{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Intro to Bayes and QInfer\n", "\n", "In this notebook, we will introduce Bayesian parameter estimation and the sequential Monte Carlo algorithm implemented by **Qinfer**. To this end, suppose we have a coin that we do not know the bias $p$ of. We will guess what $p$ is by flipping the coin many times. \n", "\n", "If we knew the bias, we could determine the exact distribution of the number of \"Heads\" we would see. If we label the number of flips $N$ and the number of heads $n$, then the distribution of $n$ is of course a Binomial distribution\n", "$$\n", "\\operatorname{Pr}(n|p) = \\binom{N}{n} p^n (1-p)^{N-n}.\n", "$$\n", "\n", "Now suppose we have flipped the coin and $n$ heads did actually occur in $N$ flips. What is the distribution of $p|n$? The answer is given by Bayes' rule:\n", "$$\n", "\\operatorname{Pr}(n|p) = \\frac{\\operatorname{Pr}(n|p)\\operatorname{Pr}(p)}{\\operatorname{Pr}(n)},\n", "$$\n", "where $\\operatorname{Pr}(n|p)$ is called the likelihood function, $\\operatorname{Pr}(p)$ the prior, $\\operatorname{Pr}(p|n)$ the posterior and $\\operatorname{Pr}(n)$ is called the evidence. The likelihood function we have determined above. The prior is the input to the problem and the evidence can be determined by normalization of probability.\n", "\n", "The input, the prior, can be anything. A typical choice for generic problems is the uniform prior $\\operatorname{Pr}(p) = 1/V$, where $V$ is the volume of the parameter space, in this case $V = 1$ since the bias can be between 0 and 1. For the uniform prior, the posterior is\n", "$$\n", "\\operatorname{Pr}(p|n) = \\frac{p^n (1-p)^{N-n}}{B(n+1,N-n+1)},\n", "$$\n", "where $B$ is the Beta function.\n", "\n", "For more complicated models, such an analytic solution is not obtainable and we must turn to numerical algorithms. The algorithm we use is called sequential Monte Carlo or the particle filter. We begin by drawing $k$ samples $\\{p_i\\}$ from the prior and approximating it as\n", "$$\n", "\\operatorname{Pr}(p) = \\frac{1}{k}\\sum_{i=1}^k \\delta(p-p_i).\n", "$$\n", "The samples are called particles. Each particle is associated a weight $w_i$ which is conventionally set to be $1/k$ initially. The weights are updated via Bayes rule as follows:\n", "$$\n", "w_i(n) \\mapsto \\Pr(n|p_i)/k.\n", "$$\n", "The set of weights $\\{w_i(n)\\}$ are not normalized so we make one final assignment\n", "$$\n", "w_i(n) \\mapsto \\frac{w_i(n)}{\\sum_j w_j(n)}.\n", "$$\n", "Then the posterior is approximated by\n", "$$\n", "\\operatorname{Pr}(p) = \\sum_{i=1}^k w_i(n) \\delta(p-p_i).\n", "$$\n", "\n", "That's it; that's the basics! Now we will go through it a little more slowly using numpy, scipy and qinfer." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Preamble\n", "\n", "Here we import all the necessary modules as well as make the code compatible with Python 2.7." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\Anaconda3\\envs\\py35\\lib\\site-packages\\IPython\\parallel.py:13: ShimWarning: The IPython.parallel package has been deprecated. You should import from ipyparallel instead.\n", " \"You should import from ipyparallel instead.\", ShimWarning)\n", "C:\\Anaconda3\\envs\\py35\\lib\\site-packages\\qinfer\\parallel.py:52: UserWarning: Could not import IPython parallel. Parallelization support will be disabled.\n", " \"Could not import IPython parallel. \"\n" ] } ], "source": [ "from __future__ import division, print_function\n", "\n", "import qinfer as qi\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline\n", "# Use nice plotting defaults if available.\n", "try: plt.style.use('ggplot')\n", "except: pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Flipping coins" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we flip our coin 10 times. What does $\\operatorname{Pr}(n|p)$ look like?" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Create a variable for the number of flips (go ahead and change this if you want).\n", "N = 10\n", "# This creates an array containing [0, 1, ..., N].\n", "n = np.arange(0, N + 1)\n", "\n", "# This sets up the figure as an matrix of subfigures with 1 row and 3 columns.\n", "fig, axarr = plt.subplots(1, 3, figsize=(15, 5))\n", "# This is the probability mass function (pmf) of the binomial distribution for p = 0.\n", "dist = sp.stats.binom.pmf(n, N, 0)\n", "# On the first (0 indexed!) subplot, make a bar plot with x-axis given by the array n and y-axis given by the pmf.\n", "axarr[0].bar(n, dist)\n", "\n", "# The rest is just annotation and repeating for different biases.\n", "axarr[0].set_xlabel(\"$n$\")\n", "axarr[0].set_ylabel(\"$\\operatorname{Pr}(n|p)$\")\n", "axarr[0].set_title(\"$p=0$\")\n", "\n", "dist = sp.stats.binom.pmf(n, N, 0.1)\n", "axarr[1].bar(n, dist)\n", "axarr[1].set_xlabel(\"$n$\")\n", "axarr[1].set_title(\"$p=0.1$\")\n", "\n", "dist = sp.stats.binom.pmf(n, N, 0.5)\n", "axarr[2].bar(n, dist)\n", "axarr[2].set_xlabel(\"$n$\")\n", "axarr[2].set_title(\"$p=0.5$\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In reality, we often have data, in this case $n$, so we are interested not in $\\operatorname{Pr}(n|p)$ but in $\\operatorname{Pr}(p|n)$. We still use $\\operatorname{Pr}(n|p)$ in Bayes' rule but think of it as a function of $p$ for fixed data $n$. Below we plot what that looks like." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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11lvIGvc1jCs8FuCZftEwcix28wZQgU6CSHj8hPWk6BhvU0m3/gIkIhIqZs+e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4YtG7EvT3cdR0Qk8lWr5jqBVFFxdevj/eQ22LgWO0dXURMRKSu79DU4WozpO8h1FJGIZfoPhX17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\niIgGXXFxM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CvreBw5coRZs2aRkpJCSkoKn3/+OVOnTqVevXoMHDjQ8b05fQUFBWRnZ5Ob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\nBp2IiIiIiIiIiIhD/w9td9Djp3PpOAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ " # This creates an array with 100 values between 0 and 1.\n", "p = np.linspace(0, 1, 100)\n", "\n", "fig, axarr = plt.subplots(1, 3, figsize=(15,5))\n", "likelihood = sp.stats.binom.pmf(0, N, p)\n", "axarr[0].plot(p, likelihood)\n", "axarr[0].set_xlabel(\"$p$\")\n", "axarr[0].set_ylabel(\"$\\operatorname{Pr}(n|p)$\")\n", "axarr[0].set_title(\"$n=0$\")\n", "\n", "likelihood = sp.stats.binom.pmf(1, N, p)\n", "axarr[1].plot(p, likelihood)\n", "axarr[1].set_xlabel(\"$p$\")\n", "axarr[1].set_title(\"$n=1$\")\n", "\n", "likelihood = sp.stats.binom.pmf(5, N, p)\n", "axarr[2].plot(p, likelihood)\n", "axarr[2].set_xlabel(\"$p$\")\n", "axarr[2].set_title(\"$n=5$\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "Bayes' rule states:\n", "$$\n", "\\operatorname{Pr}(p|n) = \\frac{\\operatorname{Pr}(n|p)\\operatorname{Pr}(p)}{\\operatorname{Pr}(n)} = \\frac{p^n (1-p)^{N-n}}{B(n+1,N-n+1)},\n", "$$\n", "For the uniform prior $\\operatorname{Pr}(p) = 1$. Since this is just proportional to $\\operatorname{Pr}(p|n)$ we should expect the posterior to look the same.\n", "\n", "(Note that $\\operatorname{Pr}(p|n)$ is not strictly a probability, but a density, or measure, and can be greater than 1 for any particular value of $p$ since only questions about the probability over intervals return non-zero answers.)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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/8o0+n8e/kZ7okzP89Zkm5AtyKSkpkqTm5ubur0/fHzVq1DnPnTVrVq8d19LS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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Rather than write it out many times, we define a function to compute the posterior which compresses further code.