From 8fd0bbe74f239dfdb944e6d8d77f3d7bfe2d7b4f Mon Sep 17 00:00:00 2001 From: Laurent Sorber Date: Sat, 24 Feb 2024 15:23:07 +0000 Subject: [PATCH 1/5] feat: add conformal Bayesian prediction --- README.md | 1 + src/neo_ls_svm/_feature_maps.py | 12 +-- src/neo_ls_svm/_neo_ls_svm.py | 178 ++++++++++++++++++++++++-------- tests/test_neo_ls_svm.py | 28 ++++- 4 files changed, 170 insertions(+), 49 deletions(-) diff --git a/README.md b/README.md index 845ea1f..06d3c00 100644 --- a/README.md +++ b/README.md @@ -11,6 +11,7 @@ Neo LS-SVM is a modern [Least-Squares Support Vector Machine](https://en.wikiped 5. 🌀 Learns an affine transformation of the feature matrix to optimally separate the target's bins. 6. 🪞 Can solve the LS-SVM both in the primal and dual space. 7. 🌡️ Isotonically calibrated `predict_proba` based on the leave-one-out predictions. +8. 🎲 Asymmetric conformal Bayesian confidence intervals for classification and regression. ## Using diff --git a/src/neo_ls_svm/_feature_maps.py b/src/neo_ls_svm/_feature_maps.py index 4619bf9..b423f56 100644 --- a/src/neo_ls_svm/_feature_maps.py +++ b/src/neo_ls_svm/_feature_maps.py @@ -153,13 +153,13 @@ def fit( def transform(self, X: FloatMatrix[F]) -> ComplexMatrix[C]: """Transform a feature matrix X ∈ Rⁿˣᵈ into φ(X) ∈ Cⁿˣᴰ⁺¹ so that φ(X)ᵢ := [φ(xᵢ)' 1]. - Notice that we can choose to solve an LS-SVM in the primal or dual space using the matrix - identity (γI + AB)⁻¹ A = A (γI + BA)⁻¹: + Notice that we can choose to solve an LS-SVM in the primal or dual space using the + push-through identity (γ𝕀 + AB)⁻¹ A = A (γ𝕀 + BA)⁻¹: - argmin ||y - φ(X)β̂||² + γ||β̂||² - = (γI + φ(X)'φ(X))⁻¹ φ(X)'y - = φ(X)' (γI + φ(X)φ(X)')⁻¹y with identity (γI + AB)⁻¹ A = A (γI + BA)⁻¹ - = φ(X)'a where a = (γI + φ(X)φ(X)')⁻¹y = (γI + k(xᵢ, xⱼ))⁻¹y + argmin ||φ(X)β̂ - y||² + γ||β̂||² + = (γ𝕀 + φ(X)'φ(X))⁻¹ φ(X)'y + = φ(X)' (γ𝕀 + φ(X)φ(X)')⁻¹y with the identity (γ𝕀 + AB)⁻¹ A = A (γ𝕀 + BA)⁻¹ + = φ(X)'α̂ where α̂ := (γ𝕀 + φ(X)φ(X)')⁻¹y = (γ𝕀 + k(xᵢ, xⱼ))⁻¹y This means that k(x, y) = φ(x)'φ(y) by definition. Now we look for a φ(x) so that k(x, y) = φ(x)'φ(y) for the Gaussian kernel k(x, y) = exp(- ||y - x||² / 2). If we take h(x) := diff --git a/src/neo_ls_svm/_neo_ls_svm.py b/src/neo_ls_svm/_neo_ls_svm.py index 6555158..cd2d812 100644 --- a/src/neo_ls_svm/_neo_ls_svm.py +++ b/src/neo_ls_svm/_neo_ls_svm.py @@ -4,9 +4,10 @@ import numpy as np import numpy.typing as npt -from scipy.linalg import eigh, lu_factor, lu_solve +from scipy.linalg import cho_factor, cho_solve, eigh, lu_factor, lu_solve from sklearn.base import BaseEstimator, clone from sklearn.isotonic import IsotonicRegression +from sklearn.linear_model import QuantileRegressor from sklearn.metrics import accuracy_score, r2_score from sklearn.metrics.pairwise import euclidean_distances, rbf_kernel from sklearn.utils.validation import check_consistent_length, check_X_y @@ -21,6 +22,7 @@ ComplexMatrix, ComplexVector, FloatMatrix, + FloatTensor, FloatVector, GenericVector, ) @@ -34,34 +36,30 @@ class NeoLSSVM(BaseEstimator): A neo Least-Squares Support Vector Machine with: - - [x] A next-generation regularisation term that penalises the complexity of the prediction - surface, decision function, and maximises the margin. - - [x] Large-scale support through state-of-the-art random feature maps. - - [x] Optional automatic selection of primal or dual problem. - - [x] Automatic optimal tuning of the regularisation hyperparameter γ that minimises the - leave-one-out error, without having to refit the model. - - [x] Automatic tuning of the kernel parameters σ, without having to refit the model. - - [x] Automatic robust shift and scaling of the feature matrix and labels. - - [x] Leave-one-out residuals and error as a free output after fitting, optimally clipped in - classification. - - [x] Isotonically calibrated class probabilities based on leave-one-out predictions. - - [ ] Automatic robust fit by removing outliers. + 1. ⚡ Linear complexity in the number of training examples with Orthogonal Random Features. + 2. 