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# AustinRochford/dataphilly-jul2016.ipynb

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DataPhilly July 2016 Introduction to Probabilistic Programming
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 { "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "skip" } }, "source": [ "To build these slides:" ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[NbConvertApp] Converting notebook ./DataPhilly July 2016 Introduction to Probabilistic Programming.ipynb to slides\n", "[NbConvertApp] Writing 561178 bytes to ./dataphilly-jul2016.slides.html\n" ] } ], "source": [ "%%bash\n", "jupyter nbconvert \\\n", " --to=slides \\\n", " --reveal-prefix=https://cdnjs.cloudflare.com/ajax/libs/reveal.js/3.2.0/ \\\n", " --output=dataphilly-jul2016 \\\n", " ./DataPhilly\\ July\\ 2016\\ Introduction\\ to\\ Probabilistic\\ Programming.ipynb" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "from __future__ import division" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "from IPython.display import Image" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "from matplotlib import pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "import scipy as sp\n", "import seaborn as sns\n", "from theano import tensor as T" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "blue, green, red, purple, gold, teal = sns.color_palette()" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "plt.rc('figure', figsize=(8, 6))\n", "\n", "LABELSIZE = 14\n", "plt.rc('axes', labelsize=LABELSIZE)\n", "plt.rc('legend', fontsize=LABELSIZE)\n", "plt.rc('xtick', labelsize=LABELSIZE)\n", "plt.rc('ytick', labelsize=LABELSIZE)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "SEED = 2285280 # from random.org" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Introduction to Probabilistic Programming\n", "\n", "## DataPhilly\n", "\n", "## July 13, 2016\n", "\n", "### [@Austin Rochford](https://twitter.com/AustinRochford) ([arochford@monetate.com](mailto:arochford@monetate.com))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Probabilistic Programming\n", "\n", "* Programming with random variables\n", "* User specifies a generative model for the observed data\n", " * \"Tell the story\" of how the data were created\n", "* The language runtime/software library automatically performs inference" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### What do we mean by inference?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "* Maximum likelihood inference\n", "* Maxumum a posteriori inference\n", "* **Full posterior inference**" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Disease Testing" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "-" } }, "source": [ "A certain rare disease affects one in 10,000 people. A test for the disease gives the correct result 99.9% of the time." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "What is the probability that a given test is positive?" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "import pymc3 as pm\n", "\n", "with pm.Model() as pretest_disease_model:\n", " # This is our prior belief about whether or not the subject has the disease,\n", " # given its prevalence of the disease in the general population\n", " has_disease = pm.Bernoulli('has_disease', 1e-4)\n", " \n", " # This is the probability of a positive test given the presence or lack\n", " # of the disease\n", " p_positive = pm.Deterministic('p_positive',\n", " T.switch(T.eq(has_disease, 1),\n", " # If the subject has the