.18965517]) + elseif ((Cirrhosis == 2) && (PBC == 1)) + platelet ~ categorical([0.06557377, 0.63934426, 0.17486339, 0.12021858]) + elseif ((Cirrhosis == 2) && (PBC == 2)) + platelet ~ categorical([0.06451613, 0.64516129, 0.16129032, 0.12903226]) + elseif ((Cirrhosis == 3) && (PBC == 1)) + platelet ~ categorical([0.06428571, 0.67142857, 0.15714286, 0.10714286]) + elseif ((Cirrhosis == 3) && (PBC == 2)) + platelet ~ categorical([0.09393939, 0.73636364, 0.13939394, 0.03030303]) + else + @assert false + end + + if ((ChHepatitis == 1) && (Cirrhosis == 1) && (THepatitis == 1) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.01754386, 0.84210526, 0.14035088]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 1) && (THepatitis == 1) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.01298701, 0.81818182, 0.16883117]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 1) && (THepatitis == 2) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.02150538, 0.8172043, 0.16129032]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 1) && (THepatitis == 2) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.01666667, 0.8, 0.18333333]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 2) && (THepatitis == 1) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.025, 0.85, 0.125]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 2) && (THepatitis == 1) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.01333333, 0.86666667, 0.12]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 2) && (THepatitis == 2) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.02409639, 0.86746988, 0.10843373]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 2) && (THepatitis == 2) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.01960784, 0.85294118, 0.12745098]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 3) && (THepatitis == 1) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.02197802, 0.89010989, 0.08791209]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 3) && (THepatitis == 1) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.01923077, 0.90384615, 0.07692308]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 3) && (THepatitis == 2) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.024, 0.904, 0.072]) + elseif ((ChHepatitis == 1) && (Cirrhosis == 3) && (THepatitis == 2) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.02197802, 0.9010989, 0.07692308]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 1) && (THepatitis == 1) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.03030303, 0.84848485, 0.12121212]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 1) && (THepatitis == 1) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.03225806, 0.79032259, 0.17741935]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 1) && (THepatitis == 2) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.02898551, 0.79710145, 0.17391304]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 1) && (THepatitis == 2) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.02469136, 0.75308642, 0.22222222]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 2) && (THepatitis == 1) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.03508772, 0.8245614, 0.14035088]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 2) && (THepatitis == 1) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.04081633, 0.83673469, 0.12244898]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 2) && (THepatitis == 2) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.03571429, 0.85714285, 0.10714286]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 2) && (THepatitis == 2) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.03333333, 0.83333334, 0.13333333]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 3) && (THepatitis == 1) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.05084746, 0.88135593, 0.06779661]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 3) && (THepatitis == 1) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.05, 0.9, 0.05]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 3) && (THepatitis == 2) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.05333333, 0.90666667, 0.04]) + elseif ((ChHepatitis == 2) && (Cirrhosis == 3) && (THepatitis == 2) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.08333333, 0.88888889, 0.02777778]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 1) && (THepatitis == 1) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.03448276, 0.81034483, 0.15517241]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 1) && (THepatitis == 1) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.01428571, 0.75714286, 0.22857143]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 1) && (THepatitis == 2) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.02173913, 0.75, 0.22826087]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 1) && (THepatitis == 2) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.00172117, 0.60240964, 0.39586919]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 2) && (THepatitis == 1) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.01785714, 0.76785715, 0.21428571]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 2) && (THepatitis == 1) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.01785714, 0.78571429, 0.19642857]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 2) && (THepatitis == 2) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.02816901, 0.80281691, 0.16901408]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 2) && (THepatitis == 2) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.00321543, 0.67524116, 0.32154341]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 3) && (THepatitis == 1) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.03508772, 0.84210526, 0.12280702]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 3) && (THepatitis == 1) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.03703704000000001, 0.9259259200000001, 0.03703704000000001]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 3) && (THepatitis == 2) && (Hyperbilirubinemia == 1)) + inr ~ categorical([0.05357143, 0.89285714, 0.05357143]) + elseif ((ChHepatitis == 3) && (Cirrhosis == 3) && (THepatitis == 2) && (Hyperbilirubinemia == 2)) + inr ~ categorical([0.065, 0.875, 0.06]) + else + @assert false + end + + if ((Cirrhosis == 1)) + alcohol ~ categorical([0.2068966, 0.7931034]) + elseif ((Cirrhosis == 2)) + alcohol ~ categorical([0.2258064, 0.7741936]) + elseif ((Cirrhosis == 3)) + alcohol ~ categorical([0.1114754, 0.8885246]) + else + @assert false + end + + if ((Cirrhosis == 1) && (PBC == 1)) + encephalopathy ~ categorical([0.05325444, 0.94674556]) + elseif ((Cirrhosis == 1) && (PBC == 2)) + encephalopathy ~ categorical([0.05172414, 0.94827586]) + elseif ((Cirrhosis == 2) && (PBC == 1)) + encephalopathy ~ categorical([0.04891304, 0.95108696]) + elseif ((Cirrhosis == 2) && (PBC == 2)) + encephalopathy ~ categorical([0.00321543, 0.99678457]) + elseif ((Cirrhosis == 3) && (PBC == 1)) + encephalopathy ~ categorical([0.05357143, 0.94642857]) + elseif ((Cirrhosis == 3) && (PBC == 2)) + encephalopathy ~ categorical([0.01515152, 0.98484848]) + else + @assert false + end + + if ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.058823529411764705, 0.15686274843137252, 0.4117647058823529, 0.37254901627450987]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.05454545054545451, 0.16363636163636364, 0.41818182418181826, 0.36363636363636365]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.04761905, 0.15873016, 0.41269841, 0.38095238]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.06451613, 0.17741935, 0.41935484, 0.33870968]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.07017544, 0.19298246, 0.42105263, 0.31578947]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.07936508, 0.19047619, 0.41269841, 0.31746032]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.0684931506849315, 0.1643835616438356, 0.4246575342465753, 0.3424657534246575]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.05882353, 0.17647059, 0.42647059, 0.33823529]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.06250000000000001, 0.17500000000000002, 0.41250000000000003, 0.35000000000000003]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.075, 0.1875, 0.425, 0.3125]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.08333333, 0.20833333, 0.43055556, 0.27777778]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.08988764, 0.2247191, 0.41573034, 0.26966292]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.0617284, 0.1728395, 0.4197531, 0.345679]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.0547945205479452, 0.1643835616438356, 0.4246575342465753, 0.3561643835616438]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.058823529411764705, 0.15294117847058825, 0.4117647058823529, 0.37647058623529417]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.06976744, 0.1627907, 0.41860465, 0.34883721]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.07792208, 0.18181818, 0.41558442, 0.32467532]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.08333333, 0.1875, 0.40625, 0.32291667]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.06862745, 0.16666667, 0.42156863, 0.34313725]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.0625, 0.1666667, 0.4270833, 0.34375]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.064, 0.168, 0.416, 0.352]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.08148148, 0.17777778, 0.42222222, 0.31851852]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.08661417086614172, 0.19685039196850393, 0.42519685425196857, 0.2913385829133859]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.12087911208791122, 0.23076922307692233, 0.395604439560444, 0.25274722527472254]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.051724140517241404, 0.15517241155172412, 0.3965517239655172, 0.3965517239655172]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.02173913, 0.13043478, 0.41304348, 0.43478261]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.0021692, 0.1084599, 0.3904555, 0.4989154]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.022727270227272705, 0.11363636113636362, 0.40909091409090914, 0.4545454545454546]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.00269542, 0.13477089, 0.40431267, 0.45822102]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.00262467, 0.1312336, 0.36745407, 0.49868766]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.01923077, 0.11538462, 0.40384615, 0.46153846]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.002079, 0.1247401, 0.4158004, 0.4573805]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.0018148800000000003, 0.12704174000000001, 0.39927405000000005, 0.47186933000000003]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.0188679201886792, 0.1320754713207547, 0.41509434415094343, 0.4339622643396226]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.02272727, 0.15909091, 0.40909091, 0.40909091]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.02083333, 0.16666667, 0.375, 0.4375]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.01724138, 0.12068966, 0.39655172, 0.46551724]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.0019193899808061003, 0.11516314884836852, 0.40307101596928985, 0.4798464452015356]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.00166389, 0.09983361, 0.38269551, 0.51580699]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.01724138, 0.10344828, 0.39655172, 0.48275862]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.02040816, 0.12244898, 0.3877551, 0.46938776]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.01818182, 0.10909091, 0.34545455, 0.52727272]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.02777778, 0.11111111, 0.38888889, 0.47222222]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.01492537, 0.11940299, 0.40298507, 0.46268657]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.01190476, 0.10714286, 0.38095238, 0.5]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.03409091, 0.11363636, 0.38636364, 0.46590909]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.02631579, 0.13157895, 0.39473684, 0.44736842]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.02777778, 0.13888889, 0.27777778, 0.55555555]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.02, 0.12, 0.4, 0.46]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.00212314, 0.12738854, 0.42462845, 0.44585987]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.0019193899808061003, 0.11516314884836852, 0.4222648757773513, 0.46065258539347415]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.02, 0.12, 0.44, 0.42]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.0024937699750623007, 0.14962593850374065, 0.448877805511222, 0.3990024860099752]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.0023753002375300238, 0.14251781425178142, 0.4275534427553443, 0.4275534427553443]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.016666669833333304, 0.11666666883333332, 0.4499999955000001, 0.4166666658333334]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.0017825300178253005, 0.12477718124777183, 0.4634581146345812, 0.4099821740998218]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.00144718, 0.11577424, 0.44862518, 0.4341534]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.028169010281690107, 0.12676056126760563, 0.46478873464788734, 0.38028169380281696]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.01724138, 0.15517241, 0.48275862, 0.34482759]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.00584795, 0.23391813, 0.46783626, 0.29239766]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.018181819818181805, 0.10909090890909091, 0.43636363563636366, 0.43636363563636366]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.0017211700172117001, 0.1032702210327022, 0.447504304475043, 0.447504304475043]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.00131406, 0.09198423, 0.42049934, 0.48620237]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.025, 0.1, 0.425, 0.45]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.01470588, 0.11764706, 0.44117647, 0.42647059]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.00369004, 0.07380074, 0.36900369, 0.55350553]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + alt ~ categorical([0.02666667, 0.09333333, 0.42666667, 0.45333333]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + alt ~ categorical([0.01176471, 0.10588235, 0.44705882, 0.43529412]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + alt ~ categorical([0.00149031, 0.08941878, 0.41728763, 0.49180328]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + alt ~ categorical([0.06896551931034481, 0.12068965879310342, 0.4655172353448277, 0.3448275865517242]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + alt ~ categorical([0.03225806, 0.19354839, 0.51612903, 0.25806452]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + alt ~ categorical([0.0456989204569892, 0.1747311817473118, 0.4274193542741935, 0.35215054352150543]) + else + @assert false + end + + if ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.01960784, 0.1372549, 0.47058824, 0.37254902]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.01818182, 0.12727273, 0.49090909, 0.36363636]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.01612903, 0.14516129, 0.46774194, 0.37096774]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.01612903, 0.16129032, 0.48387097, 0.33870968]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.018181820000000005, 0.16363636000000004, 0.5090909100000001, 0.30909091000000005]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.032258060322580606, 0.17741935177419352, 0.4838709748387098, 0.3064516130645161]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.02777778, 0.15277778, 0.48611111, 0.33333333]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.02941176, 0.14705882, 0.50000001, 0.32352941]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.02531646, 0.15189873, 0.48101266, 0.34177215]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.025, 0.175, 0.5, 0.3]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.02777778, 0.18055556, 0.52777777, 0.26388889]) + elseif ((ChHepatitis == 1) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.03370787, 0.20224719, 0.50561797, 0.25842697]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.02469136, 0.16049383, 0.4691358, 0.34567901]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.0273972602739726, 0.136986301369863, 0.4794520547945205, 0.3561643835616438]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.023809520238095204, 0.14285714142857142, 0.45238095452380955, 0.38095238380952384]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.02352941, 0.16470588, 0.45882353, 0.35294118]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.02597403, 0.16883117, 0.48051948, 0.32467532]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.03125, 0.1875, 0.4583333, 0.3229167]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.02912621, 0.16504854, 0.46601942, 0.33980583]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.03125, 0.15625, 0.4791667, 0.3333333]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.03174603, 0.15873016, 0.46031746, 0.34920635]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.036764709632352906, 0.17647058823529413, 0.47058823529411764, 0.31617646683823536]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.03937008, 0.18110236, 0.49606299, 