\n", "def posterior(p, n, N):\n", " return p ** n * (1 - p) ** (N - n) / sp.special.beta(n + 1, N - n + 1)\n", "\n", "# Note that notebooks have access to the variables defined in previous run cells, so we do not need to redefine N and p.\n", "fig, axarr = plt.subplots(1, 3, figsize=(15, 5))\n", "axarr[0].plot(p, posterior(p, 0, N))\n", "axarr[0].set_xlabel(\"$p$\")\n", "axarr[0].set_ylabel(\"$\\operatorname{Pr}(p|n)$\")\n", "axarr[0].set_title(\"$n=0$\")\n", "\n", "axarr[1].plot(p, posterior(p, 1, N))\n", "axarr[1].set_xlabel(\"$p$\")\n", "axarr[1].set_title(\"$n=1$\")\n", "\n", "axarr[2].plot(p, posterior(p, 5, N))\n", "axarr[2].set_xlabel(\"$p$\")\n", "axarr[2].set_title(\"$n=5$\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### QInfer\n", "\n", "Now we will demonstrate how to use qinfer to get a numerical approximation to the posterior. The first task is create a Model." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# We create a model which is abstracted by the Model class, which already implements common methods \n", "# among models and templates what such a class needs to look like\n", "\n", "class CoinFlipsModel(qi.FiniteOutcomeModel):\n", " \n", " # This function is called when an instance of this class is instantiated.\n", " def __init__(self):\n", " # Make sure all the necessary functionality in the Model class is brought over.\n", " super(CoinFlipsModel, self).__init__()\n", " \n", " # The following are functions that are required for the functionality of QInfer.\n", " \n", " @property\n", " def n_modelparams(self):\n", " # The dimension of the parameter space.\n", " return 1 # In this case, it is just the bias p.\n", " \n", " @property\n", " def expparams_dtype(self):\n", " # many models will have complicated experiment design descriptions. Here, it is just the number of flips.\n", " return int # The number of flips is an integer.\n", " \n", " @property\n", " def is_n_outcomes_constant(self):\n", " # We tell QInfer that the number of outcomes\n", " # depends on which experiment we want to perform.\n", " return False\n", " \n", " def n_outcomes(self, expparams):\n", " # The number of outcomes are needed to numerically simulate experiments.\n", " return expparams + 1 # the number of flips + 1\n", " \n", " def are_models_valid(self, modelparams):\n", " # Make sure any boundaries in the parameter space are respected.\n", " # In this case, the modelparams array is a bias, which must be between 0 and 1.\n", " return np.logical_or(modelparams >= 0, modelparams <= 1)[:, 0]\n", " \n", " def likelihood(self, outcomes, modelparams, expparams):\n", " # Finally, we calculate the likelihood function\n", " # Again, call some necessary internal functions.\n", " super(CoinFlipsModel,self).likelihood(outcomes, modelparams, expparams)\n", " \n", " # The tensor storing the values of the likelihood has the following expected shape.\n", " like = np.zeros([outcomes.shape[0], modelparams.shape[0], 1])\n", " \n", " # scipy.stats.binom can vectorize over one of its arguments so we'll have to loop over the other\n", " for idx in range(outcomes.shape[0]):\n", " like[idx] = sp.stats.binom.pmf(outcomes[idx], expparams, modelparams)\n", " \n", " return like" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that is a bit overkill for such a simple problem, but the functionality is there really for more \"interesting\" models. But we can see that calling model.likelihood gives the correct results." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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11lvIGvc1jCs8FuCZftEwcix28wZQgU6CSHj8hPWk6BhvU0m3/gIkIhIqZs+e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4YtG7EvT3cdR0Qk8lWr5jqBVFFxdevj/eQ22LgWO0dXURMRKSu79DU4WozpO8h1FJGIZfoPhX17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\niIgGXXFxM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CvreBw5coRZs2aRkpJCSkoKn3/+OVOnTqVevXoMHDjQ8b05fQUFBWRnZ5Ob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\nBp2IiIiIiIiIiIhD/w9td9Djp3PpOAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "model = CoinFlipsModel() # This instantiates the model we just defined.