disease,\n", " # this is the probability that the\n", " # test is positive\n", " 0.999,\n", " # If the subject does not have the\n", " # disease, this is the probability\n", " # that the test is negative\n", " 1 - 0.999))\n", " \n", " # This is the observed test result\n", " test_positive = pm.Bernoulli('test_positive', p_positive)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "samples = 40000" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 40000 of 40000 complete in 6.1 sec" ] } ], "source": [ "with pretest_disease_model:\n", " step = pm.Metropolis()\n", " pretest_disease_trace = pm.sample(samples, step, random_seed=SEED)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/plain": [ "array([0, 0, 0, ..., 0, 0, 0])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pretest_disease_trace['test_positive']" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "40000" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pretest_disease_trace['test_positive'].size" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The probability that a given test is positive is" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "0.001575" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "pretest_disease_trace['test_positive'].mean()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\n", "\\begin{align*}\n", "P(\\textrm{Test } +)\n", " = &\\ P(\\textrm{Test } +\\ |\\ \\textrm{Disease}) P(\\textrm{Disease}) \\\\\n", " & + P(\\textrm{Test } +\\ |\\ \\textrm{No disease}) P(\\textrm{No disease})\n", "\\end{align*}\n", "" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.0010998000000000008" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "0.999 * 1e-4 + (1 - 0.999) * (1 - 1e-4)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "If a subject tests positive, what is the probability they have the disease?" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "with pm.Model() as disease_model:\n", " # This is our prior belief about whether or not the subject has the disease,\n", " # given its prevalence of the disease in the general population\n", " has_disease = pm.Bernoulli('has_disease', 1e-4)\n", " \n", " # This is the probability of a positive test given the presence or lack\n", " # of the disease\n", " p_positive = pm.Deterministic('p_positive',\n", " T.switch(T.eq(has_disease, 1),\n", " # If the subject has the disease,\n", " # this is the probability that the\n", " # test is positive\n", " 0.999,\n", " # If the subject does not have the\n", " # disease, this is the probability\n", " # that the test is negative\n", " 1 - 0.999))\n", " \n", " # This is the observed positive test\n", " test_positive = pm.Bernoulli('test_positive', p_positive, observed=1)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 40000 of 40000 complete in 3.8 sec" ] } ], "source": [ "with disease_model:\n", " step = pm.Metropolis()\n", " disease_trace = pm.sample(samples, step, random_seed=SEED)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "The probability that someone who tests positive for the disease has it is" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "0.096775" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "disease_trace['has_disease'].mean()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "\n", "\\begin{align*}\n", "P(\\textrm{Disease}\\ |\\ \\textrm{Test }+)\n", " & = \\frac{P(\\textrm{Test }+\\ |\\ \\textrm{Disease}) P(\\textrm{Disease})}{P(\\textrm{Test }+)}\n", "\\end{align*}\n", "" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [ { "data": { "text/plain": [ "0.09083469721767587" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "0.999 * 1e-4 / (0.999 * 1e-4 + (1 - 0.999) * (1 - 1e-4))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## The Monty Hall Problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "If we select the first door and Monty opens the third to reveal a goat, should we change doors?" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "with pm.Model() as monty_model:\n", " # We have no idea where the prize is at the beginning\n", " prize = pm.DiscreteUniform('prize', 0, 2)\n", " \n", " # The probability that Monty opens each door\n", " p_open = pm.Deterministic('p_open',\n", " T.switch(T.eq(prize, 0), \n", " # If the prize is behind the first door,\n", " # he chooses to open one of the others\n", " # at random\n", " np.array([0., 0.5, 0.5]),\n", " T.switch(T.eq(prize, 1),\n", " # If it is behind the second door,\n", " # he must open the third door\n", " np.array([0., 0., 1.]),\n", " # If it is behind the third door,\n", " # he must open the second door\n", " np.array([0., 1., 0.]))))\n", " \n", " # Monty opened the third door, revealing a goat\n", " opened = pm.Categorical('opened', p_open, observed=2)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "samples = 10000" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 10000 of 10000 complete in 1.4 sec" ] } ], "source": [ "with monty_model:\n", " step = pm.Metropolis()\n", " monty_trace = pm.sample(samples, step, random_seed=SEED)\n", " \n", "monty_trace_df = pm.trace_to_dataframe(monty_trace)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "data": { "text/html": [ "
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Its flexibility and extensibility make it applicable to a large suite of problems." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Built on top of [theano](http://deeplearning.net/software/theano/)\n", "* Dynamic generation of C code for models\n", "* Automatic differentiation allows for gradient-based inference\n", " * Implements advanced Markov chain Monte carlo algorithms, such at the [No U-Turn Sampler](https://arxiv.org/abs/1111.4246)\n", " * Implements [automatic differentiation variational inference](http://arxiv.org/abs/1603.00788)\n", "* Interoperable with both [pandas](http://pandas.pydata.org/) and [patsy](https://patsy.readthedocs.io/en/latest/)\n", "* Provides clean support for multilevel models" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## A/B Testing\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Suppose variant A sees 510 visitors and 40 purchases, but variant B sees 505 visitors and 50 conversions." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Applied interval-transform to a_rate and added transformed a_rate_interval to model.\n", "Applied interval-transform to b_rate and added transformed b_rate_interval to model.\n" ] } ], "source": [ "with pm.Model() as ab_model:\n", " # A priori, we have no idea what the purchase rate for variant A will be\n", " a_rate = pm.Uniform('a_rate')\n", " # We observed 40 purchases from 510 visitors who saw variant A\n", " a_purchases = pm.Binomial('a_purchases', 510, a_rate, observed=40)\n", " \n", " # A priori, we have no idea what the purchase rate for variant B will be\n", " b_rate = pm.Uniform('b_rate')\n", " # We observed 40 purchases from 510 visitors who saw variant A\n", " b_purchases = pm.Binomial('b_purchases', 505, b_rate, observed=45)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "samples = 10000" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 10000 