0.28346457]) + elseif ((ChHepatitis == 1) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.05494505054945051, 0.23076923230769233, 0.46153846461538467, 0.25274725252747254]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.01754386, 0.14035088, 0.45614035, 0.38596491]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.00221729, 0.0886918, 0.48780488, 0.42128603]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.00212314, 0.08492569, 0.44585987, 0.4670913]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.00221729, 0.11086475, 0.46563193, 0.42128603]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.00269542, 0.08086253, 0.51212938, 0.40431267]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.0026954200269542006, 0.08086253080862531, 0.45822102458221026, 0.45822102458221026]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.00191939, 0.09596929, 0.46065259, 0.44145873]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.00203666, 0.0814664, 0.48879837, 0.42769857]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.00181488, 0.0907441, 0.45372051, 0.45372051]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.00184843, 0.11090573, 0.4805915, 0.40665434]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.00226757, 0.09070295, 0.52154195, 0.38548753]) + elseif ((ChHepatitis == 2) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.00212314, 0.10615711, 0.48832272, 0.40339703]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.0017211700172117001, 0.1032702210327022, 0.447504304475043, 0.447504304475043]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.00191939, 0.07677543, 0.46065259, 0.46065259]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.00166389, 0.08319468, 0.41597338, 0.49916805]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.00172117, 0.10327022, 0.4302926, 0.46471601]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.00203666, 0.0814664, 0.46843177, 0.44806517]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.00181488, 0.0907441, 0.41742287, 0.49001815]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.00142653, 0.09985735, 0.44222539, 0.45649073]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.00149031, 0.08941878, 0.46199702, 0.44709389]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.00120337, 0.08423586, 0.433213, 0.48134777]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.0113636398863636, 0.10227272897727273, 0.44318181556818187, 0.44318181556818187]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.0131578901315789, 0.0921052609210526, 0.47368421473684214, 0.4210526342105263]) + elseif ((ChHepatitis == 2) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.02777778, 0.11111111, 0.36111111, 0.5]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.0019960099800399003, 0.09980039900199601, 0.4590818354091817, 0.43912175560878247]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.00212314, 0.08492569, 0.48832272, 0.42462845]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.00191939, 0.07677543, 0.46065259, 0.46065259]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.0019960099800399003, 0.09980039900199601, 0.4790419152095809, 0.41916167580838326]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.00249377, 0.07481297, 0.54862842, 0.37406484]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.0024330900000000006, 0.07299270000000001, 0.5109489100000001, 0.41362530000000003]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.0016638900166389, 0.09983361099833611, 0.4991680549916805, 0.39933444399334445]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.00175131, 0.08756567, 0.52539405, 0.38528897]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.0014265300142653002, 0.0855920108559201, 0.49928673499286735, 0.41369472413694724]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.0014064700000000002, 0.11251758000000002, 0.5203938100000001, 0.36568214000000004]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.00172117, 0.10327022, 0.58519794, 0.30981067]) + elseif ((ChHepatitis == 3) && (RHepatitis == 1) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.00584795, 0.11695906, 0.64327486, 0.23391813]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.00181488, 0.0907441, 0.47186933, 0.43557169]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.00172117, 0.06884682, 0.48192771, 0.4475043]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.00133156, 0.0665779, 0.43941411, 0.49267643]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.00126422, 0.08849558, 0.4551201, 0.4551201]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.00149031, 0.07451565, 0.49180328, 0.43219076]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 1) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.00369004, 0.07380074, 0.36900369, 0.55350553]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 1)) + ast ~ categorical([0.0013315600133156002, 0.0932090509320905, 0.45272969452729694, 0.45272969452729694]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 2)) + ast ~ categorical([0.00116144, 0.08130081, 0.48780488, 0.42973287]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 1) && (Cirrhosis == 3)) + ast ~ categorical([0.00149031, 0.07451565, 0.43219076, 0.49180328]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 1)) + ast ~ categorical([0.01724138, 0.13793103, 0.5, 0.34482759]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 2)) + ast ~ categorical([0.03225806, 0.06451613, 0.67741936, 0.22580645]) + elseif ((ChHepatitis == 3) && (RHepatitis == 2) && (THepatitis == 2) && (Steatosis == 2) && (Cirrhosis == 3)) + ast ~ categorical([0.01075269, 0.22580645, 0.46774194, 0.29569892]) + else + @assert false + end + + if ((Cirrhosis == 1) && (RHepatitis == 1) && (THepatitis == 1)) + spleen ~ categorical([0.3235294, 0.6764706]) + elseif ((Cirrhosis == 1) && (RHepatitis == 1) && (THepatitis == 2)) + spleen ~ categorical([0.3703704, 0.6296296]) + elseif ((Cirrhosis == 1) && (RHepatitis == 2) && (THepatitis == 1)) + spleen ~ categorical([0.3623188, 0.6376812]) + elseif ((Cirrhosis == 1) && (RHepatitis == 2) && (THepatitis == 2)) + spleen ~ categorical([0.4827586, 0.5172414]) + elseif ((Cirrhosis == 2) && (RHepatitis == 1) && (THepatitis == 1)) + spleen ~ categorical([0.3023256, 0.6976744]) + elseif ((Cirrhosis == 2) && (RHepatitis == 1) && (THepatitis == 2)) + spleen ~ categorical([0.2444444, 0.7555556]) + elseif ((Cirrhosis == 2) && (RHepatitis == 2) && (THepatitis == 1)) + spleen ~ categorical([0.2156863, 0.7843137]) + elseif ((Cirrhosis == 2) && (RHepatitis == 2) && (THepatitis == 2)) + spleen ~ categorical([0.2580645, 0.7419355]) + elseif ((Cirrhosis == 3) && (RHepatitis == 1) && (THepatitis == 1)) + spleen ~ categorical([0.1621622, 0.8378378]) + elseif ((Cirrhosis == 3) && (RHepatitis == 1) && (THepatitis == 2)) + spleen ~ categorical([0.1176471, 0.8823529]) + elseif ((Cirrhosis == 3) && (RHepatitis == 2) && (THepatitis == 1)) + spleen ~ categorical([0.1111111, 0.8888889]) + elseif ((Cirrhosis == 3) && (RHepatitis == 2) && (THepatitis == 2)) + spleen ~ categorical([0.1007067, 0.8992933]) + else + @assert false + end + + if ((Cirrhosis == 1)) + spiders ~ categorical([0.6034483, 0.3965517]) + elseif ((Cirrhosis == 2)) + spiders ~ categorical([0.483871, 0.516129]) + elseif ((Cirrhosis == 3)) + spiders ~ categorical([0.1836066, 0.8163934]) + else + @assert false + end + + if ((Cirrhosis == 1)) + albumin ~ categorical([0.91222031, 0.08605852, 0.00172117]) + elseif ((Cirrhosis == 2)) + albumin ~ categorical([0.96463023, 0.00321543, 0.03215434]) + elseif ((Cirrhosis == 3)) + albumin ~ categorical([0.7393443, 0.1426229, 0.1180328]) + else + @assert false + end + + if ((Cirrhosis == 1)) + edge ~ categorical([0.7586207, 0.2413793]) + elseif ((Cirrhosis == 2)) + edge ~ categorical([0.4516129, 0.5483871]) + elseif ((Cirrhosis == 3)) + edge ~ categorical([0.2344262, 0.7655738]) + else + @assert false + end + + if ((Cirrhosis == 1)) + irregular_liver ~ categorical([0.6034483, 0.3965517]) + elseif ((Cirrhosis == 2)) + irregular_liver ~ categorical([0.3548387, 0.6451613]) + elseif ((Cirrhosis == 3)) + irregular_liver ~ categorical([0.1065574, 0.8934426]) + else + @assert false + end + + if ((Cirrhosis == 1)) + palms ~ categorical([0.5, 0.5]) + elseif ((Cirrhosis == 2)) + palms ~ categorical([0.2903226, 0.7096774]) + elseif ((Cirrhosis == 3)) + palms ~ categorical([0.1409836, 0.8590164]) + else + @assert false + end + + if ((Cirrhosis == 1) && (PBC == 1)) + carcinoma ~ categorical([0.3636364, 0.6363636]) + elseif ((Cirrhosis == 1) && (PBC == 2)) + carcinoma ~ categorical([0.3, 0.7]) + elseif ((Cirrhosis == 2) && (PBC == 1)) + carcinoma ~ categorical([0.2727273, 0.7272727]) + elseif ((Cirrhosis == 2) && (PBC == 2)) + carcinoma ~ categorical([0.2, 0.8]) + elseif ((Cirrhosis == 3) && (PBC == 1)) + carcinoma ~ categorical([0.1, 0.9]) + elseif ((Cirrhosis == 3) && (PBC == 2)) + carcinoma ~ categorical([0.01, 0.99]) + else + @assert false + end + + if ((bilirubin == 1)) + itching ~ categorical([0.875, 0.125]) + elseif ((bilirubin == 2)) + itching ~ categorical([0.6865672, 0.3134328]) + elseif ((bilirubin == 3)) + itching ~ categorical([0.5477387, 0.4522613]) + elseif ((bilirubin == 4)) + itching ~ categorical([0.3333333, 0.6666667]) + else + @assert false + end + + if ((bilirubin == 1)) + skin ~ categorical([0.99378882, 0.00621118]) + elseif ((bilirubin == 2)) + skin ~ categorical([0.8955224, 0.1044776]) + elseif ((bilirubin == 3)) + skin ~ categorical([0.7035176, 0.2964824]) + elseif ((bilirubin == 4)) + skin ~ categorical([0.1822542, 0.8177458]) + else + @assert false + end + + if ((bilirubin == 1)) + jaundice ~ categorical([0.75, 0.25]) + elseif ((bilirubin == 2)) + jaundice ~ categorical([0.5671642, 0.4328358]) + elseif ((bilirubin == 3)) + jaundice ~ categorical([0.3467337, 0.6532663]) + elseif ((bilirubin == 4)) + jaundice ~ categorical([0.1942446, 0.8057554]) + else + @assert false + end + + if ((proteins == 1)) + ascites ~ categorical([0.1280932, 0.8719068]) + elseif ((proteins == 2)) + ascites ~ categorical([0.5833333, 0.4166667]) + else + @assert false + end + + if ((platelet == 1) && (inr == 1)) + bleeding ~ categorical([0.1428571, 0.8571429]) + elseif ((platelet == 1) && (inr == 2)) + bleeding ~ categorical([0.106383, 0.893617]) + elseif ((platelet == 1) && (inr == 3)) + bleeding ~ categorical([0.09090909, 0.90909091]) + elseif ((platelet == 2) && (inr == 1)) + bleeding ~ categorical([0.1304348, 0.8695652]) + elseif ((platelet == 2) && (inr == 2)) + bleeding ~ categorical([0.1373494, 0.8626506]) + elseif ((platelet == 2) && (inr == 3)) + bleeding ~ categorical([0.425, 0.575]) + elseif ((platelet == 3) && (inr == 1)) + bleeding ~ categorical([0.2, 0.8]) + elseif ((platelet == 3) && (inr == 2)) + bleeding ~ categorical([0.1333333, 0.8666667]) + elseif ((platelet == 3) && (inr == 3)) + bleeding ~ categorical([0.25, 0.75]) + elseif ((platelet == 4) && (inr == 1)) + bleeding ~ categorical([0.5, 0.5]) + elseif ((platelet == 4) && (inr == 2)) + bleeding ~ categorical([0.255814, 0.744186]) + elseif ((platelet == 4) && (inr == 3)) + bleeding ~ categorical([0.6666667, 0.3333333]) + else + @assert false + end + + if ((encephalopathy == 1)) + urea ~ categorical([0.2173913, 0.1304348, 0.6521739]) + elseif ((encephalopathy == 2)) + urea ~ categorical([0.03550296, 0.06508876, 0.89940828]) + else + @assert false + end + + if ((encephalopathy == 1)) + density ~ categorical([0.7391304, 0.2608696]) + elseif ((encephalopathy == 2)) + density ~ categorical([0.3772189, 0.6227811]) + else + @assert false + end + + if ((encephalopathy == 1)) + consciousness ~ categorical([0.3043478, 0.6956522]) + elseif ((encephalopathy == 2)) + consciousness ~ categorical([0.01627219, 0.98372781]) + else + @assert false + end + +end diff --git a/examples/2-hepar2/hepar2_entropy.jl b/examples/2-hepar2/hepar2_entropy.jl new file mode 100644 index 0000000..4210f5a --- /dev/null +++ b/examples/2-hepar2/hepar2_entropy.jl @@ -0,0 +1,178 @@ +include("hepar2.jl") +include("../../entropy.jl") + +import Gen +import Random + +using DelimitedFiles: writedlm + +Random.seed!(1) + +OUTDIR = joinpath("results") + +# ============================================================================== +# RUNTIME EXPERIMENT + +# Crash test model. +tr = Gen.simulate(model, ()) +model_args = () + +# Define nodes. +diseases = [:PBC, :Steatosis, :Cirrhosis, :fibrosis, :ChHepatitis,] +properties = [:surgery, :sex, :age, :joints, :hepatomegaly, :bilirubin, :proteins, :platelet, :inr, :encephalopathy] +leaves_order = [:upper_pain, :fat, :flatulence, :amylase, :anorexia, :nausea, :ama, :le_cells, :pain, :triglycerides, :pain_ruq, :fatigue, :pressure_ruq, :ESR, :ggtp, :cholesterol, :hbc_anti, :hcv_anti, :hbeag, :hepatalgia, :hbsag_anti, :phosphatase, :edema, :alcohol, :alt, :ast, :spleen, :spiders, :albumin, :edge, :irregular_liver, :palms, :carcinoma, :itching, :skin, :jaundice, :ascites, :bleeding, :urea, :density, :consciousness] + +# ============================================================================== +# RUNTIME EXPERIMENT + +function experiment_entropy_runtime(observations; N=5000, M=1) + stats = [] + for K in [1, 2, 3, 4, 5, 6, 7, 8, 16] + runtime = @elapsed begin + H_lo = entropy_lower_bound(model, model_args, Gen.select(observations...), N, M, K) + H_hi = entropy_upper_bound(model, model_args, Gen.select(observations...), N, 1, K) + end + push!(stats, (runtime, H_lo, H_hi)) + println(stats[end]) + end + return stats +end + +function run_experiment_entropy_runtime() + println("Runtime (Precompilation)") + experiment_entropy_runtime(diseases) + for n in [10, 20, 40] + println("Runtime Experiment $(n)") + stats = experiment_entropy_runtime(leaves_order[1:n]) + fname = joinpath(OUTDIR, "hepar2.cmi.$(n).runtime") + open(fname, "w") do io + for stat in stats + data = join(stat, ",") + write(io, data) + write(io, "\n") + end + end + println(fname) + end +end + +# ============================================================================== +# CONDITIONAL ENTROPY RANKING EXPERIMENT + +function experiment_conditional_entropy_ranking(diseases, observations, tests; N=100, M=1, K=100) + d = diseases + O = observations + stats = [] + model_traces::Vector{Gen.Trace} = [simulate(model, model_args) for i=1:N] + Threads.@threads for t in tests + println("Running $(d) $(t)") + sel_tdO = Gen.select(vcat([t], d, O)...) + sel_td = Gen.select(vcat([t], O)...) + # H(X,Y,Z) + H_tdO_lower = entropy_lower_bound(model, model_args, sel_tdO, N, M, K; model_traces=model_traces) + H_tdO_upper = entropy_upper_bound(model, model_args, sel_tdO, N, 1, K; model_traces=model_traces) + H_tdO_approx = mean([H_tdO_lower, H_tdO_upper]) + # H (Y,Z) + H_td_lower = entropy_lower_bound(model, model_args, sel_td, N, M, K; model_traces=model_traces) + H_td_upper = entropy_upper_bound(model, model_args, sel_td, N, 1, K; model_traces=model_traces) + H_td_approx = mean([H_td_lower, H_td_upper]) + # MI(X:Y|Z) without constant terms + CH_lo = H_tdO_lower - H_td_upper + CH_hi = H_tdO_upper - H_td_lower + CH_approx = H_tdO_approx - H_td_approx + stat = ( + diseases, t, + CH_approx, CH_lo, CH_hi, + H_tdO_approx, H_tdO_lower, H_tdO_upper, + H_td_approx, H_td_lower, H_td_upper, + ) + push!(stats, stat) + end + return stats +end + +# CONDITIONAL ENTROPY EXPERIMENT +function run_experiment_conditional_entropy_ranking() + observations = vcat(leaves_order[end-5:end], properties) + tests = leaves_order[1:end-5] + for d in diseases + stats = experiment_conditional_entropy_ranking([d], observations, tests) + stats = sort(stats, by=t->t[3], rev=true) + for stat in stats + println(stat) + end + fname = joinpath(OUTDIR, "hepar2.$(d).rankings") + writedlm(fname, [stat[2:end] for stat in stats], ",") + println(fname) + end +end + +# ============================================================================== +# ENTROPY VARIANCE EXPERIMENT + +function experiment_entropy_variance(iid, diseases, observations, test, Nrep; + N=1000, M=1, K=100) + # The sign here is the opposite of experiment_conditional_entropy, i.e., + # the correct signs are used. + d = diseases + O = observations + entropies = [] + weights = [] + Threads.@threads for i=1:Nrep + println("Running variance $(d) $(test) $(i)") + sel_dtO = Gen.select(vcat(d, test, O)...) + sel_tO = Gen.select(vcat(test, O)...) + model_traces::Vector{Gen.Trace} = !iid ? [simulate(model, model_args) for i=1:N] : [] + # Lower bound. + H_tO_lower_weights = entropy_lower_bound(model, model_args, sel_tO, N, M, K; + model_traces=model_traces, return_weights=true) + H_dtO_upper_weights = entropy_upper_bound(model, model_args, sel_dtO, N, 1, K; + model_traces=model_traces, return_weights=true) + H_dtO_lower = -mean(H_dtO_upper_weights) + H_tO_upper = -mean(H_tO_lower_weights) + CH_lo = H_dtO_lower - H_tO_upper + # Upper bound. + H_tO_upper_weights = entropy_upper_bound(model, model_args, sel_tO, N, 1, K; + model_traces=model_traces, return_weights=true) + H_dtO_lower_weights = entropy_lower_bound(model, model_args, sel_dtO, N, M, K; + model_traces=model_traces, return_weights=true) + H_dtO_upper = -mean(H_dtO_lower_weights) + H_tO_lower = -mean(H_tO_upper_weights) + CH_hi = H_dtO_upper - H_tO_lower + push!(entropies, (H_dtO_lower, H_dtO_upper, H_tO_lower, H_tO_upper)) + push!(weights, ( + H_dtO_lower_weights, + H_dtO_upper_weights, + H_tO_lower_weights, + H_tO_upper_weights + )) + end + return entropies, weights +end + +function run_experiment_entropy_variance() + disease, test = :PBC, :ama + observations = vcat(leaves_order[end-5:end], properties) + N = 10000 + K = 200 + for iid in [false, true] + entropies, weights = + experiment_entropy_variance(iid, [disease], observations, test, 18; + N=N, K=K) + # Write the Nrep entropies. + fname = joinpath(OUTDIR, "hepar2.entropies.