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   "source": [
    "# GLM: Linear regression\n",
    "\n",
    "Author: Thomas Wiecki\n",
    "\n",
    "This tutorial is adapted from a [blog post by Thomas Wiecki called \"The Inference Button: Bayesian GLMs made easy with PyMC3\"](http://twiecki.github.io/blog/2013/08/12/bayesian-glms-1/).\n",
    "\n",
    "This tutorial appeared as a post in a small series on Bayesian GLMs on my blog:\n",
    "\n",
    "  1. [The Inference Button: Bayesian GLMs made easy with PyMC3](http://twiecki.github.com/blog/2013/08/12/bayesian-glms-1/)\n",
    "  2. [This world is far from Normal(ly distributed): Robust Regression in PyMC3](http://twiecki.github.io/blog/2013/08/27/bayesian-glms-2/)\n",
    "  3. [The Best Of Both Worlds: Hierarchical Linear Regression in PyMC3](http://twiecki.github.io/blog/2014/03/17/bayesian-glms-3/)\n",
    "  \n",
    "In this blog post I will talk about:\n",
    "\n",
    "  - How the Bayesian Revolution in many scientific disciplines is hindered by poor usability of current Probabilistic Programming languages.\n",
    "  - A gentle introduction to Bayesian linear regression and how it differs from the frequentist approach.\n",
    "  - A preview of [PyMC3](https://github.com/pymc-devs/pymc/tree/pymc3) (currently in alpha) and its new GLM submodule I wrote to allow creation and estimation of Bayesian GLMs as easy as frequentist GLMs in R.\n",
    "\n",
    "Ready? Lets get started!\n",
    "\n",
    "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/program/probabilistic-programming-for-advancing-machine-Learning)). \n",
    "\n",
    "This is mildly ironic because the beauty of Bayesian statistics is their generality. Frequentist stats have 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 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 *scientists* 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 of Bayesian Generalized Linear Models (GLMs) as easy as Frequentist ones in R.\n",
    "\n",
    "## Linear Regression\n",
    "\n",
    "While future blog posts will explore more complex models, I will start here with the simplest GLM -- linear regression.\n",
    "In general, frequentists think about Linear Regression as follows:\n",
    "\n",
    "$$ Y = X\\beta + \\epsilon $$\n",
    "\n",
    "where $Y$ is the output we want to predict (or *dependent* variable), $X$ is our predictor (or *independent* variable), and $\\beta$ are the coefficients (or parameters) of the model we want to estimate. $\\epsilon$ is an error term which is assumed to be normally distributed. \n",
    "\n",
    "We can then use Ordinary Least Squares or Maximum Likelihood to find the best fitting $\\beta$.\n",
    "\n",
    "## Probabilistic Reformulation\n",
    "\n",
    "\n",
    "Bayesians take a probabilistic view of the world and express this model in terms of probability distributions. Our above linear regression can be rewritten to yield:\n",
    "\n",
    "$$ Y \\sim \\mathcal{N}(X \\beta, \\sigma^2) $$\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 predictor with variance $\\sigma^2$.\n",
    "\n",
    "While this is essentially the same model, there are two critical advantages of Bayesian estimation:\n",
    "\n",
    " - Priors: We can quantify any prior knowledge we might have by placing priors on the paramters. For example, if we think that $\\sigma$ is likely to be small we would choose a prior with more probability mass on low values.\n",
    " - Quantifying uncertainty: We do not get a single estimate of $\\beta$ as above but instead a complete posterior distribution about how likely different values of $\\beta$ are. For example, with few data points our uncertainty in $\\beta$ will be very high and we'd be getting very wide posteriors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian GLMs in PyMC3\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",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "from pymc3 import  *\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "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 add data points by sampling from a Normal with the mean set to the regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "size = 200\n",
    "true_intercept = 1\n",
    "true_slope = 2\n",
    "\n",
    "x = np.linspace(0, 1, size)\n",
    "# y = a + b*x\n",
    "true_regression_line = true_intercept + true_slope * x\n",
    "# add noise\n",
    "y = true_regression_line + np.random.normal(scale=.5, size=size)\n",
    "\n",
    "data = dict(x=x, y=y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
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AOnXqRJcuXWjTpk25JlaA0aNHM2TIEBo1asRnn30WdDulVHS856Qbpq9keI+mvLhkS7lz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f412c6a3390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(7, 7))\n",
    "ax = fig.add_subplot(111, xlabel='x', ylabel='y', title='Generated data and underlying model')\n",
    "ax.plot(x, y, 'x', label='sampled data')\n",
    "ax.plot(x, true_regression_line, label='true regression line', lw=2.)\n",
    "plt.legend(loc=0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Estimating the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets fit a Bayesian linear regression model to this data. As you can see, model specifications in `PyMC3` are wrapped in a `with` statement. \n",
    "\n",
    "Here we use the awesome new [NUTS sampler](http://arxiv.org/abs/1111.4246) (our Inference Button) to draw 2000 posterior samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using ADVI...\n",
      "Average Loss = 175.98:   6%|▋         | 12609/200000 [00:00<00:11, 15847.31it/s]\n",
      "Convergence archived at 13800\n",