🚀 Hyperparameter free: zero-cost optimization of the regularisation parameter γ and + kernel parameter σ. + 3. 🏔️ Adds a new tertiary objective that minimizes the complexity of the prediction surface. + 4. 🎁 Returns the leave-one-out residuals and error for free after fitting. + 5. 🌀 Learns an affine transformation of the feature matrix to optimally separate the + target's bins. + 6. 🪞 Can solve the LS-SVM both in the primal and dual space. + 7. 🌡️ Isotonically calibrated `predict_proba` based on the leave-one-out predictions. + 8. 🎲 Asymmetric conformal Bayesian confidence intervals for classification and regression. """ def __init__( # noqa: PLR0913 self, *, - primal_feature_map: KernelApproximatingFeatureMap | None = None, - dual_feature_map: AffineSeparator | None = None, - dual: bool | None = None, - refit: bool = False, + primal_feature_map: KernelApproximatingFeatureMap | Literal["auto"] = "auto", + dual_feature_map: AffineSeparator | Literal["auto"] = "auto", + dual: bool | Literal["auto"] = "auto", + estimator_type: Literal["auto", "classifier", "regressor"] = "auto", random_state: int | np.random.RandomState | None = 42, - estimator_type: Literal["classifier", "regressor"] | None = None, ) -> None: self.primal_feature_map = primal_feature_map self.dual_feature_map = dual_feature_map self.dual = dual - self.refit = refit self.random_state = random_state self.estimator_type = estimator_type @@ -156,6 +154,7 @@ def _optimize_β̂_γ( ) # Store the leave-one-out residuals, leverage, error, and score. self.loo_residuals_ = loo_residuals[:, optimum] + self.loo_ŷ_ = y + self.loo_residuals_ self.loo_leverage_ = h @ rγ[:, optimum] self.loo_error_ = self.loo_errors_γs_[optimum] if self._estimator_type == "classifier": @@ -164,12 +163,17 @@ def _optimize_β̂_γ( self.loo_score_ = r2_score(y, ŷ_loo[:, optimum], sample_weight=s) β̂, γ = β̂ @ rγ[:, optimum], self.γs_[optimum] # Resolve the linear system for better accuracy. - if self.refit: - β̂ = np.linalg.solve(γ * C + A, φSTSy) + self.L_ = cho_factor(γ * C + A) + β̂ = cho_solve(self.L_, φSTSy) self.residuals_ = np.real(φ @ β̂) - y if self._estimator_type == "classifier": self.residuals_[(y > 0) & (self.residuals_ > 0)] = 0 self.residuals_[(y < 0) & (self.residuals_ < 0)] = 0 + # Compute the leave-one-out nonconformity with the Sherman-Morrison formula. + σ2 = np.real(np.sum(φ * cho_solve(self.L_, φ.conj().T).T, axis=1)) + σ2 = np.ascontiguousarray(σ2) + loo_σ2 = σ2 + (s * σ2) ** 2 / (1 - self.loo_leverage_) + self.loo_nonconformity_ = np.sqrt(loo_σ2) # TODO: Print warning if optimal γ is found at the edge. return β̂, γ @@ -287,6 +291,7 @@ def _optimize_α̂_γ( ) # Store the leave-one-out residuals, leverage, error, and score. self.loo_residuals_ = loo_residuals[:, optimum] + self.loo_ŷ_ = y + self.loo_residuals_ self.loo_error_ = self.loo_errors_γs_[optimum] if self._estimator_type == "classifier": self.loo_score_ = accuracy_score(y, np.sign(ŷ_loo[:, optimum]), sample_weight=s) @@ -294,12 +299,16 @@ def _optimize_α̂_γ( self.loo_score_ = r2_score(y, ŷ_loo[:, optimum], sample_weight=s) α̂, γ = α̂_loo[:, optimum], self.