$(disease).$(test).$(N).$(K).$(iid)") + rows = [vcat(row...) for row in entropies] + lines = Matrix(hcat(rows...)') + writedlm(fname, lines, ",") + println(fname) + # Write the N weights from Nrep=1. + fname = joinpath(OUTDIR, "hepar2.weights.$(disease).$(test).$(N).$(K).$(iid)") + lines = hcat(weights[1]...) + writedlm(fname, lines, ",") + println(fname) + end +end + +run_experiment_entropy_runtime() +run_experiment_conditional_entropy_ranking() +run_experiment_entropy_variance() diff --git a/examples/3-diabetes/README b/examples/3-diabetes/README new file mode 100644 index 0000000..f0d6e04 --- /dev/null +++ b/examples/3-diabetes/README @@ -0,0 +1,10 @@ +The main runner script is in diabetes_smc.jl + + $ julia diabetes_smc.jl + +This script will produce CMI for all pairs of time points, given a specific +scenario of meal and ins_abs. The default scenarios from the script are: + + # Selected evidence scenario. + idx_meal = 0 + idx_ins_abs = 0 diff --git a/examples/3-diabetes/csmc.jl b/examples/3-diabetes/csmc.jl new file mode 100644 index 0000000..04997e4 --- /dev/null +++ b/examples/3-diabetes/csmc.jl @@ -0,0 +1,57 @@ +import Gen +import Distributions + +function log_ml_estimate( + state::Gen.ParticleFilterState, + star_log_weight::Float64) + num_particles = length(state.traces) + log_weights = Vector{Float64}(undef, num_particles + 1) + log_weights[1:num_particles] = state.log_weights + log_weights[end] = star_log_weight + return state.log_ml_est + Gen.logsumexp(log_weights) - log(1 + num_particles) +end + +function maybe_resample!( + state::Gen.ParticleFilterState{U}, + star_trace::Gen.Trace, + star_log_weight::Float64; + ess_threshold::Real=(1+length(state.traces))/2, + verbose=false) where {U} + + num_particles = length(state.traces) + + # Extend the log weights. + log_weights_sample = Vector{Float64}(undef, num_particles + 1) + log_weights_sample[1:num_particles] = state.log_weights + log_weights_sample[end] = star_log_weight + + # Check resampling criteria. + (log_total_weight, log_normalized_weights) = Gen.normalize_weights(log_weights_sample) + ess = Gen.effective_sample_size(log_normalized_weights) + do_resample = ess < ess_threshold + + verbose && println("effective sample size: $ess, doing resample: $do_resample") + if do_resample + + weights = exp.(log_normalized_weights) + dist = Distributions.Categorical(weights / sum(weights)) + Distributions.rand!(dist, state.parents) + state.log_ml_est += log_total_weight - log(1 + num_particles) + + for i=1:num_particles + if state.parents[i] <= num_particles + state.new_traces[i] = state.traces[state.parents[i]] + else + @assert state.parents[i] == num_particles + 1 + state.new_traces[i] = star_trace + end + state.log_weights[i] = 0. + end + + # swap references + tmp = state.traces + state.traces = state.new_traces + state.new_traces = tmp + end + return do_resample +end diff --git a/examples/3-diabetes/diabetes_cpds.jl b/examples/3-diabetes/diabetes_cpds.jl new file mode 100644 index 0000000..afaf105 --- /dev/null +++ b/examples/3-diabetes/diabetes_cpds.jl @@ -0,0 +1,1359 @@ +normalize_probs(x, eps=1e-10) = begin y = (x .+ eps); return y / sum(y) end + +# cho | meal cho_balance (prev) +CPT_cho = Dict( + (1, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 5) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 6) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 7) => normalize_probs([0.9999, 0.0001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 8) => normalize_probs([0.9998, 0.0002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 9) => normalize_probs([0.9994, 0.0006, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 10) => normalize_probs([0.9985, 0.0015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 11) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 12) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 13) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 14) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 15) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 16) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 5) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 6) => normalize_probs([0.9999, 0.0001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 7) => normalize_probs([0.9998, 0.0002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 8) => normalize_probs([0.9994, 0.0006, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 9) => normalize_probs([0.9985, 0.0015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 10) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 11) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 12) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 13) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 14) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 15) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 16) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 5) => normalize_probs([0.9999, 0.0001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 6) => normalize_probs([0.9998, 0.0002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 7) => normalize_probs([0.9994, 0.0006, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 8) => normalize_probs([0.9985, 0.0015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 9) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 10) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 11) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 12) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 13) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 14) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 15) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 16) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 4) => normalize_probs([0.9999, 0.0001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 5) => normalize_probs([0.9998, 0.0002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 6) => normalize_probs([0.9994, 0.0006, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 7) => normalize_probs([0.9985, 0.0015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 8) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 9) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 10) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 11) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 12) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 13) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 14) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 15) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 16) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 3) => normalize_probs([0.9999, 0.0001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 4) => normalize_probs([0.9998, 0.0002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 5) => normalize_probs([0.9994, 0.0006, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 6) => normalize_probs([0.9985, 0.0015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 7) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 8) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 9) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 10) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 11) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 12) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 13) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 14) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 15) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 16) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 2) => normalize_probs([0.9999, 0.0001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 3) => normalize_probs([0.9998, 0.0002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 4) => normalize_probs([0.9994, 0.0006, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 5) => normalize_probs([0.9985, 0.0015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 6) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 7) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 8) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 9) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 10) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 11) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 12) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 13) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 14) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 15) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 16) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 1) => normalize_probs([0.9999, 0.0001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 2) => normalize_probs([0.9998, 0.0002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 3) => normalize_probs([0.9994, 0.0006, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 4) => normalize_probs([0.9985, 0.0015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 5) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 6) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 7) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 8) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 9) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 10) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 11) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 12) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 13) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 14) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 15) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 16) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 1) => normalize_probs([0.9998, 0.0002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 2) => normalize_probs([0.9994, 0.0006, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 3) => normalize_probs([0.9985, 0.0015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 4) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 5) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 6) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 7) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 8) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 9) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 10) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 11) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 12) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 13) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 14) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 15) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 16) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 1) => normalize_probs([0.9994, 0.0006, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 2) => normalize_probs([0.9985, 0.0015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 3) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 4) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 5) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 6) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 7) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 8) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 9) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 10) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 11) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 12) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 13) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 14) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 15) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 1) => normalize_probs([0.9985, 0.0015, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 2) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 3) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 4) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 5) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 6) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 7) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 8) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 9) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 10) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 11) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 12) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 13) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 14) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 1) => normalize_probs([0.9959, 0.0041, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 2) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 3) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 4) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 5) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 6) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 7) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 8) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 9) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 10) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 11) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 12) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 13) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 1) => normalize_probs([0.989, 0.011, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 2) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 3) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 4) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 5) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 6) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 7) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 8) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 9) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 10) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 11) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 12) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 1) => normalize_probs([0.9704, 0.0293, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 2) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 3) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 4) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 5) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 6) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 7) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 8) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 9) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 10) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 11) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0]), + (14, 1) => normalize_probs([0.922, 0.0757, 0.0023, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 2) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 3) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 4) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 5) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 6) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 7) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 8) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 9) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 10) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0]), + (14, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0]), + (15, 1) => normalize_probs([0.8051805651, 0.179717903, 0.0147014921, 0.0004000398, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 2) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 3) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 4) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 5) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 6) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 7) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 8) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 9) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0]), + (15, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0]), + (15, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0]), + (16, 1) => normalize_probs([0.5703568004000001, 0.3459348789000001, 0.07720767300000002, 0.006300627800000001, 0.00020001990000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 2) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 3) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 4) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 5) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 6) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 7) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 8) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0]), + (16, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0]), + (16, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0]), + (16, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0]), + (17, 1) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 2) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 3) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 4) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 5) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 6) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 7) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0]), + (17, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0]), + (17, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0]), + (17, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0]), + (17, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0]), + (17, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001]), + (18, 1) => normalize_probs([0.054200000000000005, 