AustinRochford/pydata_dc_2016_vi_in_python.ipynb

## pydata_dc_2016_vi_in_python.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "A Dockerfile that will produce a container with all the dependencies necessary to run this notebook is available [here](https://github.com/AustinRochford/notebooks)."
   ]
  },
  {
   "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 IPython.display import HTML"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "from edward.stats import bernoulli, normal, uniform\n",
    "from edward.models import Normal\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib.animation import ArtistAnimation\n",
    "from matplotlib.patches import Ellipse\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc3 as pm\n",
    "from pymc3.distributions import draw_values\n",
    "from pymc3.distributions.dist_math import bound\n",
    "from pymc3.math import logsumexp\n",
    "import scipy as sp\n",
    "import seaborn as sns\n",
    "import tensorflow as tf\n",
    "from theano import shared, tensor as tt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# configure pyplot for readability when rendered as a slideshow and projected\n",
    "plt.rc('figure', figsize=(8, 6))\n",
    "\n",
    "LABELSIZE = 14\n",
    "plt.rc('axes', labelsize=LABELSIZE)\n",
    "plt.rc('axes', titlesize=LABELSIZE)\n",
    "plt.rc('figure', titlesize=LABELSIZE)\n",
    "plt.rc('legend', fontsize=LABELSIZE)\n",
    "plt.rc('xtick', labelsize=LABELSIZE)\n",
    "plt.rc('ytick', labelsize=LABELSIZE)\n",
    "\n",
    "plt.rc('animation', writer='avconv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "blue, green, red, purple, gold, teal = sns.color_palette()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "SEED = 69972 # from random.org, for reproducibility\n",
    "\n",
    "np.random.seed(SEED)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Variational Inference in Python\n",
    "\n",
    "## PyData DC 2016\n",
    "\n",
    "## October 8, 2016\n",
    "\n",
    "### [@AustinRochford](https://twitter.com/AustinRochford) &mdash; [Monetate Labs](http://www.monetate.com/)\n",
    "\n",
    "### [arochford@monetate.com](mailto:arochford@monetate.com)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Bayesian Inference\n",
    "\n",
    "<img src=\"http://upload.wikimedia.org/wikipedia/commons/1/18/Bayes'_Theorem_MMB_01.jpg\" width=600>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The <font color=\"red\">posterior distribution</font> is equal to the <font color=\"blue\">joint distribution</font> divided by the <font color=\"green\">marginal distribution of the evidence</font>.\n",
    "\n",
    "$$\n",
    "\\color{red}{P(\\theta\\ |\\ \\mathcal{D})}\n",
    "    = \\frac{\\color{blue}{P(\\mathcal{D}\\ |\\ \\theta)\\ P(\\theta)}}{\\color{green}{P(\\mathcal{D})}}\n",
    "    = \\frac{\\color{blue}{P(\\mathcal{D}, \\theta)}}{\\color{green}{\\int P(\\mathcal{D}\\ |\\ \\theta)\\ P(\\theta)\\ d\\theta}}\n",
    "$$\n",
    "\n",
    "For many useful models the <font color=\"green\">marginal distribution of the evidence</font> is **hard or impossible to calculate analytically**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Modes of Bayesian Inference\n",
    "\n",
    "* Conjugate models with closed-form posteriors\n",
    "* **Markov chain Monte Carlo algorithms**\n",
    "* Approximate Bayesian computation\n",
    "* Distributional approximations\n",
    "    * Laplace approximations, INLA\n",
    "    * **Variational inference**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Markov Chain Monte Carlo Algorithms\n",
    "\n",
    "* Construct a Markov chain whose stationary distribution is the posterior distribution\n",
    "* Sample from the Markov chain for a long time\n",
    "* Approximate posterior quantities using the empirical distribution of the samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "To produce an interesting MCMC animation, we simulate a linear regression data set and animate samples from the posteriors of the regression coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "x_animation = np.linspace(0, 1, 100)\n",
    "y_animation = 1 - 2 * x_animation + np.random.normal(0., 0.25, size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
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n9MsvvxR7/pEjRzR48GC1a9dO6enpGjRokCZNmqT169d7onmAZfljgaLdblfS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\n9RK6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fccad52c748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "ax.scatter(x_animation, y_animation,\n",
    "           c=blue);\n",
    "\n",
    "ax.set_title('MCMC Animation Data Set');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied log-transform to tau and added transformed tau_log_ to model.\n",
      "Assigned NUTS to intercept\n",
      "Assigned NUTS to slope\n",