of 10000 complete in 3.2 sec" ] } ], "source": [ "with ab_model:\n", " step = pm.NUTS()\n", " ab_trace = pm.sample(samples, step, random_seed=SEED)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "BINS = 30\n", "\n", "ax.hist(np.clip(ab_trace['a_rate'], 0.03, 0.15),\n", " bins=BINS, normed=True, lw=0, alpha=0.75,\n", " label=\"Variant A\");\n", "ax.hist(np.clip(ab_trace['b_rate'], 0.03, 0.15),\n", " bins=BINS, normed=True, lw=0, alpha=0.75,\n", " label=\"Variant B\");\n", "\n", "ax.set_xlabel('Purchase rate');\n", "ax.set_yticklabels([]);\n", "ax.legend();" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "The probability that variant B is better than variant A is" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.7218" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(ab_trace['a_rate'] < ab_trace['b_rate']).mean()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Robust Regression" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "x = np.array([10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5])\n", "y = np.array([7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73])" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "scrolled": true, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.scatter(x, y, c='k', s=50);" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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eeafhcFhRUZF27dqlYcOGBbewICgpKVFFRYWGDBnSsK1du3YaOHCg9uzZE8TK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\nYII=\n", "text/plain": [ "" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "X = np.empty((x.size, 2))\n", "X[:, 0] = 1\n", "X[:, 1] = x\n", "\n", "coef, _, __, ___ = np.linalg.lstsq(X, y)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "plot_X = np.ones((100, 2))\n", "\n", "x_min, x_max = x.min() - 1, x.max() + 1\n", "plot_X[:, 1] = np.linspace(x_min, x_max, 100)" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false, "scrolled": true, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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KPj4+NGnSpMC2xo0bc+zYsWvet3r1Kri4OF/zdiXN29vD6BFMJScn\nhzVr1jBnzhy2bdsGgKurK9nZ2dSpU4f777+fuXPnXvbua/kvPafso3Wyn9bKPqVpnRwSym3btuXA\ngQMFth04cMCuN3udOZPpiBEcytvbg+TkNKPHMIX09HTefPMN4uKsHD58ELhU9hEePoFbb21BRsZp\n3N1r4unpxblzF4GLhs5rVnpO2UfrZD+tlX3MuE5X+yPBIaE8atQohgwZQmxsLH369GH37t0sXbqU\nyZMnO+LwYoDjx4/9WfaxiHPnrlz20bRpfdM94UVESiuHhHKrVq2YN28er776KlarlTp16jBx4kSG\nDBniiMNLCdq9exdWaxRr1rydX/bxxBPTGTVqnMo+RESKmcMavbp27UrXrl0ddTgpQZfKPj4gJiaa\nzz5T2YeIiFHUfV0KpKae49ChQ/j5+Tn06wgvXrzI6tUriY2NZu/ePQB07twFiyWCnj0DVfYhIlLC\nFMomdj0d09fj9OlTLF68gAUL4klOPomLiwsDBw4iPDySVq1uc+BvICIi10OhbGLX6pi+Xvv3/0Fc\n3DxWrFjG+fPn8fDw5NFHH2PcuFCVfYiImIBC2aSu1jG9detGUlOfs+tSts1mY9u2b7Bao9i8+T1s\nNhv16zcgJMTCsGHBuLuXns/viYiUdQplk7pax3RSUhKJiYdp0aLVFe+fk5PDxo0biImZy/fffwdA\n27btsFgi6dfvAVxc9E8vImI2+j+zSV2tY9rX15f69RsUer/09DSWL3+D+Hgrhw8fwsnJifvu60t4\neCTt23fAycmpuEcXEZEiUiiblKenF4GBfQq8pvyXwMA+l126Pn78GAkJsSxZsojU1HNUqlSJkSPH\nEhYWTpMmzS47hoiImI9C2cRmznwZoNB3X//l559/wmqNYu3a1eTk5FCrljfTpv0fo0aNo2bNmkaN\nLiIiRaBQNjE3Nzdmz36N1NTnSEw8TP36DfD09CIvL48PPtiC1RrN559/CkDz5jdjsUQycOAgKlWq\nZPDkIiJSFArlUsDT04sWLVpx4cIFli1bgtUaxW+//QrA3Xd3xWKJoEePe1T2ISJSyimUS4FTp06x\nePF8FiyIJyUlGRcXFx56aDAWS4TKPkREyhCF8v9ITT3HkSP78PT0dmilZVHs378Pq3UeK1cu5/z5\n83h6ehER8TjjxoVSt+61vxZTRERKF4Xyn4qr0vJ6XSr7+JqYmCi2bNmIzWajQQM/QkIsDB06QmUf\nIiJlmEL5T46utLxeOTk5vPfeemJi5rJz5/cAtGt3OxZLJH373q+yDxGRckD/p8dxlZZFkZ6exrJl\nS4iPt5KYeBgnJyd69+6HxRJJ+/Z3qexDRKQcUShz45WWRXHs2FESEmJ5443FpKaeo3LlyowePY7Q\n0HAaN27q0McSEZHSQaFM0Ssti+Lnn38kJiaKdeveIScnB29vH5566mlGjhxDjRoq+xARKc8Uylx/\npeX1ysvL48MPt2K1RvPFF58B4O9/C2FhEQwcOIiKFSve0PFFRKRsUCj/yZ5Ky+t14cIF3n77LWJj\no/PLPrp06U54eATdu/fS68UiIlKAQvlPf6+0TE8/hbt7zSKfIZ86dYpFixJYuDCBlJRkXF1dGTRo\nCGFhEbRs6djXpkVEpOxQKP8PT08vmjSpR3Jy2nXfd9++34mNvVT2ceHCBby8qjFhwiTGjg2hTp26\nxTCtiIiUJQrlG2Sz2fj66y+JjY1my5ZNf5Z9NCQ01MKQISNwd3c3ekQRESklFMpFlJOTw4YNa7Fa\no/jhh50A3H57AOHhkfTp0x9nZ2eDJxQRkdJGoXyd0tJSWbp0CQkJVo4cScTJyYk+ffrnl32IiIgU\nlULZTkePHskv+0hLS6VKlSqMGTOekJBwGjduYvR4IiJSBiiUr+Gnn34gJiaK9evXkJOTg49PbSIj\nH2fkyDFUr17D6PFERKQMUSgXIi8vj61bN2G1RvPll58DcMsttxIWFsGDDz6ssg8RESkWCuW/OX/+\nPKtWrWD+fCt79+4FoGvX7lgskXTv3lNlHyIiUqwUykBycjKLFiWwePF8UlJScHV1ZfDgoYSFRdCi\nRUujxxMRkXKiXIfy77//ll/2cfHixfyyj2nTJuPq6mH0eCIiUs6Uu1C22Wx89dUXWK1RbN26GYAG\nDRoSFhbOI48Mx93dHW9vjyI1eomIiNyIchPK2dnZrF+/Bqs1mp9++gGAO+64E4slkj59+qnsQ0RE\nDFfmQzk19Vx+2cfRo0eoUKEC/fo9gMUSQUBAe6PHExERyVdmQ/nIkUTi460sXfo66elpVKlShbFj\nQwgJCadRo8ZGjyciInKZMhfKP/64E6s1inXr1pCbm0vt2r489tgkgoNHq+xDRERMrUyEcl5eHu+/\nvwWrNYqvvvoCgFtuaYHFEsGAAQ+p7ENEREqFUh3K58+fZ+XKN4mLm8e+fb8D0K1bDyyWSLp166Gy\nDxERKVVKZSgnJyezcGE8ixfP59SpU7i6uvLII8MIC4vg1ltbGD2eiIhIkZSqUL5U9hHNypVvcvHi\nRapVq8Zjj01m7NgQfH3rGD2eiIjIDTF9KNtsNr788nOs1ijef38LAH5+DQkLe5RHHhlO1apVDZ5Q\nRETEMUwbyoWVfQQEtMdiiaR3774q+xARkTLHdKGcmnqON954nYQEK8eOHaVChQr07x+ExRLBHXfc\nafR4IiIixcY0oZyYeJj4eCvLli35s+yjKuPHhzF+vIWGDRsZPZ6IiEixMzyUd+78Dqs1ig0b1pGb\nm4uvbx0ef3wywcGjqVatutHjiYiIlBjDQ/nee7sDcOutLfPLPtzc3AyeSkREpOQZHsqBgfcxfryF\nLl26qexDRETKNcNDeenSlUaPICIiYgoVjB5ARERELlEoi4iImIRCWURExCQUyiIiIiahUBYRETEJ\nhbKIiIhJKJRFRERMQqEsIiJiEgplERERkyiWUI6NjcXf359//etfxXF4ERGRMsnhofzDDz+watUq\n/P39HX1oERGRMs2hoZyWlsbUqVOZOXMmHh4ejjy0iIhImefQUH766afp3bs37du3d+RhRUREygWH\nhfLKlStJTEzksccec9QhRUREyhWHfHXjgQMH+Pe//83y5ctxdnZ2xCFFRETKHSebzWa70YOsWbOG\n6dOnU6HCf0+8c3NzcXJywtnZmZ07d+Lq6nqjDyMiIlKmOSSU09PTSUpKKrDtySefpGHDhlgsFpo0\naXKjDyEiIlLmOeTytbu7O02bNi2wrXLlylSrVk2BLCIiYqdia/RycnIqrkOLiIiUSQ65fC0iIiI3\nTt3XIiIiJqFQFhERMQmFsoiIiEkolAuhb7m6uuTkZJ588kk6dOhA69at6devHzt27DB6LNPJy8vj\ntddeo2fPnrRu3ZqePXvy2muvkZeXZ/RohtqxYwcWi4UuXbrg7+/P2rVrL7tNVFQUd999N7fddhsj\nRoxg3759BkxqrKutU05ODq+88gr3338/bdu2pXPnzkyePJnjx48bOLFx7HlO/eXpp5/G39+fRYsW\nleCE9lMo/w99y9XVpaWlMWTIEJycnEhISGDTpk3MmDGDGjVqGD2a6cTHx/Pmm2/yj3/8g82bNzNj\nxgyWL19OXFyc0aMZKiMjg+bNmzNjxgwqV6582f74+HgWL17MM888w+rVq6lZsyajR48mMzPTgGmN\nc7V1unDhAnv37iU8PJw1a9ZgtVpJSkpi/Pjx5fKPvms9p/6yefNmdu3aRe3atUtwuutkk3ypqam2\nXr162b755hvb8OHDbf/85z+NHsl05syZYxsyZIjRY5QKoaGhtieffLLAtmnTptlCQ0MNmsh82rRp\nY1uzZk2BbZ06dbLFxcXl/3zhwgVb27ZtbW+99VZJj2caha3T/9q3b5/t5ptvtv32228lNJU5XWmt\njhw5YuvSpYvtjz/+sHXv3t22cOFCA6a7Np0p/42+5eraPvzwQ2677TYmTpxIx44dCQoKYtmyZUaP\nZUrt2rVj27Zt7N+/H4B9+/bxzTff0K1bN2MHM7HExERSUlLo2LFj/raKFSsSEBDAzp07DZzM/NLS\n0nBycsLT09PoUUwnNzeXyZMnEx4eTuPGjY0e56oc0uhVFvz1LVdz5swxehRTS0xMZPny5YwaNYrQ\n0FD27NnD888/D8CwYcMMns5cQkJCyMjIoG/fvjg7O5Obm0tYWBiPPPKI0aOZVkpKCk5OTtSqVavA\n9po1a3Ly5EmDpjK/7OxsXnzxRXr06GHuS7MGmTt3LjVq1GDw4MFGj3JNCmX0LVfXIy8vj9atWzNx\n4kQA/P39OXjwIMuXL1co/4/33nuP9evX8+qrr9K0aVP27NnDCy+8QL169Rg4cKDR45na/zYC2mw2\ntQReQW5uLlOmTCEjI6Pcv1+hMNu3b2fNmjWsW7fO6FHsolDm0pu7zp49S79+/fK35ebmsmPHDlas\nWKFvufobHx+fy/rMGzduzLFjxwyayLxeeeUVxo0bR+/evQFo1qwZR48eJT4+XqF8BbVq1cJms5Gc\nnFzgjO/06dOXnT3Lpf9PTZw4kX379rF06VK8vLyMHsl0tm/fTkpKCp07d87flpubyyuvvMLrr7/O\nJ598YtxwhVAoA/fccw+tWrUqsO3v33KlQP6vtm3bcuDAgQLbDhw4wE033WTQROZ1/vz5y87uKlSo\nUC7fHWuv+vXrU6tWLb766itatmwJwMWLF9mxYwdPPvmkwdOZS05OToFA1icgCjd06FDuu+++AtvG\njBlDv379GDRokEFTXZlCGX3L1fUYNWoUQ4YMITY2lj59+rB7926WLl3K5MmTjR7NdHr06EFCQgL1\n6tWjadOm/PLLLyxevJgBAwYYPZqhMjM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.scatter(x, y, c='k', s=50);\n", "ax.plot(plot_X[:, 1], plot_X.dot(coef),\n", " c='k', label='Least squares');\n", "\n", "ax.set_xlim(x_min, x_max);\n", "ax.legend(loc=2);" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Applied interval-transform to alpha and added transformed alpha_interval to model.