0.24310000000000004, 0.40080000000000005, 0.24310000000000004, 0.054200000000000005, 0.0045000000000000005, 0.00010000000000000002, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (18, 2) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (18, 3) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (18, 4) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (18, 5) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (18, 6) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (18, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (18, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (18, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (18, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0]), + (18, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0]), + (18, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0]), + (18, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0]), + (18, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0]), + (18, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001]), + (18, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441]), + (19, 1) => normalize_probs([0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (19, 2) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (19, 3) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (19, 4) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (19, 5) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (19, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (19, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (19, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (19, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0]), + (19, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0]), + (19, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0]), + (19, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0]), + (19, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0]), + (19, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001]), + (19, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441]), + (19, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.0045, 0.0542, 0.2431, 0.4008, 0.2431, 0.0542]), + (20, 1) => normalize_probs([0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (20, 2) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (20, 3) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (20, 4) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (20, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (20, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (20, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (20, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0]), + (20, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0]), + (20, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0]), + (20, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0]), + (20, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0]), + (20, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001]), + (20, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441]), + (20, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.0045, 0.0542, 0.2431, 0.4008, 0.2431, 0.0542]), + (20, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010000999989999002, 0.004700468995299531, 0.05730568994269432, 0.2570259537429741, 0.42384192357615813, 0.2570259537429741]), + (21, 1) => normalize_probs([0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (21, 2) => normalize_probs([0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (21, 3) => normalize_probs([0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (21, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (21, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (21, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (21, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0, 0.0]), + (21, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0, 0.0]), + (21, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0, 0.0]), + (21, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0, 0.0]), + (21, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001, 0.0]), + (21, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005416, 0.242024073, 0.39894012, 0.242024073, 0.054005416, 0.004400441, 0.00010001]), + (21, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010001, 0.004400441, 0.054005417, 0.242024075, 0.399040124, 0.242024075, 0.054005417, 0.004400441]), + (21, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.0045, 0.0542, 0.2431, 0.4008, 0.2431, 0.0542]), + (21, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00010000999989999002, 0.004700468995299531, 0.05730568994269432, 0.2570259537429741, 0.42384192357615813, 0.2570259537429741]), + (21, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0002000199, 0.0063006278, 0.077207673, 0.3459348789, 0.5703568004]), +) + +# activ_ins | ins_abs ins_sens +CPT_activ_ins = Dict( + (1, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 3) => normalize_probs([0.9956, 0.0044, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 4) => normalize_probs([0.0007999199000000002, 0.9907009307000001, 0.008499149400000001, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 5) => normalize_probs([0.0, 0.0011000000000000003, 0.9944000000000001, 0.0045000000000000005, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 2) => normalize_probs([0.9956, 0.0044, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 3) => normalize_probs([0.00109989, 0.992800722, 0.006099388, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 4) => normalize_probs([0.0, 0.0008, 0.9928, 0.0064, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 5) => normalize_probs([0.0, 0.0, 0.0007, 0.9932, 0.0061, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 1) => normalize_probs([0.9956, 0.0044, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 2) => normalize_probs([0.00109989, 0.992800722, 0.006099388, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 3) => normalize_probs([0.0, 0.0011000000000000003, 0.9944000000000001, 0.0045000000000000005, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 4) => normalize_probs([0.0, 0.0, 0.0005000000000000001, 0.9910000000000001, 0.008500000000000002, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0011, 0.9927, 0.0062, 0.0, 0.0, 0.0, 0.0]), + (4, 1) => normalize_probs([0.00109989, 0.992800722, 0.006099388, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 2) => normalize_probs([0.0, 0.0011000000000000003, 0.9944000000000001, 0.0045000000000000005, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 3) => normalize_probs([0.0, 0.0, 0.0007, 0.9932, 0.0061, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0008, 0.9904, 0.0088, 0.0, 0.0, 0.0, 0.0]), + (4, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0007999199000000002, 0.9907009307000001, 0.008499149400000001, 0.0, 0.0, 0.0]), + (5, 1) => normalize_probs([0.0, 0.0016, 0.9953, 0.0031, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 2) => normalize_probs([0.0, 0.0, 0.0011, 0.9946, 0.0043, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 3) => normalize_probs([0.0, 0.0, 0.0, 0.001599839, 0.994000603, 0.004399558, 0.0, 0.0, 0.0, 0.0]), + (5, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0007999199000000002, 0.9907009307000001, 0.008499149400000001, 0.0, 0.0, 0.0]), + (5, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0011, 0.9927, 0.0062, 0.0, 0.0]), + (6, 1) => normalize_probs([0.0, 0.0, 0.0011, 0.9946, 0.0043, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 2) => normalize_probs([0.0, 0.0, 0.0, 0.001599839, 0.994000603, 0.004399558, 0.0, 0.0, 0.0, 0.0]), + (6, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00109989, 0.992800722, 0.006099388, 0.0, 0.0, 0.0]), + (6, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0008, 0.9904, 0.0088, 0.0, 0.0]), + (6, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00079992, 0.98950105, 0.00969903, 0.0]), + (7, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0022, 0.9947, 0.0031, 0.0, 0.0, 0.0, 0.0]), + (7, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0015000000000000002, 0.9942000000000001, 0.004300000000000001, 0.0, 0.0, 0.0]), + (7, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.001599839, 0.994000603, 0.004399558, 0.0, 0.0]), + (7, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00079992, 0.98950105, 0.00969903, 0.0]), + (7, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.999, 0.0]), + (8, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.002199779, 0.994700532, 0.003099689, 0.0, 0.0, 0.0]), + (8, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0022, 0.9947, 0.0031, 0.0, 0.0]), + (8, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001500151, 0.993599357, 0.004900492, 0.0]), + (8, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001, 0.999, 0.0]), + (8, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9994, 0.0006]), + (9, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.004300000000000001, 0.9942000000000001, 0.0015000000000000002, 0.0, 0.0]), + (9, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0031000000000000003, 0.9944000000000001, 0.0025000000000000005, 0.0]), + (9, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0027, 0.9973, 0.0]), + (9, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9997, 0.0003]), + (9, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.002700271, 0.050205022, 0.304430131, 0.620162266, 0.02250231]), + (10, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 9.998995920407991e-05, 0.0034996479721428023, 0.07229276942454957, 0.4841517961461517, 0.43995579649795186]), + (10, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.001900189, 0.042004184, 0.956095627]), + (10, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0016, 0.9984]), + (10, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.9999]), + (11, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0022, 0.0459, 0.9519]), + (11, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0019, 0.9981]), + (11, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.9999]), + (11, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), +) + +# renal_cl | bg +CPT_renal_cl = Dict( + (1) => normalize_probs([0.0, 1.0, 0.0]), + (2) => normalize_probs([0.0, 1.0, 0.0]), + (3) => normalize_probs([0.0, 1.0, 0.0]), + (4) => normalize_probs([0.0, 0.0, 1.0]), + (5) => normalize_probs([0.0, 0.0, 1.0]), + (6) => normalize_probs([0.0, 0.0, 1.0]), + (7) => normalize_probs([0.0, 0.0, 1.0]), + (8) => normalize_probs([0.0, 0.0, 1.0]), + (9) => normalize_probs([0.0, 0.0, 1.0]), + (10) => normalize_probs([0.0, 0.0, 1.0]), + (11) => normalize_probs([0.0, 0.0, 1.0]), +) + +# ins_indep_util | bg +CPT_ins_indep_util = Dict( + (1) => normalize_probs([1.0, 0.0, 0.0]), + (2) => normalize_probs([1.0, 0.0, 0.0]), + (3) => normalize_probs([1.0, 0.0, 0.0]), + (4) => normalize_probs([0.9997, 0.0003, 0.0]), + (5) => normalize_probs([0.9963, 0.0037, 0.0]), + (6) => normalize_probs([0.951, 0.049, 0.0]), + (7) => normalize_probs([0.5, 0.5, 0.0]), + (8) => normalize_probs([0.0796, 0.9204, 0.0]), + (9) => normalize_probs([0.0072, 0.9927, 0.0001]), + (10) => normalize_probs([0.01330131, 0.96339638, 0.02330231]), + (11) => normalize_probs([0.00039996, 0.19728001, 0.80232003]), +) + +# gut_abs | cho +CPT_gut_abs = Dict( + (1) => normalize_probs([0.5171, 0.3736, 0.0993, 0.0097, 0.0003, 0.0]), + (2) => normalize_probs([0.5166999999999999, 0.3913999999999999, 0.08629999999999999, 0.005499999999999999, 9.999999999999998e-05, 0.0]), + (3) => normalize_probs([0.5074000000000001, 0.39640000000000003, 0.09010000000000001, 0.006000000000000001, 0.00010000000000000002, 0.0]), + (4) => normalize_probs([0.4222, 0.4354, 0.1307, 0.0114, 0.0003, 0.0]), + (5) => normalize_probs([0.40310000000000007, 0.44220000000000004, 0.14120000000000002, 0.013100000000000002, 0.0004000000000000001, 0.0]), + (6) => normalize_probs([0.3714, 0.507, 0.117, 0.0046, 0.0, 0.0]), + (7) => normalize_probs([0.33453313, 0.521852204, 0.137514054, 0.006100612, 0.0, 0.0]), + (8) => normalize_probs([0.21202105940000002, 0.5392541509000001, 0.23172306490000003, 0.016801704700000003, 0.00020002010000000003, 0.0]), + (9) => normalize_probs([0.1334, 0.5062, 0.3246, 0.0352, 0.0006, 0.0]), + (10) => normalize_probs([0.07729229999999998, 0.4848519799999999, 0.3953599799999999, 0.04189579999999999, 0.0005999399999999999, 0.0]), + (11) => normalize_probs([0.0574, 0.4421, 0.4421, 0.0574, 0.001, 0.0]), + (12) => normalize_probs([0.0084, 0.2886, 0.6196, 0.0827, 0.0007, 0.0]), + (13) => normalize_probs([0.0026, 0.1655, 0.6638, 0.1655, 0.0026, 0.0]), + (14) => normalize_probs([0.0, 0.03960000000000001, 0.7194000000000002, 0.23950000000000002, 0.0015000000000000002, 0.0]), + (15) => normalize_probs([0.0, 0.0057, 0.4172, 0.5632, 0.0139, 0.0]), + (16) => normalize_probs([0.0, 0.0015, 0.2395, 0.7194, 0.0396, 0.0]), + (17) => normalize_probs([0.0, 0.0, 0.0157, 0.9386, 0.0457, 0.0]), + (18) => normalize_probs([0.0, 0.0, 0.0005, 0.5439, 0.4553, 0.0003]), + (19) => normalize_probs([0.0, 0.0, 0.0, 0.027, 0.946, 0.027]), + (20) => normalize_probs([0.0, 0.0, 0.0, 0.0004, 0.4998, 0.4998]), + (21) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), +) + +# ins_dep_util | bg activ_ins +CPT_ins_dep_util = Dict( + (1, 1) => normalize_probs([0.5883, 0.3452, 0.0645, 0.002, 0.0, 0.0, 0.0, 0.0]), + (1, 2) => normalize_probs([0.08488300000000001, 0.27684499000000007, 0.45470899000000004, 0.17866400000000002, 0.0048990200000000005, 0.0, 0.0, 0.0]), + (1, 3) => normalize_probs([0.0005, 0.0085, 0.1148, 0.5198, 0.3541, 0.0023, 0.0, 0.0]), + (1, 4) => normalize_probs([0.0, 0.0, 0.0004999499, 0.0275971959, 0.5690429146, 0.4028599396, 0.0, 0.0]), + (1, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0163, 0.981, 0.0027, 0.0]), + (1, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.1074, 0.8926, 0.0]), + (1, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.9999, 0.0]), + (1, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.971, 0.029]), + (1, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (1, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0007, 0.9993]), + (2, 1) => normalize_probs([0.453645099546355, 0.40774108959225897, 0.130813028869187, 0.007800781992199219, 0.0, 0.0, 0.0, 0.0]), + (2, 2) => normalize_probs([0.0322032203220322, 0.16081611160816112, 0.4534453245344532, 0.33293323332933233, 0.0206021102060211, 0.0, 0.0, 0.0]), + (2, 3) => normalize_probs([0.00010000000000000002, 0.0019000000000000002, 0.04360000000000001, 0.36920000000000003, 0.5737000000000001, 0.011500000000000002, 0.0, 0.0]), + (2, 4) => normalize_probs([0.0, 0.0, 9.998996720328061e-05, 0.00659933781541652, 0.3096688913385611, 0.683631780878819, 0.0, 0.0]), + (2, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.005199483, 0.975002507, 0.01979801, 0.0]), + (2, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0162, 0.9838, 0.0]), + (2, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0]), + (2, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.6287, 0.3713]), + (2, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0004, 0.9996]), + (3, 1) => normalize_probs([0.29690000000000005, 0.41770000000000007, 0.25140000000000007, 0.03370000000000001, 0.00030000000000000003, 0.0, 0.0, 0.0]), + (3, 2) => normalize_probs([0.010398999480361994, 0.07349267632757096, 0.3421658829019708, 0.4896508755321457, 0.08419157579294695, 9.998996500350143e-05, 0.0, 0.0]), + (3, 3) => normalize_probs([0.0, 0.0004, 0.0142, 0.2025, 0.7236, 0.0593, 0.0, 0.0]), + (3, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0014, 0.1267, 0.8718, 0.0001, 0.0]), + (3, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0018, 0.8344, 0.1638, 0.0]), + (3, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0027, 0.9973, 0.0]), + (3, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9998, 0.0002]), + (3, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0725, 0.9275]), + (3, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0002, 0.9998]), + (4, 1) => normalize_probs([0.15638388884361612, 0.34246575665753426, 0.3835617276164383, 0.1146889188853111, 0.0028997079971002926, 0.0, 0.0, 0.0]), + (4, 2) => normalize_probs([0.0025, 0.025, 0.1915, 0.5299, 0.2495, 0.0016, 0.0, 0.0]), + (4, 3) => normalize_probs([0.0, 0.0001, 0.0035, 0.0843, 0.6858, 0.2263, 0.0, 0.0]), + (4, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0003, 0.045, 0.9529, 0.0018, 0.0]), + (4, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0003, 0.3511, 0.6486, 0.0]), + (4, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0005, 0.9995, 0.0]), + (4, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9935, 0.0065]), + (4, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0037, 0.9963]), + (4, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (4, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.9999]), + (5, 1) => normalize_probs([0.0619, 0.2087, 0.4278, 0.2792, 0.0224, 0.0, 0.0, 0.0]), + (5, 2) => normalize_probs([0.0004, 0.0061, 0.076, 0.3999, 0.5015, 0.0161, 0.0, 0.0]), + (5, 3) => normalize_probs([0.0, 0.0, 0.0006, 0.0236, 0.4282, 0.5476, 0.0, 0.0]), + (5, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0152, 0.96, 0.0248, 0.0]), + (5, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0576, 0.9424, 0.0]), + (5, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.9999, 0.0]), + (5, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.804, 0.196]), + (5, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0002, 0.9998]), + (5, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (5, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.9999]), + (6, 