      "Assigned NUTS to tau_log_\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING (theano.tensor.blas): We did not found a dynamic library into the library_dir of the library we use for blas. If you use ATLAS, make sure to compile it with dynamics library.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-------100%-------] 5000 of 5000 in 3.3 sec. | SPS: 1521.7 | ETA: 0.0"
     ]
    }
   ],
   "source": [
    "with pm.Model() as mcmc_animation_model:\n",
    "    intercept = pm.Normal('intercept', 0., 10.)\n",
    "    slope = pm.Normal('slope', 0., 10.)\n",
    "    \n",
    "    tau = pm.Gamma('tau', 1., 1.)\n",
    "    \n",
    "    y_obs = pm.Normal('y_obs', intercept + slope * x_animation, tau=tau,\n",
    "                      observed=y_animation)\n",
    "    \n",
    "    animation_trace = pm.sample(5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "animation_cov = np.cov(animation_trace['intercept'],\n",
    "                       animation_trace['slope'])\n",
    "\n",
    "animation_sigma, animation_U = np.linalg.eig(animation_cov)\n",
    "animation_angle = 180. / np.pi * np.arccos(np.abs(animation_U[0, 0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7RDIw8cqC5vzMJFcvfUH4SSHk2saDnH7vzzEYzS+9tq+znZnpUQqLK6lvPvLS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\nXO4KGrftpayihlQygXdmgonxQQZ7O4hFw1hsjmwJvmKl05uYCcSZnhi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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc7aed9ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "animation_fig = plt.figure()\n",
    "\n",
    "e = Ellipse((animation_trace['intercept'].mean(), animation_trace['slope'].mean()),\n",
    "            2 * np.sqrt(5.991 * animation_sigma[0]), 2 * np.sqrt(5.991 * animation_sigma[1]),\n",
    "            angle=animation_angle, zorder=5)\n",
    "e.set_alpha(0.5)\n",
    "e.set_facecolor(blue)\n",
    "e.set_zorder(9);\n",
    "\n",
    "animation_images = [(plt.plot(animation_trace['intercept'][-(iter_ + 1):],\n",
    "                              animation_trace['slope'][-(iter_ + 1):],\n",
    "                              '-o', c='k', alpha=0.5, zorder=10)[0],)\n",
    "                    for iter_ in range(50)]\n",
    "\n",
    "animation_ax = animation_fig.gca()\n",
    "animation_ax.add_artist(e);\n",
    "\n",
    "animation_ax.set_xticklabels([]);\n",
    "animation_ax.set_xlim(0.75, 1.3);\n",
    "\n",
    "animation_ax.set_yticklabels([]);\n",
    "animation_ax.set_ylim(-2.5, -1.5);\n",
    "\n",
    "mcmc_animation = ArtistAnimation(animation_fig, animation_images,\n",
    "                                 interval=100, repeat_delay=5000,\n",
    "                                 blit=True)\n",
    "mcmc_video = mcmc_animation.to_html5_video()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "scrolled": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "HTML(mcmc_video)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Beta-Binomial Model\n",
    "\n",
    "We observe three successes in ten trials, and want to infer the true success probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "x_beta_binomial = np.array([1, 1, 1, 0, 0, 0, 0, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$p \\sim U(0, 1)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Applied interval-transform to p and added transformed p_interval_ to model.\n"
     ]
    }
   ],
   "source": [
    "import pymc3 as pm\n",
    "\n",
    "with pm.Model() as beta_binomial_model:\n",
    "    p_beta_binomial = pm.Uniform('p', 0., 1.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$\n",
    "\\begin{align*}\n",
    "P(X_i = 1\\ |\\ p)\n",
    "    & = p\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "with beta_binomial_model:\n",
    "    x_obs = pm.Bernoulli('y', p_beta_binomial,\n",
    "                         observed=x_beta_binomial)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "$$p\\ \\left|\\ \\sum_{i = 1}^{10} X_i \\right. = 3 \\sim \\textrm{Beta}(4, 8)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "scrolled": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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xIt5oRkTjWNYSuTgZCq9X0+fFhnnD4OOCs+UdGB3j9KNExLKWTHlDLzxctQgN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc7fe27da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the true beta-binomial posterior distribution\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "prior = sp.stats.uniform(0, 1)\n",
    "posterior = sp.stats.beta(1 + x_beta_binomial.sum(), 1 + (1 - x_beta_binomial).sum())\n",
    "\n",
    "plot_x = np.linspace(0, 1, 100)\n",
    "ax.plot(plot_x, prior.pdf(plot_x),\n",
    "        '--', c='k', label='Prior');\n",
    "\n",
    "ax.plot(plot_x, posterior.pdf(plot_x),\n",
    "        c=blue, label='Posterior');\n",
    "\n",
    "ax.set_xticks(np.linspace(0, 1, 5));\n",
