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DataPhilly July 2016 Introduction to Probabilistic Programming
{
"cells": [
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"source": [
"To build these slides:"
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"[NbConvertApp] Converting notebook ./DataPhilly July 2016 Introduction to Probabilistic Programming.ipynb to slides\n",
"[NbConvertApp] Writing 561178 bytes to ./dataphilly-jul2016.slides.html\n"
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"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"
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"outputs": [],
"source": [
"%matplotlib inline"
]
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{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true,
"slideshow": {
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"outputs": [],
"source": [
"from __future__ import division"
]
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{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true,
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"outputs": [],
"source": [
"from IPython.display import Image"
]
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{
"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"
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"outputs": [],
"source": [
"blue, green, red, purple, gold, teal = sns.color_palette()"
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{
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"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": [
"<img src='./img/probabilistic_programming.png'>"
]
},
{
"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": [
"<img src=\"https://upload.wikimedia.org/wikipedia/commons/1/18/Bayes'_Theorem_MMB_01.jpg\" width=600>"
]
},
{
"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": [
"<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Monty_open_door.svg/640px-Monty_open_door.svg.png'>"
]
},
{
"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": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>p_open__0</th>\n",
" <th>p_open__1</th>\n",
" <th>p_open__2</th>\n",
" <th>prize</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>1.0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.0</td>\n",
" <td>0.5</td>\n",
" <td>0.5</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>1.0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
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" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
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"</table>\n",
"</div>"
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"text/plain": [
" p_open__0 p_open__1 p_open__2 prize\n",
"0 0.0 0.0 1.0 1\n",
"1 0.0 0.5 0.5 0\n",
"2 0.0 0.0 1.0 1\n",
"3 0.0 0.0 1.0 1\n",
"4 0.0 0.0 1.0 1"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"monty_trace_df.head()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"prize\n",
"0 0.3196\n",
"1 0.6804\n",
"dtype: float64"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(monty_trace_df.groupby('prize')\n",
" .size()\n",
" .div(monty_trace_df.shape[0]))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## [PyMC3](http://pymc-devs.github.io/pymc3/)\n",
"\n",
"> PyMC3 is a python module for Bayesian statistical modeling and model fitting which focuses on advanced Markov chain Monte Carlo fitting algorithms. 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": [
"<img src=\"https://media.giphy.com/media/3o72Fk4P77QS0zaS3e/giphy.gif\">"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## A/B Testing\n",
"\n",
"<img src=\"https://blog.mailerlite.com/wp-content/uploads/2015/06/ab-testing-blog.png\">"
]
},
{
"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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r6feG155n6JPn6JXvWP7XJifnjNW7qPTCw0N80qf8/IIK3+eVCAwMKFSzw+H0UTVSXp7v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\nAMMR1gAAGI6wBgDAcIQ1AACG+392EUIvT59s9QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff17fefa358>"
]
},
"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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ff72ysrKUmppaKcO6LH3yRHG9vJJt+ppVvbpo+fLleu211/TWW2+pRYsWV7w9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\nAMMR1gAAGI6wBgDAcIQ1AACG+392EUIvT59s9QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff17fefa358>"
]
},
"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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eeafhcFhRUZF27dqlYcOGBbewICgpKVFFRYWGDBnSsK1du3YaOHCg9uzZE8TK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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff17da31b00>"
]
},
"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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0kZo//6mzfpWEc7MtuEeMGKERI0bYNRwAoJV55JGHtGbNqobHZWVlDY8XLlwcrLKMw73K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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff17da31b00>"
]
},
"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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1I0lJSfj6+hIY2IeZM1/Gzc3N6PHEARTKIlIqHTt2lISEWN54YzGpqeeoXLky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\nsoiIiEn8Px5S5kImmtNEAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff17d8fdeb8>"
]
},
"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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1I0lJSfj6+hIY2IeZM1/Gzc3N6PHEARTKIlIqHTt2lISEWN54YzGpqeeoXLky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\nsoiIiEn8Px5S5kImmtNEAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff17d8fdeb8>"
]
},
"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": {
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tWLx4OampX/PxxxtYseItrFYLzZq1OON7IiMjiYqKITMzvc7j6ekn2bhxPffd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\nzyi9ugAdAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff18312d780>"
]
},
"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": [
"<matplotlib.figure.Figure at 0x7ff18312d780>"
]
},
"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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\nhBDCwf1/Q/Vtkesr9GkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff18312d278>"
]
},
"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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\nhBDCwf1/Q/Vtkesr9GkAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff18312d278>"
]
},
"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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\nBQAAAAAU3P8HG0KS05HIL/0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7ff17784a860>"
]
},
"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": [
"<matplotlib.figure.Figure at 0x7ff17784a860>"
]
},
"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": {
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