γs_[optimum] # Resolve the linear system for better accuracy. - if self.refit: - α̂ = np.linalg.solve(γ * ρ * np.diag(sn**-2) + K, y) + self.L_ = cho_factor(γ * ρ * np.diag(sn**-2) + K) + α̂ = cho_solve(self.L_, y) self.residuals_ = F @ α̂ - y if self._estimator_type == "classifier": self.residuals_[(y > 0) & (self.residuals_ > 0)] = 0 self.residuals_[(y < 0) & (self.residuals_ < 0)] = 0 + # Compute the nonconformity. TODO: Apply a leave-one-out correction. + K = rbf_kernel(X, X, gamma=0.5) + σ2 = 1.0 - np.sum(K * cho_solve(self.L_, K.T).T, axis=1) + self.loo_nonconformity_ = np.sqrt(σ2) # TODO: Print warning if optimal γ is found at the edge. return α̂, γ @@ -334,7 +343,9 @@ def fit( or np.issubdtype(y.dtype, np.timedelta64) ): inferred_estimator_type = "regressor" - self._estimator_type: str | None = self.estimator_type or inferred_estimator_type + self._estimator_type: str | None = ( + inferred_estimator_type if self.estimator_type == "auto" else self.estimator_type + ) if self._estimator_type == "classifier": self.classes_: GenericVector = unique_y negatives = y == self.classes_[0] @@ -346,18 +357,24 @@ def fit( message = "Target type not supported" raise ValueError(message) # Determine whether we want to solve this in the primal or dual space. - self.dual_ = X.shape[0] <= 1024 if self.dual is None else self.dual # noqa: PLR2004 + self.dual_ = X.shape[0] <= 1024 if self.dual == "auto" else self.dual # noqa: PLR2004 self.primal_ = not self.dual_ # Learn an optimal distance metric for the primal or dual space and apply it to the feature # matrix X. if self.primal_: self.primal_feature_map_ = clone( - self.primal_feature_map or OrthogonalRandomFourierFeatures() + OrthogonalRandomFourierFeatures() + if self.primal_feature_map == "auto" + else self.primal_feature_map ) self.primal_feature_map_.fit(X, y_, sample_weight_) φ = self.primal_feature_map_.transform(X) else: - self.dual_feature_map_ = clone(self.dual_feature_map or AffineSeparator()) + nz_weight = sample_weight_ > 0 + X, y_, sample_weight_ = X[nz_weight], y_[nz_weight], sample_weight_[nz_weight] + self.dual_feature_map_ = clone( + AffineSeparator() if self.dual_feature_map == "auto" else self.dual_feature_map + ) self.dual_feature_map_.fit(X, y_, sample_weight_) self.X_ = self.dual_feature_map_.transform(X) # Solve the primal or dual system. We optimise the following sub-objectives for the weights @@ -375,21 +392,94 @@ def fit( self.predict_proba_calibrator_ = IsotonicRegression( out_of_bounds="clip", y_min=0, y_max=1, increasing=True ) - ŷ_loo = y_ + self.loo_residuals_ target = np.zeros_like(y_) target[y_ == np.max(y_)] = 1.0 - self.predict_proba_calibrator_.fit(ŷ_loo, target, sample_weight_) + self.predict_proba_calibrator_.fit(self.loo_ŷ_, target, sample_weight_) + # Lazily fit conformal predictors as quantile regression models that predict the lower and + # upper bounds of the (relative) leave-one-out residuals. + self.conformal_regressors_: dict[str, dict[float, QuantileRegressor]] = { + "Δ⁺": {}, + "Δ⁻": {}, + "Δ⁺/ŷ": {}, + "Δ⁻/ŷ": {}, + } return self + def nonconformity_measure(self, X: FloatMatrix[F]) -> FloatVector[F]: + """Compute the nonconformity of a set of examples.""" + # Estimate the nonconformity as the variance of this model's Gaussian Process. + σ2: FloatVector[F] + if self.primal_: + # If β̂ := (LL')⁻¹ y* and cov(y*) := LL', then cov(β̂) = cov((LL')⁻¹ y*) = (LL')⁻¹ + # assuming 𝔼(β̂) = 0. It follows that cov(ŷ(x)) = cov(φ(x)'β̂) = φ(x)'(LL')⁻¹φ(x). + φH = cast(KernelApproximatingFeatureMap, self.primal_feature_map_).transform(X) + σ2 = np.real(np.sum(φH * cho_solve(self.L_, φH.conj().T).T, axis=1)) + σ2 = np.ascontiguousarray(σ2) + else: + # Compute the cov(ŷ(x)) as K(x, x) − K(x, X) (LL')⁻¹ K(X, x). TODO: Document derivation. + X = cast(AffineFeatureMap, self.dual_feature_map_).transform(X) + K = rbf_kernel(X, self.X_, gamma=0.5) + σ2 = 1.0 - np.sum(K * cho_solve(self.L_, K.T).T, axis=1) + # Convert