    "ax.set_xlabel(r'$p$');\n",
    "\n",
    "ax.set_yticklabels([]);\n",
    "\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xIt5oRkTjWNYSuTgZCq9X0+fFhnnD4OOCs+UdGB3j9KNExLKWTHlDLzxctQgN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc7fe27da0>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "BETA_BINOMIAL_SAMPLES = 50000\n",
    "BETA_BINOMIAL_BURN = 10000\n",
    "BETA_BINOMIAL_THIN = 20"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Assigned NUTS to p_interval_\n",
      " [-------100%-------] 50000 of 50000 in 13.1 sec. | SPS: 3829.8 | ETA: 0.0"
     ]
    }
   ],
   "source": [
    "with beta_binomial_model:\n",
    "    beta_binomial_trace_ = pm.sample(BETA_BINOMIAL_SAMPLES, random_seed=SEED)\n",
    "\n",
    "beta_binomial_trace = beta_binomial_trace_[BETA_BINOMIAL_BURN::BETA_BINOMIAL_THIN]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "bins = np.linspace(0, 1, 50)\n",
    "ax.hist(beta_binomial_trace['p'], bins=bins, normed=True,\n",
    "        color=green, lw=0., alpha=0.5,\n",
    "        label='MCMC approximate posterior');\n",
    "\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EcZDEKCe481VUtMSQYSqamgS2blZg31EYREQDj2FN3UgV2LnNdnF63HjVoa5T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\n4VisiYiIFI7FmoiISOFYrImIiBTu/7oXrDgpewytAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc7fe27da0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Pros\n",
    "\n",
    "* Asymptotically unbiased: converges to the true posterior afer many samples\n",
    "* Model-agnostic algorithms\n",
    "* Well-studied for more than 60 years"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "#### Cons\n",
    "\n",
    "* Can take a long time to converge\n",
    "    * Can be difficult to assess convergence\n",
    "* Difficult to scale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Variational Inference\n",
    "\n",
    "* Choose a class of approximating distributions\n",
    "* Find the best approximation to the true posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Variational inference minimizes the [Kullback-Leibler divergence](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence)\n",
    "\n",
    "$$\\mathbb{KL}(\\color{purple}{q(\\theta)} \\parallel \\color{red}{p(\\theta\\ |\\ \\mathcal{D})}) = \\mathbb{E}_q\\left(\\log\\left(\\frac{\\color{purple}{q(\\theta)}}{\\color{red}{p(\\theta\\ |\\ \\mathcal{D})}}\\right)\\right)$$\n",
    "\n",
    "from <font color='purple'>approximate distributons</font>, but we can't calculate the true <font color='red'>posterior distribution</font>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Minimizing the Kullback-Leibler divergence\n",
    "\n",
    "$$\n",
    "\\mathbb{KL}(\\color{purple}{q(\\theta)} \\parallel \\color{red}{p(\\theta\\ |\\ \\mathcal{D})}) = -(\\underbrace{\\mathbb{E}_q(\\log \\color{blue}{p(\\mathcal{D}, \\theta))} - \\mathbb{E}_q(\\color{purple}{\\log q(\\theta)})}_{\\color{orange}{\\textrm{ELBO}}}) + \\log \\color{green}{p(\\mathcal{D})}\n",
    "$$\n",
    "\n",
    "is equivalent to maximizing the <font color='orange'>Evidence Lower BOund (ELBO)</font>, which only requires calculating the <font color='blue'>joint distribution</font>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Variational Inference Example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "In this example, we minimize the Kullback-Leibler divergence between a full-rank covariance Gaussian distribution and a diagonal covariance Gaussian distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "SIGMA_X = 1.\n",
    "SIGMA_Y = np.sqrt(0.5)\n",
    "CORR_COEF = 0.75\n",
    "\n",
    "true_cov = np.array([[SIGMA_X**2, CORR_COEF * SIGMA_X * SIGMA_Y],\n",
    "                     [CORR_COEF * SIGMA_X * SIGMA_Y, SIGMA_Y**2]])\n",
    "true_precision = np.linalg.inv(true_cov)\n",
    "\n",
    "approx_sigma_x, approx_sigma_y = 1. / np.sqrt(np.diag(true_precision))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZI58UYinNcef2eJR1Nem//meT7r9rhUJMeAJwHSikAGwnk8lo38HDOtMTVzov5ZwV8niq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc750ee588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax  = plt.subplots(figsize=(8, 8))\n",
    "ax.set_aspect('equal');\n",
    "\n",
    "\n",
    "var, U = np.linalg.eig(true_cov)\n",
    "angle = 180. / np.pi * np.arccos(np.abs(U[0, 0]))\n",
    "\n",
    "e = Ellipse(np.zeros(2), 2 * np.sqrt(5.991 * var[0]), 2 * np.sqrt(5.991 * var[1]), angle=angle)\n",
    "e.set_alpha(0.5)\n",
    "e.set_facecolor(blue)\n",
    "e.set_zorder(10);\n",
    "ax.add_artist(e);\n",
    "\n",
    "ax.set_xlim(-3, 3);\n",
    "ax.set_xticklabels([]);\n",
    "\n",
    "ax.set_ylim(-3, 3);\n",
    "ax.set_yticklabels([]);\n",
    "\n",
    "rect = plt.Rectangle((0, 0), 1, 1, fc=blue, alpha=0.5)\n",
    "ax.legend([rect],\n",
    "          ['True distribution'],\n",