\n", "Applied interval-transform to beta and added transformed beta_interval to model.\n" ] } ], "source": [ "with pm.Model() as ols_model:\n", " # alpha is the slope and beta is the intercept\n", " alpha = pm.Uniform('alpha', -100, 100)\n", " beta = pm.Uniform('beta', -100, 100)\n", " \n", " # Ordinary least squares assumes that the noise is normally distributed\n", " y_obs = pm.Normal('y_obs', alpha + beta * x, 1., observed=y)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": true, "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "samples = 10000" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 10000 of 10000 complete in 2.2 sec" ] } ], "source": [ "with ols_model:\n", " step = pm.Metropolis()\n", " ols_trace = pm.sample(samples, step, random_seed=SEED)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [], "source": [ "post_y = ols_trace['alpha'] + np.outer(plot_X[:, 1], ols_trace['beta'])" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false, "scrolled": false, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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tWLx4OampX/PxxxtYseItrFYLzZq1OON7IiMjiYqKITMzvc7j6ekn2bhxPffd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\n+CJXXDE27qenIRLGiYlJHac1DSIx0fL/RSIi0k8s/4k/b94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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.fill_between(plot_X[:, 1],\n", " np.percentile(post_y, 2.5, axis=1),\n", " np.percentile(post_y, 97.5, axis=1),\n", " color='gray', alpha=0.5,\n", " label='95% CI');\n", "ax.scatter(x, y, c='k', s=50);\n", "ax.plot(plot_X[:, 1], plot_X.dot(coef),\n", " c='k', label='Least squares');\n", "ax.plot(plot_X[:, 1], post_y.mean(axis=1),\n", " c='r', ls='--', label='PyMC3 least squares');\n", "\n", "ax.set_xlim(x_min, x_max);\n", "ax.legend(loc=2);" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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tWLx4OampX/PxxxtYseItrFYLzZq1OON7IiMjiYqKITMzvc7j6ekn2bhxPffd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\n+CJXXDE27qenIRLGiYlJHac1DSIx0fL/RSIi0k8s/4k/b94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"text/plain": [ "" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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ctrWugs6dLRCyWlm3rJUuUiBlTUwwRAIeKujITLJKUbImZIXUtA3CwrLISnBc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\nckpby+iwdvbZz83gSrBbEKHuwYS4BRHiFkSwWyAeRvcBF/FR27Nus5i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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "z = np.linspace(-4, 4, 100)\n", "\n", "ax.plot(z, sp.stats.norm.pdf(z),\n", " label='$N(0, 1)$');\n", "ax.plot(z, sp.stats.t.pdf(z, 3),\n", " label=r'$t(\\nu = 3)$');\n", "\n", "ax.set_xlabel('Residual');\n", "ax.set_yticklabels([]);\n", "ax.set_ylabel('Probability density');\n", "ax.legend();" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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ctrWugs6dLRCyWlm3rJUuUiBlTUwwRAIeKujITLJKUbImZIXUtA3CwrLISnBc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\nckpby+iwdvbZz83gSrBbEKHuwYS4BRHiFkSwWyAeRvcBF/FR27Nus5i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"text/plain": [ "" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Applied interval-transform to alpha and added transformed alpha_interval to model.