the variance to a standard deviation. + σ = np.sqrt(σ2) + return σ + + def predict_confidence_interval( + self, X: FloatMatrix[F], *, confidence_level: float = 0.95 + ) -> FloatMatrix[F] | FloatTensor[F]: + # Compute the nonconformity measure for the given examples. + X_nonconformity = self.nonconformity_measure(X)[:, np.newaxis] + # Determine the quantiles at the edge of the confidence interval. + quantile = 1 - (1 - confidence_level) / 2 + # Lazily fit any missing conformal regressors. + # TODO: Perhaps exclude samples that were used in the feature map. + for target_type in ("Δ⁺", "Δ⁻", "Δ⁺/ŷ", "Δ⁻/ŷ"): + quantile_regressors = self.conformal_regressors_[target_type] + if quantile not in quantile_regressors: + sgn = (self.loo_residuals_ > 0) if "⁺" in target_type else (self.loo_residuals_ < 0) + eps = np.finfo(self.loo_ŷ_.dtype).eps + quantile_regressors[quantile] = QuantileRegressor( + quantile=quantile, alpha=np.sqrt(eps), solver="highs" + ).fit( + self.loo_nonconformity_[sgn, np.newaxis], + np.abs(self.loo_residuals_[sgn]) / np.maximum(np.abs(self.loo_ŷ_)[sgn], eps) + if "/ŷ" in target_type + else np.abs(self.loo_residuals_[sgn]), + ) + # Predict the confidence interval for the nonconformity measure. + ŷ = self.decision_function(X) + Δ_lower = np.minimum( + self.conformal_regressors_["Δ⁻"][quantile].predict(X_nonconformity), + np.abs(ŷ) * self.conformal_regressors_["Δ⁻/ŷ"][quantile].predict(X_nonconformity), + ) + Δ_upper = np.minimum( + self.conformal_regressors_["Δ⁺"][quantile].predict(X_nonconformity), + np.abs(ŷ) * self.conformal_regressors_["Δ⁺/ŷ"][quantile].predict(X_nonconformity), + ) + # Assemble the confidence interval. + C = np.hstack(((ŷ - Δ_lower)[:, np.newaxis], (ŷ + Δ_upper)[:, np.newaxis])) + # In case of classification, convert the decision function values to probabilities. + if self._estimator_type == "classifier": + C = np.hstack( + [ + self.predict_proba_calibrator_.transform(C[:, 0])[:, np.newaxis], + self.predict_proba_calibrator_.transform(C[:, 1])[:, np.newaxis], + ] + ) + C = np.dstack([1 - C[:, ::-1], C]) + return C + def decision_function(self, X: FloatMatrix[F]) -> FloatVector[F]: - """Evaluate this predictor's decision function.""" + """Evaluate this predictor's prediction function.""" + # Compute the point predictions ŷ(X). ŷ: FloatVector[F] if self.primal_: # Apply the feature map φ and predict as ŷ(x) := φ(x)'β̂. φ = cast(KernelApproximatingFeatureMap, self.primal_feature_map_).transform(X) ŷ = np.real(φ @ self.β̂_) + ŷ = np.ascontiguousarray(ŷ) else: - # Apply an affine transformation to X, then predict as ŷ(x) := k(x, X) â + 1'â. + # Apply an affine transformation to X, then predict as ŷ(x) := k(x, X) α̂ + 1'α̂. X = cast(AffineFeatureMap, self.dual_feature_map_).transform(X) K = rbf_kernel(X, self.X_, gamma=0.5) b = np.sum(self.α̂_) @@ -398,7 +488,7 @@ def decision_function(self, X: FloatMatrix[F]) -> FloatVector[F]: def predict(self, X: FloatMatrix[F]) -> GenericVector: """Predict the output on a given dataset.""" - # Evaluate ŷ given the feature matrix X. + # Compute the point predictions ŷ(X). ŷ_df = self.decision_function(X) if self._estimator_type == "classifier": # For binary classification, round to the nearest class label. When the decision @@ -415,23 +505,29 @@ def predict(self, X: FloatMatrix[F]) -> GenericVector: ŷ = ŷ.astype(self.y_dtype_) return ŷ - def predict_proba(self, X: FloatMatrix[F]) -> FloatMatrix[F]: - """Predict the output probability (classification) or confidence interval (regression).""" + def predict_proba( + self, + X: FloatMatrix[F], + *, + confidence_interval: bool = False, + confidence_level: float = 0.95, + ) -> FloatVector[F] | FloatMatrix[F] | FloatTensor[F]: + """Predict