    "          bbox_to_anchor=(1.5, 1.));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZI58UYinNcef2eJR1Nem//meT7r9rhUJMeAJwHSikAGwnk8lo38HDOtMTVzov5ZwV8niq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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc750ee588>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Approximate the true distribution using a diagonal covariance Gaussian from the class\n",
    "\n",
    "$$\\mathcal{Q} = \\left\\{\\left.N\\left(\\begin{pmatrix} \\mu_x \\\\ \\mu_y \\end{pmatrix},\n",
    "                              \\begin{pmatrix} \\sigma_x^2 & 0 \\\\ 0 & \\sigma_y^2\\end{pmatrix}\\ \\right|\\ \n",
    "                       \\mu_x, \\mu_y \\in \\mathbb{R}^2, \\sigma_x, \\sigma_y > 0\\right)\\right\\}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "vi_e = Ellipse(np.zeros(2), 2 * np.sqrt(5.991) * approx_sigma_x, 2 * np.sqrt(5.991) * approx_sigma_y)\n",
    "vi_e.set_alpha(0.4)\n",
    "vi_e.set_facecolor(red)\n",
    "vi_e.set_zorder(11);\n",
    "ax.add_artist(vi_e);\n",
    "\n",
    "vi_rect = plt.Rectangle((0, 0), 1, 1, fc=red, alpha=0.75)\n",
    "\n",
    "ax.legend([rect, vi_rect],\n",
    "          ['Posterior distribution',\n",
    "           'Variational approximation'],\n",
    "          bbox_to_anchor=(1.55, 1.));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Cru4uVNU2otvuRrfDA7dfC7MlFaLGCBiBBKPaVYafTm8A9Lno8Cn44wfHkJ0k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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc750ee588>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Pros\n",
    "\n",
    "* A principled method to trade complexity for bias\n",
    "* Optimization theory is applicable\n",
    "    * Assesment of convergence\n",
    "    * Scalability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Cons\n",
    "\n",
    "* Biased estimate of the true posterior\n",
    "    * Better for prediction than interpretation\n",
    "* Model-specific algorithms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Mean field variational inference\n",
    "\n",
    "Assume the variational distribution factors independently as $q(\\theta_1, \\ldots, \\theta_n) = q(\\theta_1) \\cdots q(\\theta_n)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The variational approximation can be found by **coordinate ascent**\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "q(\\theta_i)\n",
    "    & \\propto \\exp\\left(\\mathbb{E}_{q_{-i}}(\\log(\\mathcal{D}, \\boldsymbol{\\theta}))\\right) \\\\\n",
    "q_{-i}(\\boldsymbol{\\theta})\n",
    "    & = q(\\theta_1) \\cdots q(\\theta_{i - 1})\\ q(\\theta_{i + 1}) \\cdots q(\\theta_n)\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "#### Coordinate Ascent Cons\n",
    "\n",
    "* Calculations are tedious, even when possible\n",
    "* Convergence is slow when the number of parameters is large"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Automating Variational Inference in Python\n",
    "\n",
    "* Maximize <font color='orange'>ELBO</font> using gradient ascent instead of coordinate ascent\n",
    "* Tensor libraries calculate <font color='orange'>ELBO</font> gradients automatically"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<table>\n",
    "    <tr>\n",
    "        <th><center>Python Package</center></th>\n",
    "        <th><center>Tensor Library</center></th>\n",
    "        <th><center>Variational Inference Algorithm(s)</center></th>\n",
    "    <tr>\n",
    "    <tr>\n",
    "        <td><center><a href='http://edwardlib.org/'>Edward</a></center></td>\n",
    "        <td><center><a href='https://www.tensorflow.org/'>TensorFlow</a></center></td>\n",
    "        <td><center><a href='https://arxiv.org/abs/1401.0118'>Black Box Variational Inference</a> (BBVI)</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center><a href='http://pymc-devs.github.io/pymc3/'>PyMC3</a></center></td>\n",
    "        <td><center><a href='http://deeplearning.net/software/theano/'>Theano</a></center></td>\n",
    "        <td><center><a href='http://arxiv.org/abs/1603.00788'>Automatic Differentiation Variational Inference</a> (ADVI)</center></td>\n",
    "    </tr>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Common themes\n",
    "\n",
    "* Monte Carlo estimate of the <font color='orange'>ELBO</font> gradient\n",
    "* Minibatch estimates of the <font color='green'>joint distribution</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "BBVI and ADVI arise from different ways of calculating the <font color='orange'>ELBO</font> gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "#### Mathematical details\n",
    "\n",
    "* Monte Carlo estimate of the ELBO gradient\n",
    "    * For samples $\\tilde{\\theta}_1, \\ldots, \\tilde{\\theta}_K \\sim q(\\theta)$\n",
    "\n",
    "    $$\n",
    "    \\begin{align*}\n",
    "    \\nabla \\textrm{ELBO}\n",