\n", "Applied interval-transform to beta and added transformed beta_interval to model.\n" ] } ], "source": [ "with pm.Model() as robust_model:\n", " # alpha is the slope and beta is the intercept\n", " alpha = pm.Uniform('alpha', -100, 100)\n", " beta = pm.Uniform('beta', -100, 100)\n", " \n", " # t-distributed residuals are less sensitive to outliers\n", " y_obs = pm.StudentT('y_obs', nu=3., mu=alpha + beta * x, observed=y)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false, "scrolled": false, "slideshow": { "slide_type": "fragment" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 10000 of 10000 complete in 2.3 sec" ] } ], "source": [ "with robust_model:\n", " step = pm.Metropolis()\n", " \n", " robust_trace = pm.sample(samples, step, random_seed=SEED)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false, "slideshow": { "slide_type": "-" } }, "outputs": [], "source": [ "post_y_robust = robust_trace['alpha'] + np.outer(plot_X[:, 1], robust_trace['beta'])" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false, "scrolled": true, "slideshow": { "slide_type": "skip" } }, "outputs": [ { "data": { "image/png": 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bzWWhuLe3N5dc0uacPgPgwIEDvPLKq/z226/k5eU517SmpqY6k1GTyVQm/l9+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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (l_ax, r_ax) = plt.subplots(ncols=2, sharex=True, sharey=True, figsize=(16, 6))\n", "\n", "l_ax.fill_between(plot_X[:, 1],\n", " np.percentile(post_y, 2.5, axis=1),\n", " np.percentile(post_y, 97.5, axis=1),\n", " color='gray', alpha=0.5,\n", " label='95% CI');\n", "l_ax.scatter(x, y, c='k', s=50);\n", "l_ax.plot(plot_X[:, 1], plot_X.dot(coef),\n", " c='k', label='Least squares');\n", "l_ax.plot(plot_X[:, 1], post_y.mean(axis=1),\n", " c='r', ls='--', label='PyMC3 least squares');\n", "\n", "l_ax.set_xlim(x_min, x_max);\n", "l_ax.legend(loc=2);\n", "\n", "r_ax.fill_between(plot_X[:, 1],\n", " np.percentile(post_y_robust, 2.5, axis=1),\n", " np.percentile(post_y_robust, 97.5, axis=1),\n", " color='gray', alpha=0.5,\n", " label='95% CI');\n", "r_ax.scatter(x, y, c='k', s=50);\n", "r_ax.plot(plot_X[:, 1], post_y_robust.mean(axis=1),\n", " c=blue, label='PyMC3 robust');\n", "\n", "r_ax.set_xlim(x_min, x_max);\n", "r_ax.legend(loc=2);" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false, "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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bzWWhuLe3N5dc0uacPgPgwIEDvPLKq/z226/k5eU517SmpqY6k1GTyVQm/l9+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"text/plain": [ "" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Congressional Ideal Point Model" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": true, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "vote_data_uri = 'http://archive.ics.uci.edu/ml/machine-learning-databases/voting-records/house-votes-84.data'" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false, "slideshow": { "slide_type": "skip" } }, "outputs": [], "source": [ "N_BILLS = 16\n", "BILLS = list(range(N_BILLS))\n", "\n", "df = pd.read_csv(vote_data_uri, names=['party'] + BILLS)\n", "\n", "df.index.name = 'rep'\n", "\n", "df[df == 'n'] = 0\n", "df[df == 'y'] = 1\n", "df[df == '?'] = np.nan\n", "\n", "df.party, parties = df.party.factorize()\n", "\n", "N_REPS = df.shape[0]" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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