the class probability or confidence interval.""" + if confidence_interval: + # Return the confidence interval for classification or regression. + C = self.predict_confidence_interval(X, confidence_level=confidence_level) + return C if self._estimator_type == "classifier": + # Return the class probabilities for classification. ŷ_classification = self.decision_function(X) p = self.predict_proba_calibrator_.transform(ŷ_classification) P = np.hstack([1 - p[:, np.newaxis], p[:, np.newaxis]]) else: - # TODO: Replace point predictions with confidence interval. + # Return the point predictions for regression. ŷ_regression = self.predict(X) - P = np.hstack((ŷ_regression[:, np.newaxis], ŷ_regression[:, np.newaxis])) + P = ŷ_regression return P - @property - def loo_score(self) -> float: - """Compute the leave-one-out score of this classifier or regressor.""" - return cast(float, self.loo_score_) - def score( self, X: FloatMatrix[F], y: GenericVector, sample_weight: FloatVector[F] | None = None ) -> float: diff --git a/tests/test_neo_ls_svm.py b/tests/test_neo_ls_svm.py index 767f44f..db14c70 100644 --- a/tests/test_neo_ls_svm.py +++ b/tests/test_neo_ls_svm.py @@ -17,10 +17,12 @@ def test_compare_neo_ls_svm_with_svm(dataset: Dataset, table_vectorizer: TableVe X_train, X_test, y_train, y_test = dataset # Create the pipelines. num_unique = len(y_train.unique()) - if num_unique == 2: # noqa: PLR2004 + binary = num_unique == 2 # noqa: PLR2004 + multiclass = 2 < num_unique <= np.ceil(np.sqrt(len(y_train))) # noqa: PLR2004 + if binary: neo_ls_svm_pipeline = make_pipeline(table_vectorizer, NeoLSSVM()) svm_pipeline = make_pipeline(table_vectorizer, SVC()) - elif num_unique <= np.ceil(np.sqrt(len(y_train))): + elif multiclass: neo_ls_svm_pipeline = make_pipeline(table_vectorizer, OneVsRestClassifier(NeoLSSVM())) svm_pipeline = make_pipeline(table_vectorizer, OneVsRestClassifier(SVC())) else: @@ -33,6 +35,28 @@ def test_compare_neo_ls_svm_with_svm(dataset: Dataset, table_vectorizer: TableVe neo_ls_svm_score = neo_ls_svm_pipeline.score(X_test, y_test) svm_score = svm_pipeline.score(X_test, y_test) assert neo_ls_svm_score > svm_score + # Verify the coverage of the confidence interval. + if multiclass: + return + confidence_level = 0.8 + X_conf = neo_ls_svm_pipeline.predict_proba( + X_test, confidence_interval=True, confidence_level=confidence_level + ) + if binary: + assert np.all(X_conf >= 0) + assert np.all(X_conf <= 1) + assert np.all(X_conf[:, 0, 0] <= X_conf[:, 1, 0]) + assert np.all(X_conf[:, 0, 1] <= X_conf[:, 1, 1]) + is_neg = y_test == neo_ls_svm_pipeline.steps[-1][1].classes_[0] + is_pos = ~is_neg + neg_covered = np.any(X_conf[:, :, 0] > 0.5, axis=1) & is_neg # noqa: PLR2004 + pos_covered = np.any(X_conf[:, :, 1] > 0.5, axis=1) & is_pos # noqa: PLR2004 + covered = neg_covered | pos_covered + elif not multiclass: + assert np.all(X_conf[:, 0] <= X_conf[:, 1]) + covered = (X_conf[:, 0] <= y_test) & (y_test <= X_conf[:, 1]) + coverage = np.mean(covered) + assert coverage >= confidence_level def test_sklearn_check_estimator() -> None: From 7f5d20749d269db29a9548f879c5cbf57e825dfc Mon Sep 17 00:00:00 2001 From: Laurent Sorber Date: Sun, 25 Feb 2024 14:35:29 +0000 Subject: [PATCH 2/5] feat: improve quantile regressors --- src/neo_ls_svm/_neo_ls_svm.py | 36 ++++++++++++++++++++++++----------- tests/test_neo_ls_svm.py | 18 +++++++++--------- 2 files changed, 34 insertions(+), 20 deletions(-) diff --git a/src/neo_ls_svm/_neo_ls_svm.py b/src/neo_ls_svm/_neo_ls_svm.py index cd2d812..0cbb83e 100644 --- a/src/neo_ls_svm/_neo_ls_svm.py +++ b/src/neo_ls_svm/_neo_ls_svm.py @@ -427,8 +427,6 @@ def nonconformity_measure(self, X: FloatMatrix[F]) -> FloatVector[F]: def predict_confidence_interval( self, X: FloatMatrix[F], *, confidence_level: float = 0.95 ) -> FloatMatrix[F] | FloatTensor[F]: - # Compute the nonconformity measure for the given examples. - X_nonconformity = self.nonconformity_measure(X)[:, np.newaxis] # Determine the quantiles at the edge of the confidence interval. quantile = 1 - (1 - confidence_level) / 2 # Lazily fit any missing conformal regressors. @@ -438,23 +436,39 @@ def predict_confidence_interval( if quantile not in quantile_regressors: sgn = (self.loo_residuals_ > 0) if "⁺" in target_type else (self.loo_residuals_ < 0) eps = np.finfo(self.loo_ŷ_.dtype).eps - quantile_regressors[quantile] = QuantileRegressor( - quantile=quantile, alpha=np.sqrt(eps), solver="highs" - ).fit( - self.loo_nonconformity_[sgn, np.newaxis], + X_qr = np.hstack( + [ + self.loo_nonconformity_[sgn, np.newaxis], + self.loo_ŷ_[sgn, np.newaxis], + np.abs(self.loo_ŷ_[sgn, np.newaxis]), + np.sign(self.loo_ŷ_[sgn, np.newaxis]), + ] + ) + y_qr = ( np.abs(self.loo_residuals_[sgn]) / np.maximum(np.abs(self.loo_ŷ_)[sgn], eps) if "/ŷ" in target_type - else np.abs(self.loo_residuals_[sgn]), + else np.abs(self.loo_residuals_[sgn]) ) + quantile_regressors[quantile] = QuantileRegressor( + quantile=quantile, alpha=np.sqrt(eps), solver="highs" + ).fit(X_qr, y_qr) # Predict the confidence interval for the nonconformity measure. ŷ = self.decision_function(X) + X_qr = np.hstack( + [ + self.nonconformity_measure(X)[:, np.newaxis], + ŷ[:, np.newaxis], + np.abs(ŷ[:, np.newaxis]), + np.sign(ŷ[:, np.newaxis]), + ] + ) Δ_lower = np.minimum( - self.conformal_regressors_["Δ⁻"][quantile].predict(X_nonconformity), - np.abs(ŷ) * self.conformal_regressors_["Δ⁻/ŷ"][quantile].predict(X_nonconformity), + self.conformal_regressors_["Δ⁻"][quantile].predict(X_qr), + np.abs(ŷ) * self.conformal_regressors_["Δ⁻/ŷ"][quantile].predict(X_qr), ) Δ_upper = np.minimum( - self.conformal_regressors_["Δ⁺"][quantile].predict(X_nonconformity), - np.abs(ŷ) * self.conformal_regressors_["Δ⁺/ŷ"][quantile].predict(X_nonconformity), + self.conformal_regressors_["Δ⁺"][quantile].predict(X_qr), + np.abs(ŷ) * self.conformal_regressors_["Δ⁺/ŷ"][quantile].predict(X_qr), ) # Assemble the confidence interval. C = np.hstack(((ŷ - Δ_lower)[:, np.newaxis], (ŷ + Δ_upper)[:, np.newaxis])) diff --git a/tests/test_neo_ls_svm.py b/tests/test_neo_ls_svm.py index db14c70..41bacdd 100644 --- a/tests/test_neo_ls_svm.py +++ b/tests/test_neo_ls_svm.py @@ -39,22 +39,22 @@ def test_compare_neo_ls_svm_with_svm(dataset: Dataset, table_vectorizer: TableVe if multiclass: return confidence_level = 0.8 - X_conf = neo_ls_svm_pipeline.predict_proba( + ŷ_conf = neo_ls_svm_pipeline.predict_proba( X_test, confidence_interval=True, confidence_level=confidence_level ) if binary: - assert np.all(X_conf >= 0) - assert np.all(X_conf <= 1) - assert np.all(X_conf[:, 0, 0] <= X_conf[:, 1, 0]) - assert np.all(X_conf[:, 0, 1] <= X_conf[:, 1, 1]) + assert np.all(ŷ_conf >= 0) + assert np.all(ŷ_conf <= 1) + assert np.all(ŷ_conf[:, 0, 0] <= ŷ_conf[:, 1, 0]) + assert np.all(ŷ_conf[:, 0, 1] <= ŷ_conf[:, 1, 1]) is_neg = y_test == neo_ls_svm_pipeline.steps[-1][1].classes_[0] is_pos = ~is_neg - neg_covered = np.any(X_conf[:, :, 0] > 0.5, axis=1) & is_neg # noqa: PLR2004 - pos_covered = np.any(X_conf[:, :, 1] > 0.5, axis=1) & is_pos # noqa: PLR2004 + neg_covered = np.any(ŷ_conf[:, :, 0] > 0.5, axis=1) & is_neg # noqa: PLR2004 + pos_covered = np.any(ŷ_conf[:, :, 1] > 0.5, axis=1) & is_pos # noqa: PLR2004 covered = neg_covered | pos_covered elif not multiclass: - assert np.all(X_conf[:, 0] <= X_conf[:, 1]) - covered = (X_conf[:, 0] <= y_test) & (y_test <= X_conf[:, 1]) + assert np.all(ŷ_conf[:, 0] <= ŷ_conf[:, 