    "        & = \\mathbb{E}_q \\left(\\nabla\\left(\\log p(\\mathcal{D}, \\theta) - \\log q(\\theta)\\right)\\right) \\\\\n",
    "        & \\approx \\frac{1}{K} \\sum_{i = 1}^K \\nabla\\left(\\log p(\\mathcal{D}, \\tilde{\\theta}_i) - \\log q(\\tilde{\\theta}_i)\\right)\n",
    "    \\end{align*}\n",
    "    $$\n",
    "\n",
    "* Minibatch estimate of joint distribution\n",
    "    * Sample data points $\\mathbf{x}_1, \\ldots, \\mathbf{x}_B$ from $\\mathcal{D}$\n",
    "\n",
    "    $$\\log p(\\mathcal{D}, \\theta) \\approx \\frac{N}{B} \\sum_{i = 1}^B \\log(\\mathbf{x}_i, \\theta)$$\n",
    "\n",
    "BBVI and ADVI arise from different ways of calculating $\\nabla \\left(\\log p(\\mathcal{D}, \\cdot) - \\log q(\\cdot)\\right)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Variational Inference with Edward\n",
    "\n",
    "### Black Box Variational Inference (BBVI)\n",
    "\n",
    "* Model-agnostic\n",
    "    * Requires the ability to compute the joint distribution\n",
    "    * Required the ability to differentiate the variational distribution\n",
    "\n",
    "<center><img src='http://edwardlib.org/images/edward.png' width=350></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "#### Mathematical details\n",
    "\n",
    "For samples $\\tilde{\\theta}_1, \\ldots, \\tilde{\\theta}_K \\sim q(\\theta)$\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\nabla \\textrm{ELBO}\n",
    "    & = \\mathbb{E}_q \\left(\\nabla\\left(\\log p(\\mathcal{D}, \\theta) - \\log q(\\theta)\\right)\\right) \\\\\n",
    "    & = \\mathbb{E}_q \\left(\\left(\\log p(\\mathcal{D}, \\theta) - \\log q(\\theta)\\right) \\nabla \\log q(\\theta)\\right) \\\\\n",
    "    & \\approx \\frac{1}{K} \\sum_{i = 1}^K \\left(\\log p(\\mathcal{D}, \\tilde{\\theta}_i) - \\log q(\\tilde{\\theta}_i)\\right) \\nabla \\log q(\\tilde{\\theta}_i)\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Beta-binomial model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import edward as ed\n",
    "from edward.models import Bernoulli, Beta, Uniform\n",
    "\n",
    "ed.set_seed(SEED)\n",
    "\n",
    "# probability model\n",
    "p = Uniform(a=0., b=1.)\n",
    "x_edward_beta_binomial = Bernoulli(p=p)\n",
    "\n",
    "data = {x_edward_beta_binomial: x_beta_binomial}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def tf_variable(shape=None):\n",
    "    \"\"\"\n",
    "    Create a TensorFlow Variable with the given shape\n",
    "    \"\"\"\n",
    "    shape = shape if shape is not None else []\n",
    "    \n",
    "    return tf.Variable(tf.random_normal(shape))\n",
    "\n",
    "def tf_positive_variable(shape=None):\n",
    "    \"\"\"\n",
    "    Create a TensorFlow Variable that is constrained to be positive\n",
    "    with the given shape\n",
    "    \"\"\"\n",
    "    return tf.nn.softplus(tf_variable(shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# variational approximation\n",
    "q_p = Beta(a=tf_positive_variable(),\n",
    "           b=tf_positive_variable())\n",
    "q = {p: q_p}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "scrolled": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 5.83 s, sys: 880 ms, total: 6.71 s\n",
      "Wall time: 4.63 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "beta_binomial_inference = ed.MFVI(q, data)\n",
    "beta_binomial_inference.run(n_iter=10000, n_print=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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EvUlYewCT2creYxXEhPsREeLr7HI8UsroaAB+SpfNPYQQPU/C2gPsO1qB2WKT\nLnAHijP6MyAmkD1Z5VTUNDm7HCFELyNh7QF2Hu+aHTNIwtqRpo2OQVVhvWydKYToYRLWbs5mU9l9\nuIxAPy/6xwQ6uxyPljwsAoNey0+7C7E5drM6IYRoQ8LazWUV1FDbYGbMoDDZd9nBfAw6JgyPoLym\nif3HKp1djhCiF5GwdnM7D7esWjZmkKxa1hNSRscAsG63zLkWQvQcCWs3t+tQGV46DcPjQ5xdSq8w\nMCaQmHA/dmSWUtvQ7OxyhBC9hIS1GyuubKCwvIER8aEY9LJ3dU9QFIVpidFYbSqbMoqcXY4QopeQ\nsHZjGVkVACQOkrXAe9LkhCi0GoV16YWoMtBMCNEDJKzd2J6slm0bR/WXsO5JAb5ejBtipKCsniMF\nNc4uRwjRC0hYuymzxcqB7Epiwv0IC/J2djm9Tkpiy4pm62VFMyFED5CwdlOZudU0W2wk9A91dim9\n0oj4UEICDGw9UIzJbHV2OUIIDydh7aZau8Bl72qn0GgUpiRE0WiysiOz1NnlCCE8nIS1m9qTVY6X\nXsOQuGBnl9JrTR3V0hW+QZYfFUI4mIS1GyqrbqSwvIHhfUPQ6+QjdJaoUF8GxQWx/1gl5dWyuYcQ\nwnHkJ70bOjFlK2GAdIE721mjolGBjRlydy2EcBwJazfU+rx6gAwuc7bkYRF46TRs2FMkc66FEA4j\nYe1mLFYb+7IriQzxISLE19nl9Ho+Bh1JQyMoqWrkUF61s8sRQngoCWs3czivGlOzVbrAXchZo6IA\nmXMthHAcCWs383MXuIS1qxjaL4SwQG+2Hiihqdni7HKEEB5IwtrN7MmqQKfVMLSvTNlyFRpFYeqo\nKExmK9sPypxrIYT9SVi7kcpaE3mldQzrGyy7bLmYKaNk+VEhhONIWLuRjONd4PK82vVEBPswtE8w\nB3OrKKtqdHY5QggPI2HtRjKOtsyvlilbrmlKQstAs017ZZ9rIYR9SVi7CZuqsj+7ktBAA1GhMmXL\nFY0/Pud6Y4bMuRZC2JeEtZvILa6jrtHMiH6hKIri7HLEKfgYdIwbYqS4spEs2edaCGFHEtZuYl92\nSxf4iPgQJ1cizuREV/iGDOkKF0LYj4S1m9h3rBKA4fHyvNqVDY8PIcjfiy37ijFbbM4uRwjhISSs\n3YDZYuVQbhVxRj+C/LycXY44A61Gw+QRUTSYLOw+XObscoQQHkLC2g0czq+h2WJjhNxVu4Upx5cf\n3Shd4UKlPazbAAAgAElEQVQIO5GwdgP7jrU8rx7eT55Xu4M4oz99I