examples/kickscore-basics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# `kickscore` basics\n",
    "\n",
    "This notebook introduces the library's API in the context of a simple example involving [Tom and Jerry](https://en.wikipedia.org/wiki/Tom_and_Jerry).\n",
    "\n",
    "![Tom and Jerry](https://media.giphy.com/media/rjZii4RTL6I0M/giphy.gif)\n",
    "\n",
    "In this notebook, we will:\n",
    "\n",
    "1. instantiate a `kickscore` model,\n",
    "2. define items & express our prior beliefs on the temporal dynamics of the items' skill,\n",
    "3. fit the model to a toy dataset, and\n",
    "4. analyze the results.\n",
    "\n",
    "If you are not doing so already, you can [launch an interactive notebook on Google Colaboratory](https://colab.research.google.com/github/lucasmaystre/kickscore/blob/master/examples/kickscore-basics.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This is only needed for when running the notebook on Google Colaboratory.\n",
    "!pip install kickscore"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import kickscore as ks\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining & fitting the model\n",
    "\n",
    "First, we define the model. In this example, we will use a _binary_ model, which is suitable for observations of the type \"_A_ wins over _B_\".\n",
    "Richer types of observations can be handled with `TernaryModel`, `CountModel` and `DifferenceModel`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = ks.BinaryModel()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will observe outcomes of \"fights\" between three contestants: Tom (the cat), Jerry (the mouse) and Spike (the dog).\n",
    "Each contestant is an _item_, in `kickscore`'s terminology.\n",
    "\n",
    "The key assumption behind the `kickscore` models is that the outcome probability of each fight is a function of the (latent) skill of each contestant.\n",
    "This skill can **change over time**.\n",
    "For each contestant, we need to describe how we expect their skill to change over time.\n",
    "We do this by specifying a **kernel function** (a.k.a. covariance function).\n",
    "\n",
    "- Many kernel functions have a variance parameter (usually called `var`). Roughly speaking, this defines the range of possible skill values.\n",
    "- Some kernel functions have a lengthscale parameter (usually called `lscale`). This roughly defines the time interval over which we expect the skill to stay similar."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Spike's skill does not change over time.\n",
    "k_spike = ks.kernel.Constant(var=0.5)\n",
    "\n",
    "# Tom's skill changes over time, with \"jagged\" (non-smooth) dynamics.\n",
    "k_tom = ks.kernel.Exponential(var=1.0, lscale=1.0)\n",
    "\n",
    "# Jerry's skill has a constant offset and smooth dynamics.\n",
    "k_jerry = ks.kernel.Constant(var=1.0) + ks.kernel.Matern52(var=0.5, lscale=1.0)\n",
    "\n",
    "# Now we are ready to add the items in the model.\n",
    "model.add_item(\"Spike\", kernel=k_spike)\n",
    "model.add_item(\"Tom\", kernel=k_tom)\n",
    "model.add_item(\"Jerry\", kernel=k_jerry)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we add observations to the model. **Note that observations must be added in chronological order.** The `observe` method takes:\n",
    "\n",
    "- a list containing the items that _won_ the comparison (`winners`)\n",
    "- a list containing the items that _lost_ the comparison (`losers`)\n",
    "- the time of the observation (`t`)\n",
    "\n",
    "When `winners` or `losers` contains more than one item, `kickscore` considers the _sum of the corresponding items' skill_."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# At first, Jerry beats Tom a couple of times.\n",
    "model.observe(winners=[\"Jerry\"], losers=[\"Tom\"], t=0.0)\n",
    "model.observe(winners=[\"Jerry\"], losers=[\"Tom\"], t=0.9)\n",
    "\n",
    "# Then, Tom beats Spike, and then Jerry.\n",
    "model.observe(winners=[\"Tom\"], losers=[\"Spike\"], t=1.7)\n",
    "model.observe(winners=[\"Tom\"], losers=[\"Jerry\"], t=2.1)\n",
    "\n",
    "# Finally, Jerry beats Tom, and then Tom + Spike.\n",
    "model.observe(winners=[\"Jerry\"], losers=[\"Tom\"], t=3.0)\n",
    "model.observe(winners=[\"Jerry\"], losers=[\"Tom\", \"Spike\"], t=3.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to fit the model (i.e., infer the skill parameters over time)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 1, max diff: 0.69315\n",
      "iteration 2, max diff: 0.80824\n",
      "iteration 3, max diff: 0.11764\n",
      "iteration 4, max diff: 0.04363\n",
      "iteration 5, max diff: 0.00419\n",
      "iteration 6, max diff: 0.00166\n",
      "iteration 7, max diff: 0.00027\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Analyzing the results\n",
    "\n",
    "We can get a good understanding of what the model learned by plotting the skill as a function of time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAz4AAAEyCAYAAAA7lgWKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1281ea908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot_scores([\"Tom\", \"Jerry\", \"Spike\"], figsize=(14, 5));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As `kickscore` learns a posterior _distribution_ over the skills, we represent the mean skill (solid line) as well as the region corresponding to one standard deviation (the shaded area).\n",
    "\n",
    "Notice the following:\n",
    "\n",
    "- the skill of Tom is not smooth over time. Notice how the bends happen at moments corresponding to observations involving Tom.\n",
    "- in contrast, the skill of Jerry varies smoothly.\n",
    "- The skill of Spike is constant, as expected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also use the model to make predictions for any combination of items, at any time point."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chances that Jerry beats Tom at t = 4.0: 73.0%\n",
      "Chances that Jerry beats Tom at t = 2.0: 47.1%\n",
      "Chances that Jerry beats Tom at t = -1.0: 70.3%\n"
     ]
    }
   ],
   "source": [
    "# We can predict a future outcome...\n",
    "p_win, p_los = model.probabilities([\"Jerry\"], [\"Tom\"], t=4.0)\n",
    "print(\"Chances that Jerry beats Tom at t = 4.0: {:.1f}%\".format(100*p_win))\n",
    "\n",
    "# ... or simulate what could have happened in the past.\n",
    "p_win, p_los = model.probabilities([\"Jerry\"], [\"Tom\"], t=2.0)\n",
    "print(\"Chances that Jerry beats Tom at t = 2.0: {:.1f}%\".format(100*p_win))\n",
    "\n",
    "p_win, p_los = model.probabilities([\"Jerry\"], [\"Tom\"], t=-1.0)\n",
    "print(\"Chances that Jerry beats Tom at t = -1.0: {:.1f}%\".format(100*p_win))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, note that we had to make quite a few choices when we set up the model.\n",
    "In particular, we had to explicitly choose the kernel functions and their (hyper)paramaters.\n",
    "\n",
    "A principled way to compare various models and to eventually select the best one is to compare the log-marginal likelihood of the data (the higher, the better)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.050817554668693"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.log_likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can go back and change the kernels & their parameters. Can you find a better model than the one we picked?"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}