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@twiecki
Created August 6, 2013 14:16
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{
"metadata": {
"name": "GLM-blog-linear"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"The stuttering Bayesian Revolution"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There is a huge paradigm shift underway in many scientific disciplines: The Bayesian revolution. \n",
"\n",
"While the theoretical benefits of Bayesian over Frequentist stats have been discussed at length elsewhere (see *Further Reading* below), there is a major obstacle that hinders wider adoption -- usability (this is one of the reasons DARPA wrote out a huge grant to [improve Probabilistic Programming](http://www.darpa.mil/Our_Work/I2O/Programs/Probabilistic_Programming_for_Advanced_Machine_Learning_%28PPAML%29.aspx)). \n",
"\n",
"This is mildely ironic because the beauty of Bayesian statistics is it's generality. Frequentist stats has a bazillion different tests for every different scenario. In Bayesian land you define your model exactly as you think is appropriate and hit the *Inference Button(TM)* (i.e. running the magical MCMC sampling algorithm).\n",
"\n",
"Yet when I ask my colleagues why they use frequentist stats (even though they would like to use Bayesian stats) the answer is that frequentist software packages like SPSS or R make it very easy to run all those individuals tests with a single command (and more often then not they don't know the exact model and inference method being used). \n",
"\n",
"While there are great Bayesian software packages like [JAGS](http://mcmc-jags.sourceforge.net/), [BUGS](http://www.mrc-bsu.cam.ac.uk/bugs/), [Stan](http://mc-stan.org/) and [PyMC](http://pymc-devs.github.io/pymc/), they are written for Bayesians statisticians who know very well what model they want to build. \n",
"\n",
"Unfortunately, [\"The vast majority of statistical analysis is not performed by statisticians\"](http://simplystatistics.org/2013/06/14/the-vast-majority-of-statistical-analysis-is-not-performed-by-statisticians/) -- so what we really need are tools for *scientist* and not for statisticians.\n",
"\n",
"In the interest of putting my code where my mouth is I wrote a submodule for the upcoming [PyMC3](https://github.com/pymc-devs/pymc/tree/pymc3) that makes construction Bayesian Generalized Linear Model (GLM) as easy as the frequentist GLM in R.\n",
"\n",
"Generalized Linear Model\n",
"------------------------\n",
"\n",
"In general, frequentists think about a GLM as follows:\n",
"\n",
"$$ Y = f(X \\ast \\beta) + \\epsilon $$\n",
"\n",
"where $Y$ is the data we want to predict (or *dependent* variable), $X$ is our design matrix containing the predictors (or *independent* variables), $\\beta$ are the coefficients (or parameters) of our model we want to estimate. $\\epsilon$ is an error term which is often assumed to be normally distributed. Finally, $f$ is a link-function that turns this linear model into a *general* linear model. If we set $f$ to be the identity function (and assume Normal error) we get a linear regression. If we set $f$ to be a logistic function we get logistic regression.\n",
"\n",
"Bayesian Generalized Linear Model\n",
"---------------------------------\n",
"\n",
"Bayesians take a probabilistic view of the world and express this model in terms of probability distributions. For clarity I'm omitting the link function and write the case of the Bayesian linear regression:\n",
"\n",
"$$ Y \\sim \\mathcal{N}(X \\ast \\beta, \\epsilon^2) $$\n",
"\n",
"In words, we view $Y$ as a random variable (or random vector) of which each element (data point) is distributed according to a Normal distribution. The mean of this normal distribution is provided by our linear model with variance $\\epsilon^2$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Bayesian GLMs in PyMC3\n",
"----------------------\n",
"\n",
"With the new GLM module in PyMC3 it is very easy to build this and much more complex models.\n",
"\n",
"First, lets import the required modules."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from pymc import *\n",
"\n",
"# Data wrangling\n",
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"# Plotting\n",
"import matplotlib.pyplot as plt\n",
"from pandas.tools.plotting import scatter_matrix"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Generating data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create some toy data to play around with and scatter-plot it. \n",
"\n",
"Essentially we are creating a regression line defined by intercept and slope and adding data by moving over it with a Gaussian spray-can."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"size = 200\n",
"true_intercept = 1\n",
"true_slope = 2\n",
"\n",
"x = np.linspace(0, 1, size)\n",
"true_regression_line = true_intercept + true_slope * x\n",
"# y = a + b*x + noise\n",
"y = true_regression_line + np.random.normal(scale=.5, size=size)\n",
"\n",
"data = dict(x=x, y=y)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 32
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.figure(figsize=(7, 7))\n",
"plt.plot(x, y, 'x', label='sampled data')\n",
"plt.plot(x, true_regression_line, label='true regression line', lw=2.)\n",
"plt.legend(loc=0)\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.title('Generated data and underlying model')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 33,
"text": [
"<matplotlib.text.Text at 0x1407b66c>"
]
},
{
"metadata": {},
"output_type": "display_data",
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hjTfeQM+ePesnjuvZaa6iogLR0dH4+eef0alTp0AnxxD4/SMKLF2tZ7dgwQKk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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x13a25eac>"
]
}
],
"prompt_number": 33
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Estimating the model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets fit a linear model to this data. The new `glm()` function takes a [Patsy](http://patsy.readthedocs.org/en/latest/quickstart.html) linear model specifier from which it creates a design matrix. `PyMC3` then adds random variables for each of the coefficients to be estimated. \n",
"\n",
"Also by default, this function assumes `y` to be normally distributed. \n",
"\n",
"Here we use the state-of-the-art [NUTS sampler](http://arxiv.org/abs/1111.4246) to perform inference and draw 2000 posterior samples. Note that `glm` already initializes the model to a good starting point by estimating a frequentist linear model using [statsmodels](http://statsmodels.sourceforge.net/devel/)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"with Model() as model: # model specifications in PyMC3 are wrapped in a with-statement\n",
" glm.glm('y ~ x', data) # specify glm and pass in data. The resulting linear model and all its parameters are automatically added to our model.\n",
" step = NUTS() # Define MCMC sampling algorithm\n",
" trace = sample(2000, step, progressbar=False) # draw 10000 posterior samples using NUTS sampling"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 34
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you are not familiar with R's syntax, `'y ~ x'` specifies that we have an output variable `y` that we want to estimate as a linear function of `x`. By default, `Patsy` also adds an Intercept if we don't tell it not to.\n",
"\n",
"Note that this is the simplest model possible. You can get arbitrary complex as I will show in a future post."