1) => normalize_probs([0.0190018814, 0.089808912, 0.3156316907, 0.4472445617, 0.127512875, 0.0008000792, 0.0, 0.0]), + (6, 2) => normalize_probs([9.998996610338752e-05, 0.0013998590854473985, 0.02319769141598708, 0.20487991250586984, 0.6509346397330504, 0.11948790729354185, 0.0, 0.0]), + (6, 3) => normalize_probs([0.0, 0.0, 0.0001000099, 0.0053005267, 0.1761178908, 0.8176814931, 0.0008000795, 0.0]), + (6, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.005099493, 0.718128366, 0.276772141, 0.0]), + (6, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.009, 0.991, 0.0]), + (6, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9983, 0.0017]), + (6, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.1095, 0.8905]), + (6, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (6, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (6, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (7, 1) => normalize_probs([0.00539945899460054, 0.030596894969403102, 0.15618397484381602, 0.41455893358544105, 0.37166294062833705, 0.0215977969784022, 0.0, 0.0]), + (7, 2) => normalize_probs([0.0, 0.0003, 0.0064, 0.0754, 0.4873, 0.4305, 0.0001, 0.0]), + (7, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0016, 0.0723, 0.9004, 0.0257, 0.0]), + (7, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.001, 0.2065, 0.7925, 0.0]), + (7, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0025000000000000005, 0.9974000000000001, 0.00010000000000000002]), + (7, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.891089, 0.108911]), + (7, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0078, 0.9922]), + (7, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (7, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (7, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (8, 1) => normalize_probs([0.0012, 0.0078, 0.0539, 0.2358, 0.5274, 0.1739, 0.0, 0.0]), + (8, 2) => normalize_probs([0.0, 0.0001, 0.0014, 0.0209, 0.2369, 0.7338, 0.0069, 0.0]), + (8, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0005, 0.0251, 0.6836, 0.2908, 0.0]), + (8, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00010001, 0.040004, 0.95989599, 0.0]), + (8, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0009, 0.9888, 0.0103]), + (8, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2112, 0.7888]), + (8, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0009, 0.9991]), + (8, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (8, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (8, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (9, 1) => normalize_probs([0.0, 0.0004999501, 0.0067993217, 0.064193616, 0.3964600991, 0.5308471328, 0.0011998803, 0.0]), + (9, 2) => normalize_probs([0.0, 0.0, 0.00010000000000000002, 0.0021000000000000003, 0.06670000000000001, 0.8390000000000001, 0.09210000000000002, 0.0]), + (9, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0015, 0.168, 0.8305, 0.0]), + (9, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.003599642, 0.995000497, 0.001399861]), + (9, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 9.999e-05, 0.70732901, 0.292571]), + (9, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0067, 0.9933]), + (9, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (9, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (9, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (9, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 1) => normalize_probs([0.0, 0.0, 0.0002, 0.0046, 0.1048, 0.8475, 0.0429, 0.0]), + (10, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0037, 0.2804, 0.7159, 0.0]), + (10, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0086, 0.991, 0.0004]), + (10, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.8668, 0.1331]), + (10, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0211, 0.9789]), + (10, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0001, 0.9999]), + (10, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0005000501, 0.0283028042, 0.7100711065, 0.2611260392, 0.0]), + (11, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0002, 0.0512, 0.9486, 0.0]), + (11, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0012, 0.9918, 0.007]), + (11, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2498, 0.7502]), + (11, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0011, 0.9989]), + (11, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), +) + +# glu_prod | activ_ins bg +CPT_glu_prod = Dict( + (1, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (1, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (1, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (1, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (1, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (1, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (1, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (1, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (1, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (1, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (1, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (2, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (3, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (4, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (4, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (4, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (4, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (4, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (4, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (4, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (4, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (4, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0001, 0.9999]), + (4, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]), + (4, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]), + (5, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (5, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (5, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (5, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (5, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (5, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0001, 0.9999]), + (5, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.9997, 0.0003]), + (5, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.9999, 0.0001]), + (5, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]), + (5, 10) => normalize_probs([0.0, 0.0, 0.0, 0.1852, 0.8148, 0.0]), + (5, 11) => normalize_probs([0.0, 0.0, 0.0, 0.8393, 0.1607, 0.0]), + (6, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.5, 0.5]), + (6, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.9981, 0.0019]), + (6, 3) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (6, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0585, 0.9413, 0.0002]), + (6, 5) => normalize_probs([0.0, 0.0, 0.0004, 0.4996, 0.4996, 0.0004]), + (6, 6) => normalize_probs([0.0, 0.0, 0.012400000000000001, 0.7896000000000001, 0.19780000000000003, 0.00020000000000000004]), + (6, 7) => normalize_probs([0.0, 0.0002999397, 0.1064789063, 0.786442308, 0.1064789063, 0.0002999397]), + (6, 8) => normalize_probs([0.0, 0.0006, 0.1561, 0.7731, 0.0701, 0.0001]), + (6, 9) => normalize_probs([0.0, 0.00340034, 0.25142498, 0.67796796, 0.0670067, 0.00020002]), + (6, 10) => normalize_probs([0.00010000000000000002, 0.021200000000000004, 0.4207000000000001, 0.5181000000000001, 0.039700000000000006, 0.00020000000000000004]), + (6, 11) => normalize_probs([0.0035000000000000005, 0.09910000000000001, 0.46940000000000004, 0.37590000000000007, 0.05090000000000001, 0.0012000000000000001]), + (7, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0]), + (7, 2) => normalize_probs([0.0, 0.0, 0.0, 0.00020000000000000004, 0.9993000000000001, 0.0005000000000000001]), + (7, 3) => normalize_probs([0.0, 0.0, 0.0, 0.045, 0.9547, 0.0003]), + (7, 4) => normalize_probs([0.0, 0.0, 0.0003, 0.4553, 0.5439, 0.0005]), + (7, 5) => normalize_probs([0.0, 0.0, 0.0052, 0.7732, 0.2215, 0.0001]), + (7, 6) => normalize_probs([0.0, 0.0, 0.06390000000000001, 0.8542000000000001, 0.08180000000000001, 0.00010000000000000002]), + (7, 7) => normalize_probs([0.0, 0.0006, 0.1561, 0.7731, 0.0701, 0.0001]), + (7, 8) => normalize_probs([0.0, 0.0008, 0.1865, 0.7564, 0.0562, 0.0001]), + (7, 9) => normalize_probs([0.0, 0.005300533, 0.3045301705, 0.6406643587, 0.0494049277, 0.0001000101]), + (7, 10) => normalize_probs([0.0002, 0.0359, 0.4639, 0.4639, 0.0359, 0.0002]), + (7, 11) => normalize_probs([0.00049995011493351, 0.061993821851755455, 0.5459451163073806, 0.37186311110755116, 0.019598010585392577, 9.999003298670229e-05]), + (8, 1) => normalize_probs([0.0, 0.0007000697, 0.1708169351, 0.7655767091, 0.0628062761, 0.00010001]), + (8, 2) => normalize_probs([0.0, 0.00459954, 0.28627099, 0.65413499, 0.0547945, 0.00019998]), + (8, 3) => normalize_probs([0.0001, 0.0293, 0.4706, 0.4706, 0.0293, 0.0001]), + (8, 4) => normalize_probs([0.001, 0.0864, 0.5892, 0.3107, 0.0127, 0.0]), + (8, 5) => normalize_probs([0.007300727, 0.197219909, 0.590958728, 0.197219909, 0.007300727, 0.0]), + (8, 6) => normalize_probs([0.035003532000000004, 0.3228322940000001, 0.5035504580000001, 0.13271312100000002, 0.005900595000000001, 0.0]), + (8, 7) => normalize_probs([0.06350000000000001, 0.36840000000000006, 0.44780000000000003, 0.11410000000000001, 0.006100000000000001, 0.00010000000000000002]), + (8, 8) => normalize_probs([0.07199277575530595, 0.3862608772260587, 0.4342568743962147, 0.10228999396898196, 0.005099488699334146, 9.99899541045923e-05]), + (8, 9) => normalize_probs([0.110378, 0.41101799, 0.38352299, 0.0896821, 0.00529894, 9.998e-05]), + (8, 10) => normalize_probs([0.1724, 0.4353, 0.3197, 0.0683, 0.0042, 0.0001]), + (8, 11) => normalize_probs([0.2161218574, 0.4320427149, 0.2851288118, 0.062106159, 0.004500447, 0.0001000099]), + (9, 1) => normalize_probs([0.0, 0.0177, 0.4823, 0.4823, 0.0177, 0.0]), + (9, 2) => normalize_probs([0.0003, 0.0482, 0.5476, 0.3869, 0.017, 0.0]), + (9, 3) => normalize_probs([0.001, 0.0864, 0.5892, 0.3107, 0.0127, 0.0]), + (9, 4) => normalize_probs([0.002900289, 0.137213966, 0.602359849, 0.247924938, 0.009600958, 0.0]), + (9, 5) => normalize_probs([0.012498808, 0.255074158, 0.58084236, 0.147385091, 0.004199583, 0.0]), + (9, 6) => normalize_probs([0.0299, 0.3458, 0.5201, 0.1016, 0.0026, 0.0]), + (9, 7) => normalize_probs([0.054700000000000006, 0.38680000000000003, 0.4620000000000001, 0.09330000000000001, 0.0032000000000000006, 0.0]), + (9, 8) => normalize_probs([0.0863, 0.4118, 0.4118, 0.0863, 0.0038, 0.0]), + (9, 9) => normalize_probs([0.1405, 0.4263, 0.3504, 0.078, 0.0047, 0.0001]), + (9, 10) => normalize_probs([0.21269999999999994, 0.4415999999999999, 0.28489999999999993, 0.057099999999999984, 0.003599999999999999, 9.999999999999998e-05]), + (9, 11) => normalize_probs([0.2570259537429741, 0.42384192357615813, 0.2570259537429741, 0.05730568994269432, 0.004700468995299531, 0.00010000999989999002]), + (10, 1) => normalize_probs([0.12240000000000002, 0.37070000000000003, 0.37070000000000003, 0.12240000000000002, 0.013300000000000003, 0.0005000000000000001]), + (10, 2) => normalize_probs([0.1478149157, 0.3728367875, 0.3458348029, 0.1180119327, 0.0148014916, 0.0007000696]), + (10, 3) => normalize_probs([0.159, 0.3814, 0.3366, 0.1093, 0.0131, 0.0006]), + (10, 4) => normalize_probs([0.1952, 0.3853, 0.3072, 0.0988, 0.0128, 0.0007]), + (10, 5) => normalize_probs([0.2478249356, 0.3904388985, 0.26922693, 0.0812080789, 0.0107010972, 0.0006000598]), + (10, 6) => normalize_probs([0.28580000000000005, 0.39200000000000007, 0.24400000000000002, 0.06890000000000002, 0.008800000000000002, 0.0005000000000000001]), + (10, 7) => normalize_probs([0.305, 0.3943, 0.2313, 0.0616, 0.0074, 0.0004]), + (10, 8) => normalize_probs([0.3353, 0.3901, 0.213, 0.0546, 0.0066, 0.0004]), + (10, 9) => normalize_probs([0.37266283600000005, 0.3791618332000001, 0.19268091520000002, 0.04889507850000001, 0.006199377300000001, 0.0003999598000000001]), + (10, 10) => normalize_probs([0.43905603, 0.36236403, 0.15768401, 0.0361964, 0.00439956, 0.00029997]), + (10, 11) => normalize_probs([0.46720000000000006, 0.35590000000000005, 0.14300000000000002, 0.030300000000000004, 0.0034000000000000002, 0.00020000000000000004]), +) + +# ins_indep | renal_cl ins_indep_util +CPT_ins_indep = Dict( + (1, 1) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0]), + (1, 2) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (1, 3) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (2, 1) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (2, 2) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (2, 3) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (3, 1) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (3, 2) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (3, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0003, 0.9997]), +) + +# cho_bal | cho gut_abs +CPT_cho_bal = Dict( + (1, 1) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 5) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 6) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 1) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 2) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 5) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 6) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 1) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 2) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 3) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 5) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 6) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 1) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 2) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 3) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 4) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 5) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 6) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 1) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 2) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 3) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 4) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 5) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 6) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 2) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 3) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 4) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 5) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 6) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 3) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 4) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 5) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 6) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 4) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 5) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 6) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 5) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 6) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 6) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (11, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (12, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (12, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (13, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (13, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (13, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (13, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (14, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (14, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (14, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (14, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (14, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (15, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (15, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (15, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (15, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (15, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (15, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (16, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (16, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (16, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (16, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (16, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (16, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (17, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (17, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (17, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (17, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (17, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (17, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (18, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (18, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (18, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (18, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (18, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (18, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (19, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (19, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (19, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (19, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (19, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (19, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (20, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (20, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (20, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (20, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (20, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (20, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (21, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (21, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (21, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (21, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (21, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (21, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), +) + +# ins_dep | ins_dep_util glu_prod +CPT_ins_dep = Dict( + (1, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (1, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (1, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (1, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (1, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (1, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (2, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (2, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (2, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (2, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (2, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (3, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (3, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (3, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (3, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (4, 1) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (4, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (4, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (5, 1) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 2) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (5, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (6, 1) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 2) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 3) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (7, 1) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 2) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 3) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 4) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 1) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 2) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 3) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 4) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 5) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), +) + +# endo_bal | ins_indep ins_dep +CPT_endo_bal = Dict( + (1, 1) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (1, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (1, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (1, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (1, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (1, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (2, 1) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 2) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (2, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (2, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (2, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (2, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (3, 1) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 2) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 3) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (3, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (3, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (3, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (4, 1) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 2) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 3) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 4) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (4, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (4, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (5, 1) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 2) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 3) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 4) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 5) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (5, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), +) + +# basal_bal | gut_abs endo_bal +CPT_basal_bal = Dict( + (1, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 4) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 5) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 6) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 7) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 8) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 17) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (2, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 3) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 4) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 5) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 6) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 7) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (2, 17) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (3, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 2) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 3) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 4) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 5) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 6) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (3, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (3, 17) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (4, 1) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 2) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 3) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 4) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 5) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (4, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (4, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (4, 17) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (5, 1) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 2) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 3) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 4) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (5, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (5, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (5, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (5, 17) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (6, 1) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 2) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 3) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (6, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (6, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (6, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (6, 16) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (6, 17) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), +) + +# tot_bal | basal_bal met_irr +CPT_tot_bal = Dict( + (1, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 4) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 5) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 6) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 7) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 3) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 4) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 5) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 6) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 7) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 2) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 3) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 4) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 5) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 6) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 1) => normalize_probs([0.9997, 0.0003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 2) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 3) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 4) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 5) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 1) => normalize_probs([0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 2) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 3) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 4) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 1) => normalize_probs([0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 2) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 3) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 1) => normalize_probs([0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 2) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (8, 1) => normalize_probs([0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (8, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (9, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (9, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (9, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (10, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (10, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (10, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (10, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (11, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (11, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (11, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (11, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (11, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (12, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0, 0.0]), + (12, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (12, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (12, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (12, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (12, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (12, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (13, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0, 0.0]), + (13, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (13, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (13, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (13, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (13, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (13, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (14, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0, 0.0]), + (14, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (14, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (14, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (14, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (14, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (14, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (15, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0, 0.0]), + (15, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (15, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (15, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (15, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (15, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (15, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (16, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003, 0.0]), + (16, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (16, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (16, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (16, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (16, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (16, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (17, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.00030003, 0.99939994, 0.00030003]), + (17, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (17, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (17, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (17, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (17, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (17, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (18, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0003, 0.9997]), + (18, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (18, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (18, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (18, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (18, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (18, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (19, 1) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (19, 2) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (19, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (19, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (19, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (19, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (19, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), +) + +# bg | bg tot_bal +CPT_bg = Dict( + (1, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 5) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 6) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 7) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 8) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 9) => normalize_probs([0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 10) => normalize_probs([0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 11) => normalize_probs([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (1, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]), + (1, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]), + (2, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 5) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 6) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 7) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 8) => normalize_probs([0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 9) => normalize_probs([0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 10) => normalize_probs([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (2, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]), + (2, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]), + (2, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]), + (3, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 5) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 6) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 7) => normalize_probs([0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 8) => normalize_probs([0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 9) => normalize_probs([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (3, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]), + (3, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]), + (3, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]), + (3, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9804, 0.0196]), + (4, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 5) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 6) => normalize_probs([0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 7) => normalize_probs([0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 8) => normalize_probs([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (4, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]), + (4, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]), + (4, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]), + (4, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9804, 0.0196]), + (4, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (5, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 4) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 5) => normalize_probs([0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 6) => normalize_probs([0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 7) => normalize_probs([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (5, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]), + (5, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]), + (5, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]), + (5, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9804, 0.0196]), + (5, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (5, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (6, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 3) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 4) => normalize_probs([0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 5) => normalize_probs([0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 6) => normalize_probs([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (6, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]), + (6, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]), + (6, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]), + (6, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9804, 0.0196]), + (6, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (6, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (6, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (7, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 2) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 3) => normalize_probs([0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 4) => normalize_probs([0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 5) => normalize_probs([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (7, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]), + (7, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]), + (7, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]), + (7, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9804, 