\n", "\n", "# Recall that model.expparams_dtype was int and we defined N to be an integer above.\n", "expparams = np.array([N], dtype=int)\n", "# In the model we asked for outcomes.shape[0], so we have to define it as an object with a shape!\n", "outcome = np.array([0])\n", "\n", "fig, axarr = plt.subplots(1, 3, figsize=(15, 5))\n", "# Note that modelparams are expected to have at least 2D shape;\n", "# indexing by None adds an axis to the (100,) array we defined above for p.\n", "axarr[0].plot(p, model.likelihood(outcome, p[:, None], expparams)[0, :, 0]) \n", "axarr[0].set_xlabel(\"$p$\")\n", "axarr[0].set_ylabel(\"$\\operatorname{Pr}(n|p)$\")\n", "axarr[0].set_title(\"$n=0$\")\n", "\n", "outcome = np.array([1])\n", "axarr[1].plot(p, model.likelihood(outcome, p[:, None], expparams)[0, :, 0])\n", "axarr[1].set_xlabel(\"$p$\")\n", "axarr[1].set_title(\"$n=1$\")\n", "\n", "outcome = np.array([5])\n", "axarr[2].plot(p, model.likelihood(outcome, p[:, None], expparams)[0, :, 0])\n", "axarr[2].set_xlabel(\"$p$\")\n", "axarr[2].set_title(\"$n=5$\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "The next step is creating a distribution. For most (and by most, I mean nearly all) distributions used in practice, there is built-in functionality. In particular, the uniform prior discussed above is defined in QInfer as follows. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 0.61395162]]\n" ] } ], "source": [ "# This instantiates the built-in uniform prior over the interval [0, 1].\n", "prior = qi.UniformDistribution([0, 1])\n", "# prior.sample() returns a single randomly drawn sample.\n", "print(prior.sample())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The last thing to do is define an SMCUpdater which implements the sequential Monte Carlo algorithm. An SMCUpdater takes a model and prior and then its update function takes data and experiment parameters to produce the posterior distribution. The number of particles used controls the approximation." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# The number of particles we will use.\n", "n_particles = 1000\n", "\n", "# Instantiates an updater, takes the model and prior we defined above.\n", "updater = qi.SMCUpdater(model, n_particles, prior)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "OK, now we can plug in some data and see how well it does." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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4BCw/QgjAyQVwcoGoWQ/o0AMyOhLy9G+Qpw5nJ4P2jhD1m0E0bJE9xZHTGomISj0mZERE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EbxdKyMsLcNPUnCNhw81s6uulYqjrZxoLGNTxvaOBp1DvAHfDAqHKIwJ4XRWSFGhIOMDKcwMjNI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\n9bz66qvce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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# In the model we asked for outcomes.shape[0], so we have to define it as an object with a shape!\n", "outcome = np.array([5])\n", "\n", "# Call the update function to change the state of the updater, now it stores the posterior.\n", "updater.update(outcome, expparams)\n", "\n", "plt.figure(figsize=(10, 5))\n", "\n", "plt.plot(p, posterior(p, 5, N), label = 'True Posterior')\n", "updater.plot_posterior_marginal(smoothing=0.075, other_plot_args={'label': 'QInfer approximation'})\n", "\n", "plt.xlabel(\"$p$\")\n", "plt.ylabel(\"$\\operatorname{Pr}(n|p)$\")\n", "\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Not bad! Now go forth and multiply... likelihoods by priors." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "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": "3.5.2" }, "widgets": { "state": {}, "version": "1.1.1" } }, "nbformat": 4, "nbformat_minor": 0 }