1]) + covered = (ŷ_conf[:, 0] <= y_test) & (y_test <= ŷ_conf[:, 1]) coverage = np.mean(covered) assert coverage >= confidence_level From 70ab03a1b3b231329204e66fa62d1b9c15f68355 Mon Sep 17 00:00:00 2001 From: Laurent Sorber Date: Sun, 25 Feb 2024 14:37:06 +0000 Subject: [PATCH 3/5] docs: add conformal prediction to README --- README.md | 77 +- poetry.lock | 1871 ++++++++++++++++++++++++++++++++++++------------ pyproject.toml | 2 + 3 files changed, 1490 insertions(+), 460 deletions(-) diff --git a/README.md b/README.md index 06d3c00..1a02b5c 100644 --- a/README.md +++ b/README.md @@ -15,35 +15,92 @@ Neo LS-SVM is a modern [Least-Squares Support Vector Machine](https://en.wikiped ## Using +### Installing + First, install this package with: ```bash pip install neo-ls-svm ``` +### Classification and regression + Then, you can import `neo_ls_svm.NeoLSSVM` as an sklearn-compatible binary classifier and regressor. Example usage: ```python from neo_ls_svm import NeoLSSVM +from pandas import get_dummies from sklearn.datasets import fetch_openml from sklearn.model_selection import train_test_split from sklearn.pipeline import make_pipeline -from skrub import TableVectorizer # Vectorizes a pandas DataFrame into a NumPy array. # Binary classification example: -X, y = fetch_openml("credit-g", version=1, return_X_y=True, as_frame=True, parser="auto") -X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.15, random_state=42) -model = make_pipeline(TableVectorizer(), NeoLSSVM()) -model.fit(X_train, y_train) -print(model.score(X_test, y_test)) # 76.7% (compared to sklearn.svm.SVC's 70.7%) +X, y = fetch_openml("churn", version=3, return_X_y=True, as_frame=True, parser="auto") +X_train, X_test, y_train, y_test = train_test_split(get_dummies(X), y, test_size=0.15, random_state=42) +model = NeoLSSVM().fit(X_train, y_train) +model.score(X_test, y_test) # 93.1% (compared to sklearn.svm.SVC's 89.6%) # Regression example: X, y = fetch_openml("ames_housing", version=1, return_X_y=True, as_frame=True, parser="auto") -X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.15, random_state=42) -model = make_pipeline(TableVectorizer(), NeoLSSVM()) -model.fit(X_train, y_train) -print(model.score(X_test, y_test)) # 81.8% (compared to sklearn.svm.SVR's -11.8%) +X_train, X_test, y_train, y_test = train_test_split(get_dummies(X), y, test_size=0.15, random_state=42) +model = NeoLSSVM().fit(X_train, y_train) +model.score(X_test, y_test) # 82.4% (compared to sklearn.svm.SVR's -11.8%) +``` + +### Confidence intervals + +Neo LS-SVM implements conformal prediction with a Bayesian nonconformity estimate to compute confidence intervals for both classification and regression. Example usage: + +```python +from neo_ls_svm import NeoLSSVM +from pandas import get_dummies +from sklearn.datasets import fetch_openml +from sklearn.model_selection import train_test_split + +# Load a regression problem and split in train and test. +X, y = fetch_openml("ames_housing", version=1, return_X_y=True, as_frame=True, parser="auto") +X_train, X_test, y_train, y_test = train_test_split(get_dummies(X), y, test_size=50, random_state=42) + +# Fit a Neo LS-SVM model. +model = NeoLSSVM().fit(X_train, y_train) + +# Predict the house prices and confidence intervals on the test set. +ŷ = model.predict(X_test) +ŷ_conf = model.predict_proba(X_test, confidence_interval=True, confidence_level=0.95) +# ŷ_conf[:, 0] and ŷ_conf[:, 1] are the lower and upper bound of the confidence interval for the predictions ŷ, respectively ``` +Let's visualize the confidence intervals on the test set: + + + +