0.0196]), + (7, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (7, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (7, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (7, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (8, 1) => normalize_probs([1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 2) => normalize_probs([0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 3) => normalize_probs([0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 4) => normalize_probs([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (8, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]), + (8, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]), + (8, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]), + (8, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9804, 0.0196]), + (8, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (8, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (8, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (8, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (8, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (9, 1) => normalize_probs([0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 2) => normalize_probs([0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 3) => normalize_probs([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (9, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]), + (9, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]), + (9, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]), + (9, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9804, 0.0196]), + (9, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (9, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (9, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (9, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (9, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (9, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 1) => normalize_probs([0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 2) => normalize_probs([0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (10, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0]), + (10, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]), + (10, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0]), + (10, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.9804, 0.0196]), + (10, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (10, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 1) => normalize_probs([0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 2) => normalize_probs([0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 3) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0, 0.0]), + (11, 4) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0, 0.0]), + (11, 5) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0]), + (11, 6) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0]), + (11, 7) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.5714, 0.4286, 0.0]), + (11, 8) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.043, 0.957]), + (11, 9) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 10) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 11) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 12) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 13) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 14) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), + (11, 15) => normalize_probs([0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0]), +) diff --git a/examples/3-diabetes/diabetes_entropy_estimators.jl b/examples/3-diabetes/diabetes_entropy_estimators.jl new file mode 100644 index 0000000..6efcb9a --- /dev/null +++ b/examples/3-diabetes/diabetes_entropy_estimators.jl @@ -0,0 +1,133 @@ +import Gen + +using Statistics: mean + +using Gen: + assess, + complement, + project, + generate, + GenerativeFunction, + get_choices, + get_score, + get_selected, + Selection, + simulate + +function logmeanexp(arr::AbstractArray{T}) where {T <: Real} + return Gen.logsumexp(arr) - log(length(arr)) +end + +# Implementation of entropy estimators for including +# background constraints that are always included in the +# forward simulation and model. It is essential that these +# constraints are root choices, such that their weights are +# the same for any execution of generate. +# +# It is especially needed for upper bounds, since we have to +# generate an exact sample of (latents, targets) from the +# joint model distribution. Consider +# latent -> constraint -> target +# In this case, sampling latent from the prior and constraining +# constraint and target no longer maintains the property that +# the joint sample gives us a posterior sample from distribution +# latent | (constraint, target) + +"""Entropy lower bound using default proposal.""" +function entropy_lower_bound( + model::GenerativeFunction, + model_args::Tuple, + targets::Selection, + constraints::Gen.ChoiceMap, + N::Integer, + M::Integer, + K::Integer, + model_traces::Vector{Gen.Trace}=Gen.Trace[]; + return_weights::Bool=false) + # Verify offset is constant. + log_w_offset = generate(model, model_args, constraints)[2] + @assert log_w_offset == generate(model, model_args, constraints)[2] + # Run estimator. + wi_list = [] + for i=1:N + # Sample observations from model. + tr_p = model_traces[i] + observations = get_selected(get_choices(tr_p), targets) + observations_and_constraints = merge(observations, constraints) + wj_list = [] + for j=1:M + wk_list::Vector{Float64} = [] + for k=1:K + # Sample latents (particle k) from default proposal + # and retrieve weight w_k, + # which is p(observations | latents) + tr_q, log_w = generate(model, model_args, observations_and_constraints) + push!(wk_list, log_w - log_w_offset) + end + # Compute overall log importance weight, + # which is log [1/K sum w_k] + wk_avg = logmeanexp(wk_list) + !isinf(wk_avg) || throw("Invalid proposal (infinite log weight)") + push!(wj_list, wk_avg) + end + wj_avg = mean(wj_list) + push!(wi_list, wj_avg) + end + return return_weights ? wi_list : mean(wi_list) +end + +"""Entropy upper bound using default proposal.""" +function entropy_upper_bound( + model::GenerativeFunction, + model_args::Tuple, + targets::Selection, + constraints::Gen.ChoiceMap, + N::Integer, + M::Integer, + K::Integer, + model_traces::Vector{Gen.Trace}=Gen.Trace[]; + return_weights::Bool=false) + @assert(M == 1) + # Verify offset is constant + log_w_offset = generate(model, model_args, constraints)[2] + @assert log_w_offset == generate(model, model_args, constraints)[2] + # Run estimator + wi_list = [] + for i=1:N + # Sample latents + observations from model. + tr_p = model_traces[i] + observations = get_selected(get_choices(tr_p), targets) + observations_and_constraints = merge(observations, constraints) + wj_list = [] + for j=1:M + tr_pk = tr_p + wk_list::Vector{Float64} = [] + # Retrieve weight of exact posterior sample (particle 1) + # using default proposal, which is + # p(observations | latents) + log_w = Gen.project(tr_pk, targets) + push!(wk_list, log_w) + for k=2:K + # Sample latents (particle k) from default proposal + # and retrieve weight w_k, + # which is p(observations | latents) + tr_pk, log_w = generate(model, model_args, observations_and_constraints) + push!(wk_list, log_w - log_w_offset) + end + # Compute overall log importance weight, which is + # log [1 / (1/K sum w_k)] + # = - log [1/K sum w_k] + wk_avg = -logmeanexp(wk_list) + @assert !isinf(wk_avg) + push!(wj_list, wk_avg) + # TODO: MCMC step iterating the latents in tr_p + # if j < M + # tr_p = metropolis_hastings(tr_p, complement(targets); + # check=true, observations=observations) + # end + end + wj_avg = -mean(wj_list) + push!(wi_list, wj_avg) + end + return return_weights ? wi_list : mean(wi_list) +end diff --git a/examples/3-diabetes/diabetes_sir.jl b/examples/3-diabetes/diabetes_sir.jl new file mode 100644 index 0000000..ffcbcb8 --- /dev/null +++ b/examples/3-diabetes/diabetes_sir.jl @@ -0,0 +1,55 @@ +include("diabetes_ts.jl") +include("diabetes_entropy_estimators.jl") + +import Gen +import Random + +using Combinatorics: combinations + +Random.seed!(1) + +n = 24 +model_args = (n,) +trace = Gen.simulate(model, model_args) + +meal_lookup = [100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 0] +meal_values = [0, 30, 0, 30, 0, 0, 50, 0, 20, 0, 0, 0, 50, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] +meal_evidence = [((:meal => i), findall(x -> x==v, meal_lookup)[1]) for (i, v) in enumerate(meal_values)] + +ins_abs_lookup = [100_0, 70_7, 50_0, 35_5, 25_0, 17_7, 12_5, 8_9, 6_4, 3_2, 1_6] +ins_abs_values = [1_6, 1_6, 3_2, 3_2, 6_4, 6_4, 6_4, 6_4, 6_4, 3_2, 3_2, 3_2, 3_2, 3_2, 3_2, 6_4, 6_4, 6_4, 6_4, 3_2, 3_2, 3_2, 3_2, 3_2] +ins_abs_evidence = [((:ins_abs => i), findall(x -> x==v, ins_abs_lookup)[1]) for (i, v) in enumerate(ins_abs_values)] + +evidence = Gen.choicemap(vcat(meal_evidence, ins_abs_evidence)...) + +N = 1000 +K = 100 + +# Model traces must be generated with background evidence. +model_traces = Gen.Trace[generate(model, model_args, evidence)[1] for i=1:N] +log_w_baseline = generate(model, model_args, evidence)[2] + +x = [:ins_sens] + +indexes = collect(combinations(1:n, 2)) +selections = [collect(:bg => i for i in x) for x in indexes] +y = selections[1] + +Threads.@threads for y in selections[1:5] + println("Analyzing $(y)") + sel_xy = Gen.select(vcat(x, y)...) + sel_y = Gen.select(y...) + # H(X,Y) bounds + H_xy_lo = entropy_lower_bound(model, model_args, sel_xy, evidence, N, 1, K, model_traces) + H_xy_hi = entropy_upper_bound(model, model_args, sel_xy, evidence, N, 1, K, model_traces) + H_xy_approx = mean([H_xy_lo, H_xy_hi]) + # H(Y) bounds + H_y_lo = entropy_lower_bound(model, model_args, sel_y, evidence, N, 1, K, model_traces) + H_y_hi = entropy_upper_bound(model, model_args, sel_y, evidence, N, 1, K, model_traces) + H_y_approx = mean([H_y_lo, H_y_hi]) + # H(X|Y) bounds + CH_lo = H_y_lo - H_xy_hi + CH_hi = H_y_hi - H_xy_lo + # Report + println((y, CH_lo, CH_hi)) +end diff --git a/examples/3-diabetes/diabetes_smc.jl b/examples/3-diabetes/diabetes_smc.jl new file mode 100644 index 0000000..370a690 --- /dev/null +++ b/examples/3-diabetes/diabetes_smc.jl @@ -0,0 +1,354 @@ +using Combinatorics: combinations + +import Gen +import Random + +include("diabetes_ts.jl") +include("diabetes_entropy_estimators.jl") +include("csmc.jl") + +Random.seed!(1) + +# ============================================================================== +# PREAMBLE +# ============================================================================== + +N_model = 25 +model_args = (N_model,) +trace = Gen.simulate(model, model_args) + +lookup_meal = [100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, 45, 40, 35, 30, 25, 20, 15, 10, 5, 0] +lookup_ins_abs = [100_0, 70_7, 50_0, 35_5, 25_0, 17_7, 12_5, 8_9, 6_4, 3_2, 1_6] + +evidence_scenarios_meal = Dict( + 0 => [0, 30, 0, 30, 0, 0, 50, 0, 20, 0, 0, 0, 50, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + 1 => [0, 0, 0, 100, 0, 0, 0, 0, 20, 0, 50, 0, 50, 0, 30, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0], +) + +evidence_scenarios_ins_abs = Dict( + 0 => [1_6, 1_6, 3_2, 3_2, 6_4, 6_4, 6_4, 6_4, 6_4, 3_2, 3_2, 3_2, 3_2, 3_2, 3_2, 6_4, 6_4, 6_4, 6_4, 3_2, 3_2, 3_2, 3_2, 3_2], + 1 => [6_4, 6_4, 6_4, 6_4, 6_4, 6_4, 6_4, 6_4, 6_4, 3_2, 3_2, 3_2, 3_2, 3_2, 3_2, 6_4, 6_4, 6_4, 6_4, 3_2, 3_2, 3_2, 3_2, 3_2], + 2 => [70_7, 50_0, 50_0, 50_0, 35_5, 35_5, 35_5, 6_4, 6_4, 3_2, 25_0, 25_0, 25_0, 25_0, 25_0, 6_4, 6_4, 6_4, 6_4, 6_4, 6_4, 6_4, 6_4, 6_4], +) + +function make_evidence(addr, values, lookup) + return [((addr => i), findall(x -> x==v, lookup)[1]) for (i, v) in enumerate(values)] +end + +# Selected evidence scenario. +idx_meal = 0 +idx_ins_abs = 0 + +scenario_meal = evidence_scenarios_meal[idx_meal] +scenario_ins_abs = evidence_scenarios_ins_abs[idx_ins_abs] + +# Build evidence. +k_meal = min(N_model, length(scenario_meal)) +k_ins_abs = min(N_model, length(scenario_ins_abs)) +evidence_meal_all = make_evidence(:meal, scenario_meal[1:k_meal], lookup_meal) +evidence_ins_abs_all = make_evidence(:ins_abs, scenario_ins_abs[1:k_ins_abs], lookup_ins_abs) +evidence_all = Gen.choicemap(vcat(evidence_meal_all, evidence_ins_abs_all)...) + +# Weight offsets from intervention variables for times 1:N_model +log_weight_intervention = generate(model, model_args, evidence_all)[2] +@assert log_weight_intervention == generate(model, model_args, evidence_all)[2] + +log_weights_intervention = Vector{Float64}(undef, N_model) +for i=1:N_model + x = generate(model, (i,), evidence_all)[2] + @assert x == generate(model, (i,), evidence_all)[2] + log_weights_intervention[i] = x +end +@assert log_weights_intervention[end] == log_weight_intervention + +# Query traces. +N_samples_Y = 1000 +model_traces = Gen.Trace[generate(model, model_args, evidence_all)[1] for i=1:N_samples_Y] + +# Quick assertion on offsets. +for j=1:N_model + j_meal = min(j, length(evidence_meal_all)) + j_ins_abs = min(j, length(evidence_ins_abs_all)) + addr_meal_j = [t[1] for t in evidence_meal_all[1:j_meal]] + addr_ins_abs_j = [t[1] for t in evidence_ins_abs_all[1:j_ins_abs]] + selection = Gen.select(addr_meal_j..., addr_ins_abs_j...) + for i=1:5 + x = Gen.project(model_traces[i], selection) + @assert isapprox(x, log_weights_intervention[j]) + end +end + +# ============================================================================== +# (CONDITIONAL) SEQUENTIAL MONTE CARLO +# ============================================================================== + +function make_evidence_cell(addr, i, value, lookup) + value_i = findall(x -> x==value, lookup)[1] + return (addr => i, value_i) +end + +# Initial constraints. +function get_constraints_initial_smc( + observation::Gen.ChoiceMap, + ins_sens::Bool, + bg_addrs::Vector{Pair{Symbol,Int64}}) + # Prepare the constraints. + constraints = [] + if ins_sens + c_ins_sens = (:ins_sens, observation[:ins_sens]) + push!(constraints, c_ins_sens) + end + if bg_addrs[1][end] == 1 + c_bg = (bg_addrs[1], observation[bg_addrs[1]]) + push!(constraints, c_bg) + end + c_meal_value = scenario_meal[1] + c_meal = make_evidence_cell(:meal, 1, c_meal_value, lookup_meal) + push!(constraints, c_meal) + c_ins_abs_value = scenario_ins_abs[1] + c_ins_abs = make_evidence_cell(:ins_abs, 1, c_ins_abs_value, lookup_ins_abs) + push!(constraints, c_ins_abs) + # Return constraints as Gen.ChoiceMap + return Gen.choicemap(constraints...) +end + +function get_constraints_t_smc( + t::Integer, + observation::Gen.ChoiceMap, + bg_addrs::Vector{Pair{Symbol,Int64}}) + @assert 1 < t + # Obtain meal and insulin interventions at t. + constraints = [] + if t == bg_addrs[1][end] + c_bg_1 = (bg_addrs[1], observation[bg_addrs[1]]) + push!(constraints, c_bg_1) + end + if t == bg_addrs[2][end] + c_bg_2 = (bg_addrs[2], observation[bg_addrs[2]]) + push!(constraints, c_bg_2) + end + if t <= length(scenario_meal) + c_meal_value = scenario_meal[t] + c_meal = make_evidence_cell(:meal, t, c_meal_value, lookup_meal) + push!(constraints, c_meal) + end + if t <= length(scenario_ins_abs) + c_ins_abs_value = scenario_ins_abs[t] + c_ins_abs = make_evidence_cell(:ins_abs, t, c_ins_abs_value, lookup_ins_abs) + push!(constraints, c_ins_abs) + end + # Return constraints as Gen.ChoiceMap + return Gen.choicemap(constraints...) +end + +function run_smc( + N_model::Integer, + observation::Gen.ChoiceMap, + ins_sens::Bool, + bg_addrs::Vector{Pair{Symbol,Int64}}, + N_particles::Integer, + seed::Integer; + star_traces::Vector{Gen.Trace}=Gen.Trace[], + star_log_weights::Vector{Float64}=Float64[]) + # Which times is BG being queried? + t1 = bg_addrs[1][end] + t2 = bg_addrs[2][end] + @assert 1 <= t1 < t2 <= N_model + # Verify star traces. + @assert length(star_traces) == length(star_log_weights) + @assert length(star_traces) in [0, t2, N_model] + csmc = length(star_traces) > 1 + # Fix the seed. + Random.seed!(seed) + # Initialize the PF. + evidence_init = get_constraints_initial_smc(observation, ins_sens, bg_addrs) + state = Gen.initialize_particle_filter(model, (1,), evidence_init, N_particles) + # Run through 2:t2 + # No need to run up to N_model + for t=2:t2 + new_args = (t,) + if !csmc + Gen.maybe_resample!(state) + else + maybe_resample!( + state, + star_traces[t-1], + star_log_weights[t-1]) + end + evidence_t = get_constraints_t_smc(t, observation, bg_addrs) + # Run the PF step. + argdiffs = (Gen.UnknownChange(),) + log_inc_w, = Gen.particle_filter_step!(state, new_args, argdiffs, evidence_t) + @assert length(log_inc_w) == N_particles + end + # Compute ML estimate. + if !csmc + log_ml_est = Gen.log_ml_estimate(state) + else + log_ml_est = log_ml_estimate(state, star_log_weights[t2]) + end + # Offset the ML estimate by the intervention weight. + log_ml_est_offset = log_ml_est - log_weights_intervention[t2] + return (state, log_ml_est_offset) +end + +# ============================================================================== +# ENTROPY LOWER BOUND +# ============================================================================== + +function compute_entropies_lower_bound( + N_model::Integer, + ins_sens::Bool, + bg_addrs::Vector{Pair{Symbol,Int64}}, + N_particles::Integer, + N_samples_Y::Integer, + M_samples_Y::Integer) + wi_list::Vector{Float64} = Vector{Float64}(undef, N_samples_Y) + Threads.@threads for i=1:N_samples_Y + # Extract the observation. + sel_xy = Gen.select(:ins_sens, bg_addrs...) + observation = Gen.get_selected(get_choices(model_traces[i]), sel_xy) + wj_list::Vector{Float64} = [] + for j=1:M_samples_Y + seed = max(i, j)^2 + max(j, 2*j-i) + state, log_ml_est = run_smc( + N_model, + observation, + ins_sens, + bg_addrs, + N_particles, + seed) + push!