{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Marginalized Gaussian Mixture Model\n",
    "\n",
    "Author: [Austin Rochford](http://austinrochford.com)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "SEED = 383561\n",
    "\n",
    "np.random.seed(SEED) # from random.org, for reproducibility"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gaussian mixtures are a flexible class of models for data that exhibits subpopulation heterogeneity.  A toy example of such a data set is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N = 1000\n",
    "\n",
    "W = np.array([0.35, 0.4, 0.25])\n",
    "\n",
    "MU = np.array([0., 2., 5.])\n",
    "SIGMA = np.array([0.5, 0.5, 1.])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "component = np.random.choice(MU.size, size=N, p=W)\n",
    "x = np.random.normal(MU[component], SIGMA[component], size=N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.5/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe35088abe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.hist(x, bins=30, normed=True, lw=0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A natural parameterization of the Gaussian mixture model is as the [latent variable model](https://en.wikipedia.org/wiki/Latent_variable_model)\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\mu_1, \\ldots, \\mu_K\n",
    "    & \\sim N(0, \\sigma^2) \\\\\n",
    "\\tau_1, \\ldots, \\tau_K\n",
    "    & \\sim \\textrm{Gamma}(a, b) \\\\\n",
    "\\boldsymbol{w}\n",
    "    & \\sim \\textrm{Dir}(\\boldsymbol{\\alpha}) \\\\\n",
    "z\\ |\\ \\boldsymbol{w}\n",
    "    & \\sim \\textrm{Cat}(\\boldsymbol{w}) \\\\\n",
    "x\\ |\\ z\n",
    "    & \\sim N(\\mu_z, \\tau^{-1}_i).\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "An implementation of this parameterization in PyMC3 is available [here](gaussian_mixture_model.ipynb).  A drawback of this parameterization is that is posterior relies on sampling the discrete latent variable $z$.  This reliance can cause slow mixing and ineffective exploration of the tails of the distribution.\n",
    "\n",
    "An alternative, equivalent parameterization that addresses these problems is to marginalize over $z$.  The marginalized model is\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\mu_1, \\ldots, \\mu_K\n",
    "    & \\sim N(0, \\sigma^2) \\\\\n",
    "\\tau_1, \\ldots, \\tau_K\n",
    "    & \\sim \\textrm{Gamma}(a, b) \\\\\n",
    "\\boldsymbol{w}\n",
    "    & \\sim \\textrm{Dir}(\\boldsymbol{\\alpha}) \\\\\n",
    "f(x\\ |\\ \\boldsymbol{w})\n",
    "    & = \\sum_{i = 1}^K w_i\\ N(x\\ |\\ \\mu_i, \\tau^{-1}_i),\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$N(x\\ |\\ \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2 \\pi} \\sigma} \\exp\\left(-\\frac{1}{2 \\sigma^2} (x - \\mu)^2\\right)$$\n",
    "\n",
    "is the probability density function of the normal distribution.\n",
    "\n",
    "Marginalizing $z$ out of the model generally leads to faster mixing and better exploration of the tails of the posterior distribution.  Marginalization over discrete parameters is a common trick in the [Stan](http://mc-stan.org/) community, since Stan does not support sampling from discrete distributions.  For further details on marginalization and several worked examples, see the [_Stan User's Guide and Reference Manual_](http://www.uvm.edu/~bbeckage/Teaching/DataAnalysis/Manuals/stan-reference-2.8.0.pdf).\n",
    "\n",
    "PyMC3 supports marginalized Gaussian mixture models through its `NormalMixture` class.  (It also supports marginalized general mixture models through its `Mixture` class.)  Below we specify and fit a marginalized Gaussian mixture model to this data in PyMC3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "with pm.Model() as model:\n",
    "    w = pm.Dirichlet('w', np.ones_like(W))\n",
    "    \n",
    "    mu = pm.Normal('mu', 0., 10., shape=W.size)\n",
    "    tau = pm.Gamma('tau', 1., 1., shape=W.size)\n",
    "    \n",
    "    x_obs = pm.NormalMixture('x_obs', w, mu, tau=tau, observed=x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using advi...\n",
      "Average ELBO = -6,663.8: 100%|██████████| 10000/10000 [00:06<00:00, 1582.50it/s]\n",
      "Finished [100%]: Average ELBO = -6,582.7\n",
      "100%|██████████| 5000/5000 [-1:54:12<00:00, -0.07s/it]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    trace = pm.sample(5000, n_init=10000, tune=1000, random_seed=SEED)[1000:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see in the following plot that the posterior distribution on the weights and the component means has captured the true value quite well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.5/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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aeUlNGE4PWyCXiLC7oxY80qODTm8Yc1YfguHl/Us6m7nEFJAuElaCyx/GyaVOkUopi8Yl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AghhCSbiFqo7r//ftx77724/vrrk37NDk7g5NvU5Y8EBCdRfFBrFSFk9AgeQyUIAsrLy6FURt5R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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe31ed99a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace, varnames=['w', 'mu']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.5/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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vvfYmPv21GDtOtSSe7LwSNNY1YNHqPwAADbUtxcjG/53G7xdaliX3DDPbL2DfkD+5Kgqa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faf1mICqHtWhbNaO+RP7hOAiXOehFZXYz37J/cJqBs/rg6+MFbclk6bC014L7vlDSk1kdAXnbZb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\nyEn/D+xkyQwYHhKnAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe31eae4be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.plot_posterior(trace, varnames=['w', 'mu']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also sample from the model's posterior predictive distribution, as follows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 5000/5000 [03:28<00:00, 23.93it/s]\n"
     ]
    }
   ],
   "source": [
    "with model:\n",
    "    ppc_trace = pm.sample_ppc(trace, 5000, random_seed=SEED)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the posterior predictive samples have a distribution quite close to that of the observed data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.5/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family ['sans-serif'] not found. Falling back to DejaVu Sans\n",
      "  (prop.get_family(), self.defaultFamily[fontext]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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7po1hVX80eDz03bNnT2VnZysnJ0dFRUWy2+2y2WxevfGpU6dUVFQkSfr+++/1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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe31eb26eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.hist(x, bins=30, normed=True,\n",
    "        histtype='step', lw=2,\n",
    "        label='Observed data');\n",
    "ax.hist(ppc_trace['x_obs'], bins=30, normed=True,\n",
    "        histtype='step', lw=2,\n",
    "        label='Posterior predictive distribution');\n",
    "\n",
    "ax.legend(loc=1);"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
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