/3Zk1VOTX2zs8sRQngAnbML\nEO3bd6wSrUZhSB/XWGJUVVUsFeWYcnNpLi7CWlODtbYWa13Lf6rVhqLVomi1oNWi8fJCFxyCLjQU\nXUgo+tBQvKJj0AW7xvtxhCkJ0Xyw5hCb9xeTOr6Ps8sRQrg5CWsXV99k5lhRDYNig/AxOOfjUi0W\nGg9lUr8nnaZjRzHl5WJraDj1wcdDWrVawWo9Y7u6kBAM/eLxju+Pd/8B+AwegsbLM57JTxwRyYrv\nD7Mxo0jCWgjRbRLWLu5AdhWqSo8/rzbX1lL904/Up6dTv28vqqmp5QuKgj4iEt8RCRj69MEQE4s2\nMBBtQCDagAA03t5t5oGrNhs2kwlLZQWWinLMFS3/N+Xl0XTsKPW7dlK/a2dL015e+A4bjt+o0fgl\nJqIPC+/R92xPQX5ejBoQyu4j5eSX1hFr9Hd2SUIINyZh7eJ6cn61qqo0HT5M1bq1HNq2FdVsBkAf\nEYlfYgp+o0bjM2gwGoOhw20qGg1aHx+0PrEYYmJP+rqlqpKmY8doPHSQ+j3p1Kfvpj59N7wLhn7x\nBE6ZSuCESWgDAuz2PnvKlFHR7D5Szsa9RSycMcjZ5Qgh3JiiyrqILu2Wx76joqaJ9x45F53WMeMB\nbc3NFK/5nqJVq2nIzgHAOyaayNRzCJs4AZ/YGIdc91Saikuo3L6Diq3bqNq1G2w2FJ2O0OQkImae\nTUjSuJZn4W7AZLby24e+xteg499/mo1GIyvPCSG6xuF31qWltY6+hMcqr24iv7Se0QPDqKyot3v7\nqsVC9cb1VHzxGZaKCtBq8R8/geDpM+ibMoGysjrqgLqe/Aw1PuiSpxKRPJXQ6mpqN2+iesN6yjdt\npnzTZvTGCEJmzyFwylmdusN3lqQhRn5KL2T99pweXdDGaAyQf3tuSj4792Y0OqYXULrBXdjPXeD2\n/SGv2mzUbkmj/LNPMZcUo+j1hMyeS8icueiCWkZou8L647qgIEJmzyU4dQ6m3Byq1q6hdtNGSt59\nm7JPPyF4xtkEz0xFFxjo7FJPa0pCFD+lF7Jxb5GsPieE6DIJaxe2//gSo/Z8Xm3Ky6X4rddpysoC\nrZagGTMJm38+umDXncOtKAreffsRdc31hF90CVVr11C1dg0VX3xO5bffEHLObELmzEPr63q7kQ3u\nE0xYoIFtB0u5arYVg949uvCFEK5FwtpFqarKvmMVBPl5ERPu1+32bOZmKr74nIqvvwKrlYDkCYQv\nWIjeaLRDtT1HFxRE+EULCJ13HtXr11Hx1RdUfPk5VWu/J3TeeQTPnOVS3eMaRWHSyCi+3JTNzkOl\nTBoR5eyShBBuSMLaReWX1VPTYGbSyMhud0k3ZB6k+M3XMRcXoQsNJeKqa/BPHG2nSp1DYzAQMiuV\noLOmUbXmWyq+/oqyj1dQueYbjJdcRsCkyS7RlQ8tXeFfbsombW+xhLUQokskrF3Ugezju2z17Xr3\ntGqzUf75p1R88RkAwbNSCb94ARpvH7vU6Ao0BgOh584naPrZVK5eReW3qyn69ytUr/uBiCuuxtDH\n+QuSRIf5ER8VQEZWBdX1zbIZixCi02RtcBd1IKcKgGFdXA/cUlND/tNPUvH5p+hCQ+nzxweJ+M2V\nHhXUv6T18yN8waXEP/IP/MaOo/FQJtmP/IWS99/F2mD/kfSdNTkhCpuqsmVfsbNLEUK4IQlrF2RT\nVQ7mVBIW6I0xuPPh2njoENl//TMN+/filziafv/3MD4De8eiHPpwI7G330Xs0t+hDzdSteZbjv3f\ng9Tt3uXUuiYOj0SjKGzcKztxCSE6T8LaBeWV1FHfZGFY385vdFH1/XfkPv4o1upqwi9ZSMwdS9D6\n976lLv0SEun38N8Iu/BirHW1FCx7hsJ/v4K1rs4p9QT6eZEwIJTsoloKypx/py+EcC8S1i6oK13g\nqs1G6UcrKHnvHbR+/sT9/j5C552Houm9H7FGryfs/Avp9+eHMcT3p3bTRo795UHqjq9F3tMmj2wZ\nXLZJ7q6FEJ3Ue3+Su7ATg8uGdXBwmWqxUPTvV6n8+iv0kVH0feD/8B06zJEluhVDbBx97/8T4Qsu\nxVZfT8HyZyl68z/YTKYerWPs4HC8vbSk7S3CJqv8CiE6QcLaxdhsKgdzqzAGexMW5N3u8dbGRvKf\nfYrazZvwHjiIvn980O3mTvcERasl9Nz59P3zwxj69KXmp3XkPPIQptycHqvBS69l/NAIymtMHMqt\n6rHrCiHcn4S1i8ktqaPRZGFoB+6qLbU15P3rHzTs34ffmLHE/e5et9ydqicZYmLp88D/EXzObJqL\nCsn5+1+p/O5bemo/m8kjIwHpChdCdI6EtYvZ38H51da6OvKefBxTbi5B02cQc9udLrVylyvT6PVE\nLLqCmLvuRuPjQ+kH71Kw/NkemeI1tG8IIQEGth4oxWyxOvx6QgjPIGHtYg7kHH9efYbBZdb6evKe\nepzmvFyCZswk4qprevVAsq7yTxxNv788gu/wEdTv3kXOIw9jys116DU1GoVJIyJpNFnYfbjcodcS\nQngO+QnvQqw2G5m5VUSG+BAScOq7ZGtDA3lPP4EpJ5vAlGlEXHGVyyyr6Y50wcHE3v17Qs+dj7m0\nhJxHH6EmbaNDrymjwoUQnSVh7UKyi+poarae9nm1rallMJnp2FECp5xF5NXXyh21HSgaDeELLiX6\ntjtRNBqKXnuFkvfeQbVYHHK9uAh/4oz+pB8pp67R7JBrCCE8i/ykdyEHW7vAT14MRbVYKHh+GU1H\nDhMwaTKR114vQW1nAeOS6Punv+AVE0PV99+R98yTDltEZUpCFFabytYDJQ5pXwjhWeSnvQvZn3Pq\n+dWqqlL81huto76jrrtRgtpBvKKi6fvAn1vWFz+wn5xHH6G5yP7d1RNHRKIAmzKkK1wI0T75ie8i\nLFYbh3KriQ7zJdi/7fPqii8+o2bjegzx/Ym+6RYUrdZJVfYOGm9vYm69g5C552IuLibnH3+lYf8+\nu14jJMDAsH4hHM6vpqSq0a5tCyE8j4S1izhWVIvJbD3prrpm00bKP/0EXXg4sXculelZPUTRaDBe\nehmR192IzWQi7+knqPpxrV2vcWKgWZoMNBNCtEPC2kWceF499BebdzQcPEDRG/9G4+tL7F2/QxcU\n5Kzyeq2gqWfR5/f3ofX1o+TtNylb+ZHdFlBJGmrES6dhU0ZRjy3KIoRwTxLWLqJ1847jd9bNJSUU\nPL8MgJjb7sQQE+O02no7n8FD6PPA/6GPiKTiqy8o/s9rdhkp7mPQMWZwOMWVjWQV1tihUiGEp5Kw\ndgEWq43DeS3PqwP9vLA1N1P44jJsDfVEXn0tvsOGO7vEXs8rIoI+9z+Id/8B1GzaQP6yZ7A1df9Z\nc2tXeEZxt9sSQnguCWsXkFNch8lsZWifYFRVpeSdt1qXEQ06K8XZ5YnjdAGBxP3+PvwSR9OwN4Pc\nfz2Gpbp7G3KM7B9KgK+ezfuLsVhtdqpUCOFpJKxdwMHclufVQ/oGU/PTutaR38ZFVzi5MvFrGoOB\nmNvvImjaDEw52eT+81HMZaVdbk+n1TBheCR1jWb2Hq2wY6VCCE8iYe0CMo8/rx5ADSXvvY3Gz4+Y\nW29Ho/dycmXiVBStloirr2lZorSkmNx//gNTQUGX25uSIMuPCiHOTMLayWw2lcy8auL8FerefBnV\naiX6ppvRh4U7uzRxBoqiEL7gUsIXXo6lspLcf/2DpmNHu9RWfFQAkaG+7DxURqPJMUucCiHcm4S1\nk+WV1tHYZGZe8QYs5eWEnX8hfgmJzi5LdFDonHlE/vY6bPX15D3xTxoOHuh0G4qiMGVkJGaLjW0H\nZflRIcTJJKyd7GBOFYk1hwkrPIzPsOGEzr/A2SWJTgqaNp3om2/FZjaT/+xT1O/N6HQbE1sXSJFR\n4UKIk0lYO1nugaOcU7YVxceHqOtlzW93FTB+AjG33wU2GwXLnqF+T3qnzo8I9mFQXBAHsiupqGly\nUJVCCHclyeBENouFgVu/wEu1EHnlb9GHhjm7JNEN/omjiblzKSgKBc8/R92unZ06f8rIKFRg8z65\nuxZCtCVh7UTZH/+P6IYSSmKHEThpsrPLEXbgNzKB2CW/A42GgheXU7t9a4fPHT8sAp1WkVHhQoiT\nSFg7SdOxozSv+YoanS/quQudXY6wI99hw4ldeg+KTk/hyy9Su21Lh87z99GTODCcvNJ6coprHVyl\nEMKdSFg7ga25mcLXXkax2fgyYiqDB0c7uyRhZ75DhhL3u9+j8fKi8JWXqN2+rUPnTR4ZCchAMyFE\nWxLWTlD++aeYi4pIDx9JlbEfkSE+zi5JOIDPwEEtd9h6LwpfeZG6nTvaPSdxYDi+Bh2b9hVhs8lO\nXEKIFhLWPcyUm0vl6lUoIWF8G5jIkD7BKIri7LKEg/gMGkzc0t+h6HQUvPQ8dbt3nfF4vU5D8vAI\nquua2Z9d2UNVCiFcnYR1D1JtNorfeh1sNspTzses0bfZv1p4Jp/BQ4i9624UrZbCF5dTl777jMef\nWH50Y4YMNBNCtJCw7kFV36+h6WgWARMnsUeJAGBIHwnr3sB36DBij0/rKnxhGQ3795322EGxQRiD\nvdmRWUpTsyw/KoSQsO4x5vJyyj75CI2fH8bLryAztwp/Hz0x4X7OLk30EN/hI4i5YwkA+cufpfHI\n4VMepygKk0dGYTJb2ZHZ9R29hBCeQ8K6B6iqSsm7b6GaTBgvW0SVqqe8ponBcUFo5Hl1r+I3MoHo\nm29FNZvJf+ZJmnKyT3