(wj_list, log_ml_est) + end + wj_avg = mean(wj_list) + wi_list[i] = wj_avg + end + return -mean(wi_list) +end + +# ============================================================================== +# ENTROPY UPPER BOUND +# ============================================================================== + +function get_star_trajectory( + N_model::Integer, + ins_sens::Bool, + bg_addrs::Vector{Pair{Symbol,Int64}}, + star_trace::Gen.Trace + ) + # Which times is BG being queried? + t1 = bg_addrs[1][end] + t2 = bg_addrs[2][end] + @assert 1 <= t1 < t2 <= N_model + # Extract star trajectories for star trace. + star_choices = Gen.get_choices(star_trace) + star_traces::Vector{Gen.Trace} = [] + star_log_weights::Vector{Float64} = [] + # Compute selections in star trace from 1:t2 + for j=1:t2 + star_selections::Vector{Any} = [] + # Global insulin sensitivity. + if ins_sens + push!(star_selections, :ins_sens) + end + # Meal interventions from 1:j + j_meal = min(j, length(evidence_meal_all)) + addr_meal_j = [t[1] for t in evidence_meal_all[1:j_meal]] + append!(star_selections, addr_meal_j) + # Insulin interventions from 1:j + j_ins_abs = min(j, length(evidence_ins_abs_all)) + addr_ins_abs_j = [t[1] for t in evidence_ins_abs_all[1:j_ins_abs]] + append!(star_selections, addr_ins_abs_j) + # Query variables. + if bg_addrs[1][end] <= j + push!(star_selections, bg_addrs[1]) + end + if bg_addrs[2][end] <= j + push!(star_selections, bg_addrs[2]) + end + # Compute star trace observation weight from 1:j. + log_weight_j = Gen.project(star_trace, Gen.select(star_selections...)) + push!(star_log_weights, log_weight_j) + # Create a prefix star trace from 1:j + trace_j, = Gen.generate(model, (j,), star_choices) + push!(star_traces, trace_j) + # Confirm weights from project and generate agree. + log_weight_check = Gen.project(trace_j, Gen.select(star_selections...)) + @assert isapprox(log_weight_j, log_weight_check) + end + # Return the star trajectory and log weights. + return (star_traces, star_log_weights) +end + +function compute_entropies_upper_bound( + N_model::Integer, + ins_sens::Bool, + bg_addrs::Vector{Pair{Symbol,Int64}}, + N_particles::Integer, + N_samples_Y::Integer, + M_samples_Y::Integer) + wi_list::Vector{Float64} = Vector{Float64}(undef, N_samples_Y) + Threads.@threads for i=1:N_samples_Y + # Extract the observation and star trajectory. + star_trace = model_traces[i] + sel_xy = Gen.select(:ins_sens, bg_addrs...) + observation = Gen.get_selected(get_choices(star_trace), sel_xy) + star_traces, star_log_weights = + get_star_trajectory(N_model, ins_sens, bg_addrs, star_trace) + # Run CSMC. + wj_list::Vector{Float64} = [] + for j=1:M_samples_Y + seed = max(i, j)^2 + max(j, 2*j-i) + state, log_ml_est = + run_smc( + N_model, + observation, + ins_sens, + bg_addrs, + N_particles, + seed; + star_traces=star_traces, + star_log_weights=star_log_weights) + push!(wj_list, log_ml_est) + end + wj_avg = mean(wj_list) + wi_list[i] = wj_avg + end + return -mean(wi_list) +end + +# ============================================================================== +# EXPERIMENT RUNNER +# ============================================================================== + +# Query address pairs. +bg_all_pairs = [collect(:bg => i for i in x) for x in combinations(1:N_model, 2)] + +bg_addrs = bg_all_pairs[end] +ins_sens = true +N_particles = 100 +N_samples_Y = 100 +M_samples_Y = 1 + +# The naming is reversed, as the lower bound is computed +# on log[p(Y)] not -log[p(Y)], so entropy_lower_bound +# actually gives the upper bound, and entropy_upper_bound +# gives the lower bound. +for bg_addrs in bg_all_pairs + H_hi = compute_entropies_lower_bound( + N_model, + ins_sens, + bg_addrs, + N_particles, + N_samples_Y, + M_samples_Y) + H_lo = compute_entropies_upper_bound( + N_model, + ins_sens, + bg_addrs, + N_particles, + N_samples_Y, + M_samples_Y) + line = "bg_$(bg_addrs[1][end]),bg_$(bg_addrs[2][end]),$(H_lo),$(H_hi)" + println(line) +end diff --git a/examples/3-diabetes/diabetes_ts.jl b/examples/3-diabetes/diabetes_ts.jl new file mode 100644 index 0000000..407c593 --- /dev/null +++ b/examples/3-diabetes/diabetes_ts.jl @@ -0,0 +1,110 @@ +using Gen: + @gen, + @trace, + categorical + +include("diabetes_cpds.jl") + +@gen function model(n::Integer) + meal::Vector{Int} = Vector{Int}(undef, n) + cho::Vector{Int} = Vector{Int}(undef, n) + bg::Vector{Int} = Vector{Int}(undef, n) + activ_ins::Vector{Int} = Vector{Int}(undef, n) + ins_abs::Vector{Int} = Vector{Int}(undef, n) + gut_abs::Vector{Int} = Vector{Int}(undef, n) + renal_cl::Vector{Int} = Vector{Int}(undef, n) + ins_indep_util::Vector{Int} = Vector{Int}(undef, n) + ins_dep_util::Vector{Int} = Vector{Int}(undef, n) + glu_prod::Vector{Int} = Vector{Int}(undef, n) + ins_indep::Vector{Int} = Vector{Int}(undef, n) + ins_dep::Vector{Int} = Vector{Int}(undef, n) + endo_bal::Vector{Int} = Vector{Int}(undef, n) + cho_bal::Vector{Int} = Vector{Int}(undef, n) + basal_bal::Vector{Int} = Vector{Int}(undef, n) + met_irr::Vector{Int} = Vector{Int}(undef, n) + tot_bal::Vector{Int} = Vector{Int}(undef, n) + + # global: cho_init + p_cho_init = [.01, .01, .01, .01, .01, .01, .01, .01, .01, .01, .01, .01, .01, .01, .01, .85] + cho_init = @trace(categorical(p_cho_init), :cho_init) + + # global: ins_sens + p_ins_sens = [.2, .2, .2, .2, .2] + ins_sens = @trace(categorical(p_ins_sens), :ins_sens) + + for i=1:n + + # meal + p_meal = [.01, .01, .01, .01, .01, .01, .01, .01, .01, .01,.01, .01, .01, .01, .01, .01, .01, .01, .01, .01, .8] + meal[i] = @trace(categorical(p_meal), :meal => i) + + # cho + cho_parent = i == 1 ? cho_init : cho_bal[i-1] + p_cho = CPT_cho[(meal[i], cho_parent)] + cho[i] = @trace(categorical(p_cho), :cho => i) + + # gut_abs + p_gut_abs = CPT_gut_abs[cho[i]] + gut_abs[i] = @trace(categorical(p_gut_abs), :gut_abs => i) + + # cho_bal + p_cho_bal = CPT_cho_bal[(cho[i], gut_abs[i])] + cho_bal[i] = @trace(categorical(p_cho_bal), :cho_bal => i) + + # bg + if i == 1 + p_bg = [.01, .01, .02, .07, .15, .3, .2, .15, .07, .01, .01] + else + p_bg = CPT_bg[(bg[i-1], tot_bal[i-1])] + end + bg[i] = @trace(categorical(p_bg), :bg => i) + + # ins_abs + p_ins_abs = [.03, .04, .04, .04, .1, .15, .2, .2, .1, .06, .04] + ins_abs[i] = @trace(categorical(p_ins_abs), :ins_abs => i) + + # activ_ins + p_activ_ins = CPT_activ_ins[(ins_abs[i], ins_sens)] + activ_ins[i] = @trace(categorical(p_activ_ins), :active_ins => i) + + # renal_cl + p_renal_cl = CPT_renal_cl[bg[i]] + renal_cl[i] = @trace(categorical(p_renal_cl), :renal_cl => i) + + # ins_indep_util + p_ins_indep_util = CPT_ins_indep_util[bg[i]] + ins_indep_util[i] = @trace(categorical(p_ins_indep_util), :ins_indep_util => i) + + # ins_dep_util + p_ins_dep_util = CPT_ins_dep_util[(bg[i], activ_ins[i])] + ins_dep_util[i] = @trace(categorical(p_ins_dep_util), :ins_dep_util => i) + + # glu_prod + p_glu_prod = CPT_glu_prod[(activ_ins[i], bg[i])] + glu_prod[i] = @trace(categorical(p_glu_prod), :glu_prod => i) + + # ins_indep + p_ins_indep = CPT_ins_indep[(renal_cl[i], ins_indep_util[i])] + ins_indep[i] = @trace(categorical(p_ins_indep), :ins_indep => i) + + # ins_dep + p_ins_dep = CPT_ins_dep[(ins_dep_util[i], glu_prod[i])] + ins_dep[i] = @trace(categorical(p_ins_dep), :ins_dep => i) + + # endo_bal + p_endo_bal = CPT_endo_bal[(ins_indep[i], ins_dep[i])] + endo_bal[i] = @trace(categorical(p_endo_bal), :endo_bal => i) + + # basal_bal + p_basal_bal = CPT_basal_bal[(gut_abs[i], endo_bal[i])] + basal_bal[i] = @trace(categorical(p_basal_bal), :basal_bal => i) + + # met_irr + p_met_irr = [.02, .05, .18, .5, .18, .05, .02] + met_irr[i] = @trace(categorical(p_met_irr), :met_irr => i) + + # tot_bal + p_tot_bal = CPT_tot_bal[(basal_bal[i], met_irr[i])] + tot_bal[i] = @trace(categorical(p_tot_bal), :tot_bal => i) + end +end diff --git a/mutinf.jl b/mutinf.jl new file mode 100644 index 0000000..af70334 --- /dev/null +++ b/mutinf.jl @@ -0,0 +1,55 @@ +include("entropy.jl") + +using Gen: + GenerativeFunction, + Selection + +struct OrSelection <: Selection + selections::Vector{Selection} +end +get_address_schema(::Type{OrSelection}) = @assert false # ??? +Base.isempty(selection::OrSelection) = all(isempty(s) for s in selection.selections) +Base.in(addr, selection::OrSelection) = any(addr in s for s in selection.selections) +function Base.getindex(selection::OrSelection, addr) + for s in selection.selections + sel = s[addr] + if !isempty(sel) + return sel + end + end + return EmptySelection() +end + +"""Mutual information lower bound using default proposal.""" +function mutinf_lower_bound( + model::GenerativeFunction, + model_args::Tuple, + X::Selection, + Y::Selection, + Z::Selection, + N::Integer, + M::Integer, + K::Integer) + H_XYZ_lower = entropy_lower_bound(model, model_args, OrSelection([X, Y, Z]), N, M, K) + H_XZ_upper = entropy_upper_bound(model, model_args, OrSelection([X, Z]), N, 1, K) + H_YZ_upper = entropy_upper_bound(model, model_args, OrSelection([Y, Z]), N, 1, K) + H_Z_lower = isempty(Z) ? 0 : entropy_lower_bound(model, model_args, Z, N, M, K) + return H_XYZ_lower - H_XZ_upper - H_YZ_upper + H_Z_lower +end + +"""Mutual information upper bound using default proposal.""" +function mutinf_upper_bound( + model::GenerativeFunction, + model_args::Tuple, + X::Selection, + Y::Selection, + Z::Selection, + N::Integer, + M::Integer, + K::Integer) + H_XYZ_upper = entropy_upper_bound(model, model_args, OrSelection([X, Y, Z]), N, 1, K) + H_XZ_lower = entropy_lower_bound(model, model_args, OrSelection([X, Z]), N, M, K) + H_YZ_lower = entropy_lower_bound(model, model_args, OrSelection([Y, Z]), N, M, K) + H_Z_upper = isempty(Z) ? 0 : entropy_upper_bound(model, model_args, Z, N, 1, K) + return H_XYZ_upper - H_XZ_lower - H_YZ_lower + H_Z_upper +end diff --git a/sir.jl b/sir.jl new file mode 100644 index 0000000..583ba7f --- /dev/null +++ b/sir.jl @@ -0,0 +1,155 @@ +import Gen +using Gen: GenerativeFunction, Trace, ChoiceMap +using Gen: simulate, generate, categorical + +######################### +# resampling combinator # +######################### + +# compile-time arguments to the combinator (generative function constructor) +# 1. the model generative function +# 2. the proposal generative function +# 3. the arguments to the model +# 4. the number of particles (K) + +# the resulting generative function has the same support over choice maps as +# the proposal generative function + +# run-time arguments to the generative function: +# 1. the arguments to the proposal, whose last entry is the +# observations on the model + +# requirement: for any choice map in the support of the proposal generative +# function on the given arguments, the merger of that choice map with the +# observations must result in a choice map that is in the support of the model +# generative function's distribution on choice maps + +# NOTE: project, update, regenerate, choice_gradients, and +# accumulate_param_gradients! are not yet implemented for the resulting +# functions + +struct SIRGF{T,U} <: GenerativeFunction{T,Trace} + model::GenerativeFunction + proposal::GenerativeFunction{T,U} + model_args::Tuple + num_particles::Int +end + +# construct using default constructor + +struct SIRGFTrace{T,U} <: Gen.Trace + gen_fn::SIRGF{T,U} + # arguments to the model generative function + model_args::Tuple + # arguments to the proposal generative function + proposal_args::Tuple + # when combined with choices made by proposal, + # uniquely determine a model trace + observations::ChoiceMap + # number of particles + num_particles::Int + # the chosen trace of proposal generative function + chosen_particle::U + # score + score::Float64 +end + +Gen.get_gen_fn(trace::SIRGFTrace) = trace.gen_fn + +function Gen.get_args(trace::SIRGFTrace) + return trace.proposal_args +end + +Gen.get_score(trace::SIRGFTrace) = trace.score +Gen.get_retval(trace::SIRGFTrace) = get_retval(trace.chosen_particle) +Base.getindex(trace::SIRGFTrace, addr) = trace.chosen_particle[addr] +Gen.get_choices(trace::SIRGFTrace) = get_choices(trace.chosen_particle) + +function Gen.simulate(gen_fn::SIRGF{T,U}, args::Tuple) where {T,U} + model = gen_fn.model + model_args = gen_fn.model_args + num_particles = gen_fn.num_particles + proposal_args = args + observations = proposal_args[end] + proposal_traces = Vector{U}(undef, num_particles) + log_weights = Vector{Float64}(undef, num_particles) + model_scores = Vector{Float64}(undef, num_particles) + for i in 1:num_particles + # sample from proposal + proposal_trace = simulate(gen_fn.proposal, proposal_args) + proposal_traces[i] = proposal_trace + proposed_choices = get_choices(proposal_trace) + # combine latents with observations to form a model trace + constraints = merge(observations, proposed_choices) + (model_trace, model_score) = generate(model, model_args, constraints) + # for now, make sure all of the choices in the model are constrained + @assert isapprox(model_score, get_score(model_trace)) + # record the model joint density (model_score) and importance weight + model_scores[i] = model_score + log_weights[i] = model_score - get_score(proposal_trace) + end + # sample particle in proposal to weights + log_total_weight = Gen.logsumexp(log_weights) + normalized_weights = exp.(log_weights .- log_total_weight) + chosen_idx = categorical(normalized_weights) + chosen_particle = proposal_traces[chosen_idx] + # compute score (our estimate of the marginal density of our choices) + log_ml_estimate = log_total_weight - log(num_particles) + score = model_scores[chosen_idx] - log_ml_estimate + # NOTE: we do not retain the other particles in our trace + return SIRGFTrace( + gen_fn, + model_args, + proposal_args, + observations, + num_particles, + chosen_particle, + score) +end + +function Gen.generate(gen_fn::SIRGF, args::Tuple, constraints::ChoiceMap) + model = gen_fn.model + model_args = gen_fn.model_args + num_particles = gen_fn.num_particles + proposal_args = args + observations = proposal_args[end] + # combine observations and constraints to form model trace + constraints_model = merge(observations, constraints) + (model_trace, model_score) = generate(model, model_args, constraints_model) + # for now, make sure all of the choices in the model are constrained + @assert isapprox(model_score, get_score(model_trace)) + # form the chosen particle (the trace of the proposal) + # and check that all of the proposal choices are constrained + (chosen_particle, proposal_score) = generate(gen_fn.proposal, proposal_args, constraints) + @assert isapprox(get_score(chosen_particle), proposal_score) + # sample the other particles, just to compute the score + # (we do not retain the other particles in our trace) + log_weights = Vector{Float64}(undef, num_particles) + log_weights[1] = model_score - proposal_score + for i in 2:num_particles + # sample from proposal + proposal_trace = simulate(gen_fn.proposal, proposal_args) + proposed_choices = get_choices(proposal_trace) + # combine latents with observations to form a model trace + constraints_i = merge(observations, proposed_choices) + (model_trace_i, model_score_i) = generate(model, model_args, constraints_i) + # for now, make sure all of the choices in the model are constrained + @assert isapprox(model_score_i, get_score(model_trace_i)) + # record the importance weight + log_weights[i] = model_score_i - get_score(proposal_trace) + end + # compute the score + log_total_weight = Gen.logsumexp(log_weights) + log_ml_estimate = log_total_weight - log(num_particles) + score = model_score - log_ml_estimate + # NOTE: we do not retain the other particles in our trace + trace = SIRGFTrace( + gen_fn, + model_args, + proposal_args, + observations, + num_particles, + chosen_particle, + score) + return (trace, score) +end diff --git a/sir_test.jl b/sir_test.jl new file mode 100644 index 0000000..bd389fc --- /dev/null +++ b/sir_test.jl @@ -0,0 +1,56 @@ +using Gen: @gen, normal, simulate, generate, get_choices, choicemap +using Gen: has_value, get_score + +include("sir.jl") + +@gen function model(a) + x ~ normal(a, 1.0) + y ~ normal(x, 1.0) +end + +@gen function proposal(a, observations::ChoiceMap) + y = observations[:y] + x ~ normal((a + y) / 2.0, 3.0) +end + + +a = 0. +y = -2 +observations = choicemap((:y, y)) +model_args = (a,) +num_particles = 100 + +sir = SIRGF(model, proposal, model_args, num_particles) + +proposal_args = (a, observations) + +# smoke test for simulate +sir_trace = simulate(sir, proposal_args) +sir_choices = get_choices(sir_trace) +display(sir_choices) +println(get_score(sir_trace)) +@assert has_value(sir_choices, :x) +@assert !has_value(sir_choices, :y) + +# smoke test for generate +choices = choicemap((:x, -1.5)) +(sir_trace, sir_score) = generate(sir, proposal_args, choices) +sir_choices = get_choices(sir_trace) +display(sir_choices) +println(get_score(sir_trace)) +@assert has_value(sir_choices, :x) +@assert !has_value(sir_choices, :y) +@assert sir_choices[:x] == -1.5 + +# TODO: next steps +# +# 1. work out what the posterior density of x given y is using Gaussian math +# +# 2. as num_particles increases, the score returned by calling get_score(trace) +# where trace is obtained by calling simulate on the SIRGF, should approach the +# log posterior density on x given y for the sampled value of x; verify this is +# indeed the case +# +# 3. do the same for the log_weight that is returned by calling generate on the +# SIRGF, which should approach the log posterior density for the given value of +# x that is passed in the constraints to generate; verify that this is indeed the case