{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Posterior Predictive Checks\n", "\n", "PPCs are a great way to validate a model. The idea is to generate data sets from the model using parameter settings from draws from the posterior. \n", "\n", "Elaborating slightly one can say that - Posterior predictive checks (PPCs) analyze the degree to which data generated from the model deviate from data generated from the true distribution. So often you'll want to know if for example your posterior distribution is approximating your underlying distribution. The visualization aspect of this model evaluation method is also great for a 'sense check' or explaining your model to others and getting criticism. \n", "\n", "\n", "`PyMC3` has random number support thanks to [Mark Wibrow](https://github.com/mwibrow) as implemented in [PR784](https://github.com/pymc-devs/pymc3/pull/784).\n", "\n", "Here we will implement a general routine to draw samples from the observed nodes of a model." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import pymc3 as pm\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "from collections import defaultdict" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets generate a very simple model:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 5000 of 5000 complete in 2.5 sec" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/Users/santon/anaconda/envs/pymc3/lib/python2.7/site-packages/theano/scan_module/scan_perform_ext.py:135: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n", " from scan_perform.scan_perform import *\n" ] } ], "source": [ "data = np.random.randn(100)\n", "\n", "with pm.Model() as model: \n", " mu = pm.Normal('mu', mu=0, sd=1, testval=0)\n", " sd = pm.HalfNormal('sd', sd=1)\n", " n = pm.Normal('n', mu=mu, sd=sd, observed=data)\n", " \n", " step = pm.NUTS()\n", " trace = pm.sample(5000, step)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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S7qTHmzlzps/bWCwWvvnmm25sjW+VtW2obWmHzmhBijzwvkmRMJqtYBg7xMLw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2yEOJjMNrz7eSEYAI/dN5oSLoSAaJkYa5dNxKv/PocPTpTAYmEx7/YU6jpIAm7o0KF48MEHsWDB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YuO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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This function will randomly draw 50 samples of parameters from the trace. Then, for each sample, it will draw 100 random numbers from a normal distribution specified by the values of `mu` and `std` in that sample." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "ppc = pm.sample_ppc(trace, samples=500, model=model, size=100)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, `ppc` contains 500 generated data sets (containing 100 samples each), each using a different parameter setting from the posterior:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(500, 100)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.asarray(ppc['n']).shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One common way to visualize is to look if the model can reproduce the patterns observed in the real data. For example, how close are the inferred means to the actual sample mean:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plt.subplot()\n", "sns.distplot([n.mean() for n in ppc['n']], kde=False, ax=ax)\n", "ax.axvline(data.mean())\n", "ax.set(title='Posterior predictive of the mean', xlabel='mean(x)', ylabel='Frequency');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Comparison between PPC and other model evaluation methods. \n", "An excellent introduction to this is given on [Edward](http://edwardlib.org/tut_PPC) and since I can't write this acny better I'll just quote this. \n", "\"PPCs are an excellent tool for revising models, simplifying or expanding the current model as one examines how well it fits the data. They are inspired by prior checks and classical hypothesis testing, under the philosophy that models should be criticized under the frequentist perspective of large sample assessment.\n", "\n", "PPCs can also be applied to tasks such as hypothesis testing, model comparison, model selection, and model averaging. It’s important to note that while they can be applied as a form of Bayesian hypothesis testing, hypothesis testing is generally not recommended: binary decision making from a single test is not as common a use case as one might believe. We recommend performing many PPCs to get a holistic understanding of the model fit.\" \n", "\n", "An important lesson to learn as someone using Probabilistic Programming is to not overfit your understanding or your criticism of models to only one metric. Model evaluation is a skill that can be honed with practice. \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prediction\n", "\n", "The same pattern can be used for prediction. Here we're building a logistic regression model. Note that since we're dealing the full posterior, we're also getting uncertainty in our predictions for free." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Use a theano shared variable to be able to exchange the data the model runs on\n", "from theano import shared" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def invlogit(x):\n", " return np.exp(x) / (1 + np.exp(x))\n", "\n", "n = 4000\n", "n_oos = 50\n", "coeff = 1.\n", "\n", "predictors = np.random.normal(size=n)\n", "# Turn predictor into a shared var so that we can change it later\n", "predictors_shared = shared(predictors)\n", "\n", "outcomes = np.random.binomial(1, invlogit(coeff * predictors))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([1, 1, 0, ..., 0, 1, 1])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "outcomes" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "predictors_oos = np.random.normal(size=50)\n", "outcomes_oos = np.random.binomial(1, invlogit(coeff * predictors_oos))" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 500 of 500 complete in 2.9 sec" ] } ], "source": [ "def tinvlogit(x):\n", " import theano.tensor as t\n", " return t.exp(x) / (1 + t.exp(x))\n", "\n", "with pm.Model() as model:\n", " coeff = pm.Normal('coeff', mu=0, sd=1)\n", " p = tinvlogit(coeff * predictors_shared)\n", "\n", " o = pm.Bernoulli('o', p, observed=outcomes)\n", " \n", " start = pm.find_MAP()\n", " step = pm.NUTS(scaling=start)\n", " trace = pm.sample(500, step)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Changing values here will also change values in the model\n", "predictors_shared.set_value(predictors_oos)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Simply running PPC will use the updated values and do prediction\n", "ppc = pm.sample_ppc(trace, model=model, samples=500)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Mean predicted values plus error bars to give sense of uncertainty in prediction" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Wedwu+XzM24DcRCIHYBurqnd1SeKG0Xk//KmX/i9NUcEqK+8Ym+4QbIFL6wBs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\ne3e6Q8p4mzdv1sKFC9MdRsb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.errorbar(x=predictors_oos, y=np.asarray(ppc['o']).mean(axis=0), yerr=np.asarray(ppc['o']).std(axis=0), linestyle='', marker='o')\n", "plt.plot(predictors_oos, outcomes_oos, 'o')\n", "plt.ylim(-.05, 1.05)\n", "plt.xlabel('predictor')\n", "plt.ylabel('outcome')" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "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": 1 }