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Analyzing the model"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Bayesian inference does not give us only one best fitting line (as maximum likelihood does) but rather a whole posterior distribution of likely parameters. Lets plot this posterior distribution and the individual samples we drew."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.figsize(12, 6)\n",
"traceplot(trace);\n",
"plt.tight_layout()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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tO1b4YunSpYUGFgBUr14dS5YssVwvMzMTCxcuROPGjTF69Gj85z//wf333++U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CQB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\nb2boHxAmtJ4AAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x14fed66c>"
]
}
],
"prompt_number": 35
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The left side shows our marginalized posterior. For each parameter value on the x-axis we get a probability on the y-axis that tells us how likely that parameter value is."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the GLM we thus do not only have one best fitting regression line, but many. A posterior predictive plot takes multiple samples from the posterior (intercepts and slopes) and plots a regression line for each of them. Here we are using the `glm.plot_posterior_predictive()` convenience function for this."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.figure(figsize=(7, 7))\n",
"plt.plot(x, y, 'x', label='data')\n",
"glm.plot_posterior_predictive(trace, samples=100, label='posterior predictive regression lines')\n",
"plt.plot(x, true_regression_line, label='true regression line', lw=3., c='y')\n",
"\n",
"plt.title('Posterior predictive regression lines')\n",
"plt.legend(loc=0)\n",
"plt.xlabel('x')\n",
"plt.ylabel('y');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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99983Huf1TExMePLJJ5k9ezZXrlwBIDk5mZ07dwLw8MMPs2rVKs6fP09+fn61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ISEUFZWRk1NDWazmeLiYjQazWxU2yd2k0y2O2uu3iwJwlw1Z8Kur6+P2NhYJBIJJ06c4L777qO1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\nSUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x150577ec>"
]
}
],
"prompt_number": 36
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, our estimated regression lines are very similar to the true regression line. But since we only have limited data we have *uncertainty* in our estimates, here expressed by the variability in the lines."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets look at the summary statistics of our posterior (`.describe()` is a `Pandas` method that runs commonly used summary stats)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"trace_to_dataframe(trace).describe()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Intercept</th>\n",
" <th>sigma</th>\n",
" <th>x</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td> 2000.000000</td>\n",
" <td> 2000.000000</td>\n",
" <td> 2000.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td> 0.953334</td>\n",
" <td> 0.502502</td>\n",
" <td> 2.081858</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td> 0.068899</td>\n",
" <td> 0.024445</td>\n",
" <td> 0.117116</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td> 0.728961</td>\n",
" <td> 0.430717</td>\n",
" <td> 1.696266</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td> 0.905576</td>\n",
" <td> 0.485796</td>\n",
" <td> 2.006499</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td> 0.955918</td>\n",
" <td> 0.501705</td>\n",
" <td> 2.081545</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td> 1.001403</td>\n",
" <td> 0.517717</td>\n",
" <td> 2.162936</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td> 1.177215</td>\n",
" <td> 0.604589</td>\n",
" <td> 2.511642</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 37,
"text": [
" Intercept sigma x\n",
"count 2000.000000 2000.000000 2000.000000\n",
"mean 0.953334 0.502502 2.081858\n",
"std 0.068899 0.024445 0.117116\n",
"min 0.728961 0.430717 1.696266\n",
"25% 0.905576 0.485796 2.006499\n",
"50% 0.955918 0.501705 2.081545\n",
"75% 1.001403 0.517717 2.162936\n",
"max 1.177215 0.604589 2.511642"
]
}
],
"prompt_number": 37
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, the posterior mean of each variable is very close to the true parameters used to generate the data (`x` is the regression coefficient and `sigma` is the noise)."
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Summary"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - GLMs have a natural probabilistic expression that allows them to be estimated in a Bayesian framework.\n",
" - `PyMC3` allows GLM specification with convenient syntax borrowed from R.\n",
" - Posterior predictive plots allow us to evaluate fit and our uncertainty in it.\n",
"\n",
"*Further reading*: \n",
"\n",
" - The excellent book [Doing Bayesian Data Analysis by John Kruschke](http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/).\n",
" - [Andrew Gelman's blog](http://andrewgelman.com/)\n",
" - [Baeu Cronins blog post on Probabilistic Programming](https://plus.google.com/u/0/107971134877020469960/posts/KpeRdJKR6Z1)"
]
}
],
"metadata": {}
}
]
}
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