      "Interrupted at 13,800 [6%]: Average Loss = 359.45\n",
      "100%|██████████| 3500/3500 [00:04<00:00, 804.61it/s]\n"
     ]
    }
   ],
   "source": [
    "with Model() as model: # model specifications in PyMC3 are wrapped in a with-statement\n",
    "    # Define priors\n",
    "    sigma = HalfCauchy('sigma', beta=10, testval=1.)\n",
    "    intercept = Normal('Intercept', 0, sd=20)\n",
    "    x_coeff = Normal('x', 0, sd=20)\n",
    "    \n",
    "    # Define likelihood\n",
    "    likelihood = Normal('y', mu=intercept + x_coeff * x, \n",
    "                        sd=sigma, observed=y)\n",
    "    \n",
    "    # Inference!\n",
    "    trace = sample(3000, cores=2) # draw 3000 posterior samples using NUTS sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This should be fairly readable for people who know probabilistic programming. However, would my non-statistican friend know what all this does? Moreover, recall that this is an extremely simple model that would be one line in R. Having multiple, potentially transformed regressors, interaction terms or link-functions would also make this much more complex and error prone. \n",
    "\n",
    "The new `glm()` function instead takes a [Patsy](http://patsy.readthedocs.org/en/latest/quickstart.html) linear model specifier from which it creates a design matrix. `glm()` then adds random variables for each of the coefficients and an appopriate likelihood to the model. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using ADVI...\n",
      "Average Loss = 171.74:   7%|▋         | 13463/200000 [00:00<00:12, 14993.68it/s]\n",
      "Convergence archived at 14100\n",
      "Interrupted at 14,100 [7%]: Average Loss = 341.38\n",
      "100%|██████████| 3500/3500 [00:04<00:00, 809.71it/s]\n"
     ]
    }
   ],
   "source": [
    "with Model() as model:\n",
    "    # specify glm and pass in data. The resulting linear model, its likelihood and \n",
    "    # and all its parameters are automatically added to our model.\n",
    "    glm.GLM.from_formula('y ~ x', data)\n",
    "    trace = sample(3000, cores=2) # draw 3000 posterior samples using NUTS sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Much shorter, but this code does the exact same thing as the above model specification (you can change priors and everything else too if we wanted). `glm()` parses the `Patsy` model string, adds random variables for each regressor (`Intercept` and slope `x` in this case), adds a likelihood (by default, a Normal is chosen), and all other variables (`sigma`). Finally, `glm()` then initializes the parameters to a good starting point by estimating a frequentist linear model using [statsmodels](http://statsmodels.sourceforge.net/devel/).\n",
    "\n",
    "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`."
   ]
  },
  {
   "cell_type": "markdown",
   "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 the posterior distribution of our parameters and the individual samples we drew."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4122bcf908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wKeRXLFVEKwcjPbHij5Oqfth0yMaatIGllDoX+BAwD9ggIveJyIWTlkyjmc68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Mzt1S0ODh8ti9jHd/SB2nbq22PlNAy2WPrW9D54SeQGTWpLmCtl3T6OVFSGRLZLs9UwruZDUo58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\n2IKYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4129780940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 7))\n",
    "traceplot(trace[100:])\n",
    "plt.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The left side shows our marginal 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.\n",
    "\n",
    "There are a couple of things to see here. The first is that our sampling chains for the individual parameters (left side) seem well converged and stationary (there are no large drifts or other odd patterns).\n",
    "\n",
    "Secondly, the maximum posterior estimate of each variable (the peak in the left side distributions) is very close to the true parameters used to generate the data (`x` is the regression coefficient and `sigma` is the standard deviation of our normal)."
   ]
  },
  {
   "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 `plot_posterior_predictive_glm()` convenience function for this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tw8dgGk3jAdWE02NMR9tWWVkZYWFhHDlyZEgDkDL2qc+XVkeV5lgq6Q2X4Zho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\n2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YrycGQiIjIWbq3enG5WznPyk68tZvtbJWxbnsyvjl7iJ19bzMp5Tk+HJiIiY6Ce3jit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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f40fc05e8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(7, 7))\n",
    "plt.plot(x, y, 'x', label='data')\n",
    "plot_posterior_predictive_glm(trace, samples=100, \n",
    "                              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');"
   ]
  },
  {
   "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 of the lines."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " - Usability is currently a huge hurdle for wider adoption of Bayesian statistics.\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."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Further reading"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the first post of a small series on Bayesian GLMs I am preparing. Next week I will describe how the Student T distribution can be used to perform robust linear regression.\n",
    "\n",
    "Then there are also other good resources on Bayesian statistics:\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)"
   ]
  }
 ],
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