+Expand to see the code that generated the above graph. + +```python +import matplotlib.pyplot as plt +import matplotlib.ticker as ticker +import numpy as np + +idx = np.argsort(-ŷ) +y_ticks = np.arange(1, len(X_test) + 1) +plt.figure(figsize=(4, 5)) +plt.barh(y_ticks, ŷ_conf[idx, 1] - ŷ_conf[idx, 0], left=ŷ_conf[idx, 0], label="95% Confidence interval", color="lightblue") +plt.plot(y_test.iloc[idx], y_ticks, "s", markersize=3, markerfacecolor="none", markeredgecolor="cornflowerblue", label="Actual value") +plt.plot(ŷ[idx], y_ticks, "s", color="mediumblue", markersize=0.6, label="Predicted value") +plt.xlabel("House price") +plt.ylabel("Test house index") +plt.yticks(y_ticks, y_ticks) +plt.tick_params(axis="y", labelsize=6) +plt.grid(axis="x", color="lightsteelblue", linestyle=":", linewidth=0.5) +plt.gca().xaxis.set_major_formatter(ticker.StrMethodFormatter('${x:,.0f}')) +plt.gca().spines["top"].set_visible(False) +plt.gca().spines["right"].set_visible(False) +plt.legend() +plt.tight_layout() +plt.show() +``` +
+ ## Benchmarks We select all binary classification and regression datasets below 1M entries from the [AutoML Benchmark](https://arxiv.org/abs/2207.12560). Each dataset is split into 85% for training and 15% for testing. We apply `skrub.TableVectorizer` as a preprocessing step for `neo_ls_svm.NeoLSSVM` and `sklearn.svm.SVC,SVR` to vectorize the pandas DataFrame training data into a NumPy array. 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a/pyproject.toml +++ b/pyproject.toml @@ -43,8 +43,10 @@ typeguard = ">=3.0.2" [tool.poetry.group.dev.dependencies] # https://python-poetry.org/docs/master/managing-dependencies/ cruft = ">=2.14.0" +ipykernel = ">=6.29.2" ipython = ">=8.19.0" lightgbm = ">=4.2.0" +matplotlib = ">=3.8.3" pdoc = ">=13.1.1" tabulate = ">=0.9.0" viztracer = ">=0.16.1" From f663cbbdef5ed9ecfc7362bb256811062ee25443 Mon Sep 17 00:00:00 2001 From: Laurent Sorber Date: Sun, 25 Feb 2024 14:59:06 +0000 Subject: [PATCH 4/5] fix: fix negative confidence interval deltas --- src/neo_ls_svm/_neo_ls_svm.py | 2 ++ 1 file changed, 2 insertions(+) diff --git a/src/neo_ls_svm/_neo_ls_svm.py b/src/neo_ls_svm/_neo_ls_svm.py index 0cbb83e..f671b97 100644 --- a/src/neo_ls_svm/_neo_ls_svm.py +++ b/src/neo_ls_svm/_neo_ls_svm.py @@ -431,6 +431,7 @@ def predict_confidence_interval( quantile = 1 - (1 - confidence_level) / 2 # Lazily fit any missing conformal regressors. # TODO: Perhaps exclude samples that were used in the feature map. + # TODO: Perhaps enforce a positive slope for the nonconformity measure. for target_type in ("Δ⁺", "Δ⁻", "Δ⁺/ŷ", "Δ⁻/ŷ"): quantile_regressors = self.conformal_regressors_[target_type] if quantile not in quantile_regressors: @@ -470,6 +471,7 @@ def predict_confidence_interval( self.conformal_regressors_["Δ⁺"][quantile].predict(X_qr), np.abs(ŷ) * self.conformal_regressors_["Δ⁺/ŷ"][quantile].predict(X_qr), ) + Δ_lower, Δ_upper = np.maximum(0, Δ_lower), np.maximum(0, Δ_upper) # Assemble the confidence interval. C = np.hstack(((ŷ - Δ_lower)[:, np.newaxis], (ŷ + Δ_upper)[:, np.newaxis])) # In case of classification, convert the decision function values to probabilities. From 3b2a314ffe8584d2e4914d83ff542e923df213a7 Mon Sep 17 00:00:00 2001 From: Laurent Sorber Date: Sun, 25 Feb 2024 15:01:45 +0000 Subject: [PATCH 5/5] docs: simplify example imports --- README.md | 1 - 1 file changed, 1 deletion(-) diff --git a/README.md b/README.md index 1a02b5c..ebf80c2 100644 --- a/README.md +++ b/README.md @@ -31,7 +31,6 @@ from neo_ls_svm import NeoLSSVM from pandas import get_dummies from sklearn.datasets import fetch_openml from sklearn.model_selection import train_test_split -from sklearn.pipeline import make_pipeline # Binary classification example: X, y = fetch_openml("churn", version=3, return_X_y=True, as_frame=True, parser="auto")