nc5OPLj26SrnAhBBLWPaJu+1bq03fjM2w4gVPO4lBuNQBDpQu8V/Ifm0TU\nDTdha2oi/6knTrm9ZmSoLwNjAtmXXUllrckJVQohXImEtYPZTCZK//s+ik5H5NXXoCgKB3Nb9q8e\nIoPLeq3AiZOJvPparHW15D35L5pLT95ta3JCFKoqy48KISSsHa5i1RdYKisJmTMPr8iWrs1DeVUY\nvLT0ifB3cnXCmYKmTcd4+W+wVleR/9TjWKqq2nx9wvBItBpFRoULISSsHclcWkrl16vQhYQQeu58\nAGrqmyksb2BQbBBa2WGr1wtJnUPo+RdiLi0l7+knsNbXt36tZfnRMPJK62T5USF6OUkLByr98ANU\ni4XwSy9DYzAALXfVIFO2xM/CLriI4JmzaM7PI/+5p7GZfn5GfWLOtWzuIUTvJmHtIA3791G3Yzve\nAwcRMGFS6+uZxweXDYkLclZpwsUoioJx0ZUETJxE05HDFLy4HNXSMr86cWA4ft460vYVy/KjQvRi\nEtYOoFqtlHzwHigKEb+5qs1yopl5Vei0CgNiAp1YoXA1ikZD1HU34puQSEPGHor+8yqqzday/Oiw\nluVH9x2rcHaZQggnkbB2gOof19Kcn0fg1BS84+NbX280WcgprqV/dCB6ndZ5BQqXpOh0xNx6O96D\nBlO7ZTOlKz5AVVWmJLTsyrZRusKF6LUkrO3MWldH2aefoPHxIXzBpW2+diS/GlWV59Xi9DQGA7F3\nLMErJoaq776h8utVDIwNJCLEhx0HS2k0yfKjQvRGEtZ2VrHqS2z19YTOvwBdYNuu7hPzqwfHSViL\n09P6+xO79B50IaGUfbyC2k0bmZIQRbPFxrYDJ8/HFkJ4PglrOzJXVFD1/XfoQkMJnjnrpK8fyq1C\noWWjBiHORB8aRuzSe9D4+lL0xr8ZrykDZCcuIXorCWs7Kv/sf6hmM2EXXIxG79Xma2aLlazCWvpE\n+uPrrXNShcKdGGJjib2zZWvN+rdfZVJQEwdzqyitanR2aUKIHiZhbSemggJqNvyEV0wMgVOmnvT1\no4W1WKw2hkgXuOgEn8GDiV7csvHHtH1fEmyulTnXQvRCDr/FMxoDHH0Jl7D/tU9BVRlw7dWERZ7c\nzb12dyEA40dGu833xF3q9HTG2dPxtjaR9dIrXF7wHavTg7j+wlFtpgSe8jz5/NyWfHbi1xwe1qWl\nnr9MYmPWESrSNuM9cBDW/sNO+Z53HmzZjCEyyOAW3xOjMcAt6uwtdOOnEHpuAXz1BSkZX7BxywiG\nDIg47fHy+bkv+ezcm6N+0ZJu8G5SVZWyjz8EIPyShae827HZVA7nVRMZ6kuQn9dJXxeiI8IuvgRb\nQhKxpjIq3mhZNEUI0TtIWHdTw949NB48gN+oRHyHDD3lMbkldTQ1W2WJUdEtiqIw+LZbyPOPIbTg\nEEXvvI2qyhKkQvQGEtbdoKoqZZ+sBEUhfMHC0x6XmSubdwj70HrpqTz3Ckq8gqldt5bKb752dklC\niB4gYd0N9em7MWUfwz9pPIY+fU57nIS1sKdJ4/rzYfQsmgx+lH20gtrtW51dkhDCwSSsu0hVVco/\n/xSAsPkXnPG4zLwqQgIMhAd591R5woPFhvsR3jeK9yPPRvHyoui1V2g8ctjZZQkhHEjCuosaMvZg\nOna05a467vR31UUVDdQ2mBkcF9TuVBshOmrqqGiKvUIpmHEpqsVCwfJnaS6VpUiF8FQS1l3Qclf9\nPwDC5l94xmMP5R3fv1q6wIUdTRwRiU6r8E1VAMYrrsZaW0v+s09hratzdmlCCAeQsO6Chr0ZNGVl\n4T826YzPquEXz6tl5TJhR37eesYONlJY3kDF0CRC5szDXFREwQvLUC2yM5cQnkbCupN++aw69PzT\nP6s+4VBeFX7eOmKMfo4uTfQyZyW27HO9YU8R4ZcsxD9pPI2ZByl+63WZ0iWEh5Gw7qSG/ftoOnIY\nvzFj8e7b74zHVtaaKK1qYlBsEBp5Xi3sbGR8KMH+XmzeV4zZqhJ1/U0Y4vtTs3EDeR9+7OzyhBB2\nJGHdCaqqUtE6AvzMz6qh5a4aYLA8rxYOoNEoTEmIptFkYeehMjQGA7F3LkEXGkbOu+9Tu2Wzs0sU\nQtiJhHUnNGYepPFQJn6Jo/GOj2/3eHleLRxt6qgoANbvadkoRhcUTOySu9H6+FD0n1dlSpcQHkLC\nuhMqv/4KgNDzzu/Q8Zm51eh1GuKjZQcd4RjRYX4MjA1k39EKKmqaADDExjH0D/eg2mwULH8Wc1mp\nk6sUQnSXhHUHmfJyqd+Tjs/gIfgMHNTu8Q1NZvJL6xgQHYhOK99m4ThnjYpGBTZm/LzPdci4sUT8\n5qqWKV3PPYO1sdF5BQohuk1SpIMqV7eswRwy99wOHX8orxoVeV4tHC95WCReOg3r9xS2GQUefPZM\ngmel0lyQT+HLL6JarU6sUgjRHRLWHWCuKKdmSxpeMTH4jUrs0DmZeSfWA5edtoRj+XrrGDfUSEll\nY+siPCcYL1uEb0IiDRnplK74wEkVCiG6S8K6A6q+/QasVkLmzEPRdOxbdii3GkWBgTES1sLxzhrV\nMud6fXphm9cVrZbom2/FKyaWqjXfUrV2jTPKE0J0k4R1O6z19VSt+xFtcDCBEyd36Jxms5WjhTX0\njQzAx6BzcIVCwLB+IYQHebPlQDGNprYrmGl9fIi9aynagABK3n+X+r0ZTqpSCNFVEtbtqP5xLaqp\niZDUOSi6jgXv0cIarDZVpmyJHqNRFFISo2k229iyv/ikr+vDjcTcsQRFo6HwpedpLixwQpVCiK6S\nsD4Dm7mZyu++QePjQ9C0GR0+7+f9q6ULXPScqaOiURT46Vdd4Sf4DBxE5LXXY2tsbBkhLpt+COE2\nJKzPoGbTRqw1NQRNPxutj0+Hz8s8PshnsNxZix4UGujNqAFhZBXUkF1Yc8pjAidNIfS88zGXlsim\nH0K4EQnr01BVtWVgmVZLyDmpHT7ParNxOL+aqFBfAv28HFihECdLOb65xzdbsk97TNiFF+M/LonG\nzIOUvPe2bPohhBuQsD6Nhn17aS4sIGDCRHTBIR0+L6+kHlOzVbrAhVOMHhROgK+etdvyMFtspzxG\n0WiIumExhr79qF73Y8svpUIIlyZhfRpVa74FIGTmOZ067+Dx59XSBS6cQafVMCUhitqGZnYeOv0y\noxqDgZg7lqANCqb0ww+o35Peg1UKITpLwvoUmouLqd+TjvfAQXj3H9Cpcw8dD+uhsnKZcJKUxBjg\n9APNTtCHhhJz+10oOh2Fr7yIqSC/J8oTQnSBhPUpVK39DlSV4Fmdu6tWVZXMvCpCAgyEBXk7qDoh\nziwm3I/h8aHsO1pBWfWZ1wT3GTCAyGtvwNbYSMGyZ7DW1vZQlUKIzpCw/hVbUyM1639CGxxMwLjx\nnTq3qKKB2gYzQ/sEoyiKgyoUon2pE/qicvKKZqcSOHESofPPx1xaSsGLy2WEuBAuSML6V6o3bsDW\n1ETwjJkdXgTlhNbn1dIFLpzsrDGxGLy0rN9TiM3W/mjvsAtkhLgQrkzC+hdUm42qNd+i6HQETZ/R\n6fMPtS6GImEtnMvHoGPSiEgqakxkHC1v9/jWEeJ9+raMED8+wFII4RokrH+hYW8G5uJiAiZORhcQ\n2OnzM3Or8PfRExPm64DqhOic6WNaBpr9sLNjS4tqDAZi7lyCNjCQ0v++L2uIC+FCJKx/ofL43URn\nB5YBlFU3Ul5jYnBckDyvFi4hPiqQflEB7D5SRmWtqUPn6EPDWkaIa7Uta4gXtf/MWwjheBLWxzUX\nFdGQsQefwUPw7tuv0+cfym1ZYlS6wIUrmTEmBlWFn3Z3fOMOn4GDiPztdS1riC97Fmt9vQMrFEJ0\nhIT1cdU/rgUg+OxZXTo/M0+eVwvXM3FEJAYvLevSCzo00OyEwClTCZl7LubiIgpffgHVanVglUKI\n9khY07K7VvXG9WgDAvEfl9SlNjJzqzB4aekb6W/n6oToOm8vHZOPDzTbk9X+QLNfCl9wKX6Jo2nY\nt5fS/77voAqFEB0hYQ3UbduGrb6ewLNSOj1dC6CmvpnC8gYGxQah1ci3VLiW6WNiAfhxV+f2sFY0\nGqIX34JXbBxV339H1Y8/OKA6IURHSLIAVT+uBUUhaNr0Lp1/6EQXeJxs3iFcT7+oAPpHtww0q6hp\n6tS5Gm8fYu9Ygsbfn5L33qbh4AEHVSmEOJNeH9am/DyaDh/Cd8RIvIwRXWojUwaXCRc3fUxsy0Cz\nDqxo9mt6o5GYW+8AoODF5TSXlti7PCFEO3p9WLcOLJtxdpfbyMytQqdVGBDT+bnZQvSECcMj8PbS\nsm53AVbbqbfOPBPfocOIuPJqbHV1FCx7FmvjmdccF0LYV68Oa5vJRM2mjWiDg/FLHNOlNhpNFnJK\naukfHYhep7VzhULYh7eXjskjo6isNbHnSEWX2gieNoPgWak0F+RT9OpLqF0IfSFE1/TqsK7duhlb\nYyNBKdNRtF0L2iP51aiqdIEL1zdjbMtAs+935nW5DeNli/AdMZL69N2UrfzIXqUJIdrRq8O66ofj\nA8tSpnW5jYOyHrhwE30i/BkUF0RGVgUllQ1dakPRaom++Tb0kVFUfv0VNZs22LlKIcSp9Nqwbso+\nhunYUfwSR6MPDetyO5m5VSgKDIqVkeDC9c0c13J3vXZnfpfb0Pr5EXvnEjQ+PhS/+TqNRw7bqzwh\nxGn02rCuPj5nNGh61weWNZutHC2soW9kAD6Gzs/PFqKnjR8aQaCvnvXphZjMXV+VzCsqmuhbbke1\nWil4/jnMFZ1bcEUI0Tm9MqxtJhO1W9LQhYbilzCqy+0cKajBYlUZKl3gwk3otBqmjYmhvsnClv3F\n3WrLb2QCxsuvwFpTQ8Hy57CZOrZZiBCi83plWNdt34atqYnAKWehdGPFsYM5lQAM7SthLdzHjDGx\nKAp8vyMfVe34euGnEjzrHIKmTceUk03Rf16VEeJCOEivDOvqDT8BEDj1rG61k5lbhYIMLhPuJTTQ\nm7GDjWQX1ZJVWNOtthRFIeKKq/EZMpS67dso//xTO1UphPilXhfWzSUlNB48gM/QYV1esQzAbLFx\npKCGuAh//Lz1dqxQCMc7+/hAs++3d32g2QmKTkfMrXegDzdS8fmn1G7Z3O02hRBt9bqwrtnYclcd\ndFZKt9o5WliD2WKT59XCLY3oF0JUqC9bDxRT29Dc7fa0AQHE3LkUjbc3Ra+/RtPRLDtUKYQ4oVeF\ntWqzUbNhAxpvb/zHje9WW/K8WrgzRVE4e1wsFqvapfXCT8UQG0vU4ltQLRbylz+HubLSLu0KIXpZ\nWDfs34elsoKACRPRGAzdaksWQxHubmpCFF56DWt35HdpvfBT8U8cQ/ill2GtrqJg+bMyQlwIO+lV\nYV2zfh0AgVO71wVusdo4nF9NbLgfAb5e9ihNiB7n661nSkI05TVN7DpUZrd2Q2bPJXBqCqbsYxS9\n/pqMEBfCDnpNWFvr6qjbuQOv6Bi8BwzsVlvHimppNtsYIl3gws2dkxQHwLfbur5e+K8pikLEVb/F\nZ/AQ6rZtlRHiQthBrwnr2i1pqBYLgWeloChKt9pqfV4tXeDCzcWE+5HQP5TM3Cqyi2rt1q5Gryf6\ntp9HiNdsSbNb20L0Rg5dIzM+Ph6b7eRFF7Zvzzjl8UlJCad83R7HV6//Cauqcumf76f6gXu71f6V\n970DnBzWjqy/p4/XaJTWz84V6pHjHXf86yt+JONoBd9ty+WG+SPs2n6ctzdPjh1P8ev/Rh8egc+A\nAXavX46X413p+Jyc7FN+vbscvqC1RnPyXazRGNDhY+1xfP2xY5hystlVU02tzXrSeZ1qX9FwJL+a\nWKM/g/qH90j9zjr+xJ9dpR45vnPH//q80x1/9oR+fPjDETbvL+HmS0YTEuhtt3oKmk0M+8M97Pvb\noxS9+Byjn/gXhvAwu7XvqccbjQEuVY8c3/Xj7UVRu7veYDtKS+3XtdblGlZ8QOU3XxN96x0EJHVv\nytbRwhoeeXMb08fEcM3cYXaq0PUYjQEu8dmJruns57d2Rx5vf5PJBVPjuShlQPsndFLlt6sp/e/7\nGPr2o899D3R7NoYnk3977u10Yd5dHv/MWrXZqNmchsbXD7/E0d1u72BOy5QteV4tPMmUhGh8DTp+\n2Noe1HUAACAASURBVJmP2WL/0dvB58xuXUO88LWXZYS4EJ3k8WHdsH8f1uoqApKT0ei7vyzoz4uh\nhHS7LSFchcFLy7QxMdQ0mLu9G9eptK4hPmw49Tt3UPbJx3a/hhCezOPDuiZtIwCBk6Z0uy2bTSUz\nr5qIYB9CAqQbT3iWmeNaduP6dltut3fjOhVFpyPmltvRR0ZSuerL1g11hBDt8+iwtplM1O3Yjj7c\niPegwd1uL7ekjkaTReZXC48UHuRD0hAjOcV1ZB5foc/etP7+xN55NxpfP4rfeoOGzIMOuY4Qnsaj\nw7pu53ZUk4mASZO7PbcaYH92Sxf4cOkCFx4qNbkPAKu35DrsGl5RUcTcdgcABS8so7mkxGHXEsJT\neHRY12yyXxc4wIHjz6uH9ZOwFp5pUGwQA2MD2XW4jIKyeoddx3fYcCKv/C22ujoKnnsaa73jriWE\nJ/DYsLZUV9Gwby/e/QfgFRXV/fasNg7mVhEV6ivPq4XHUhSFuRP6AfD1lhyHXito2nRC5syluaiQ\ngheXo1osDr2eEO7MY8O6dvNmUFUCJk22S3vZRbWYmq1yVy083tjB4USG+JC2t4iqOsfumhV+yWX4\njR1H44H9FL/zlkMGtgnhCTw2rGvSNoJWS8CEiXZp70QX+HAJa+HhNBqFORP6YrGqfGfHDT5ORdFo\niL7xZgz94qlZv47Kr1c59HpCuCuPDGtTfj6mnGz8RiagCwi0S5snBpcNlZHgoheYkhBFoK+etTvz\naTQ5tntaYzAQe+cSdCGhlH28gtrt2xx6PSHckUeGtT3nVgOYLTYO5VUTZ/QjUPavFr2Al17LrKQ4\nGk0W1u0ucPj1dMEhxN61FMXgTdG/X6ExK8vh1xTCnXhcWKuqSu3mNDTe3viNGWuXNrMKqjFbbPK8\nWvQqZ4+Lw0uv4dttuVisjl8e1NCnL9E334JqNlOw7BnMZaUOv6YQ7sLjwrop6wiWinL8xyah8bLP\nXXDr/GoJa9GL+PvoSUmMoaLGxNb9PTMX2j9xDBG/uRJrbQ35zz6NtUGmdAkBHhjWtVs2A9htYBnA\ngexKFEU27xC9z5zkPmgUhVWbs3tspHbwzHMITp1Dc2EBBS/IlC4hwMPCWrXZqN22BY2fH77DR9il\nTZPZypGCGvpFBuDr3f2NQIRwJ+H/3959x0dVpX0A/907NZmS3jskIb0QQhEEEdG1I7K2fV1xdX31\nVXfVd62sZS1YVhE3i3Utry7Kwgo2dCOsDcNSQhqQHhLSezKZlqnn/SMQjQRJucmdmTzfz2c+MZc7\nzzwzxztP7rn3nOPrhdzkYDR3GVFa2zNtrxv0y6uhysoeGtL13v/RkC4y43lUsTZXV8Gh00GTkwtO\nKhUkZm2zDg4noy5wMmNdvGhokpRP9zZMW9HkeB5hv70Vitg4DBTsQe/OT6fldQlxVR5VrPUH9gEQ\ntgv85PVqurmMzFSRQWrMTQxCfdsAyhv6pu11h4d0BQSg56Ptw9MHEzITeUyxZnY79IcKIfHxhVfi\nHMHiVhzvg4TnkBDpI1hMQtzNJWf9cHY9naQ+voj4/T3gvb3R/s6bMFWUT+vrE+IqPKZYG8uPwmk0\nQpObC44X5m2ZBu1oaB9AXLgWSrkw3eqEuKPYUC3SZwWguql/ypbPPB1FeATCb/8dOI5D68t5sLRM\n7axqhLgijynW+oMn7gLPFa4LvLq5H4wBSbQkJiG49KxYAMBn03x2DQDec5IQcuNNcJrNaHlpA+z9\n09cdT4gr8Ihi7bRaYSwugjQwEMpZswWLW0njqwkZFh/pg6RoXxyp70V928C0v752wSIErl4De2/v\n0Bhss3nacyBELB5RrI2Hy+AcHIQmdwE4jhMsbnlDH2RSHvERwswvToi7E/PsGgD8LrwYPsvOgaWp\nEW00BpvMIB5RrE/eBa4V8C7wfoMFzV0GJEb6QCaVCBaXEHeWFOOH2RFaFNd0o6nTMO2vz3Ecgq+7\nHqqsbJgqjqL9nTdpDDaZEdy+WDsHzTCWlUIeGgZ5ZJRgccsbegEAqXEBgsUkxN1xHDd8dv3J9/Xi\n5CCRIOy3t0I5azb0+/6D7u3/FCUPQqaT2xdrQ2kpmM0Gde58QbvAj9YPXa9OjfMXLCYhniB9VgBm\nhWtxqLoLx9v1ouQwNAb7LshCQtD3xU70f7VblDwImS7uX6wLDwIANLnzBYvJGMPRhl5oVXJEBqkE\ni0uIJ+A4DlcsnQUA2LFHvKUsJRoNIu76X0i0WnR+sJnWwSYeza2LtXNwEMYjZZCHhUMRHiFY3OYu\nIwaMVqTG+gl6tk6Ip0iJ8UNilC/K6npQ26ITLQ95UDAifn8POLkC7W+8ClNVpWi5EDKV3LpYGw+X\nDXWBz8sVNO7R+pPXq6kLnJDRcByHK86OAwB8JOLZNQAoY2IRfvudYIyh9a8vwdLUKGo+hEwFty7W\n+sIDAABNzjxB4x49cXNZSiwVa0JOZ060H1Lj/FHe0IeqRnEnKVGlpCLsplvgHBxE88YXYO2anvW3\nCZkublusnRYLjIfLIAsJhTwiUrC4VpsD1U39iAxSwVetECwuIZ7oirNPXLv+7pjoQ6g08xcg6Jrr\n4NDp0PLiC7APTP/ELYRMFbct1sYjZWBWKzTzcgW9rlzTrIPN7qQucELGYFa4Flnxgahu1g33SInJ\nb8VK+F90CWydHWjZ+ALNckY8htsW65N3gaunqAucijUhY7PqxLVrVzi7BoCAK66E9uylsDQeR+tf\nX4LTZhU7JUImzS2LtdNqhaGsFLKgYCiiogWNfbS+F1IJj8RIX0HjEuKpokM0mJcUjPo2PQqrusRO\nBxzHIeS/boB6bg7MVZVoe+0VMIdD7LQImRS3LNamo4fBLBaoBe4C1xmtaOo0IDHKB3IZTTFKyFhd\nuWwWJDyHD7+pg93hFDsdcBIJQn97K7yTU2AsKUbH/70F5hQ/L0Imyi2Ltf7kRCg5wg7ZKqcucEIm\nJMTPG+dkR6Cz34yvi1vETgcAwMtkCL/9TijjZmFgbwG6tm5xiW56QibC7Yq102aFsbQE0sBAKGJi\nBI09PL6ahmwRMm6XLo6Fl0KCTwsaYBq0iZ0OAIBXeiHi9/dAHh6O/t1fovezT8ROiZAJcbtibTp6\ndGg5zBxhu8AZYzha3wuttwyRwWrB4hIyU2i95bhoYQwMZhs+3+c6E5NI1GpE3H0vpIGB6Pl4B/p2\n5YudEiHj5nbFWn/o5F3gwnaBt3QZoTNakRLrD56mGCVkQlbOi4KfRoFdhU3oHRgUO51hMj8/RN5z\nHyQ+vuj6xwfQffet2CkRMi5uVayZ3T7UBe7vD2VcnKCxS+u6AQDps2lJTEImSi6T4IqzZ8Fmd2L7\nd+JOQ/pT8uBgRP7vvZCoNeh47x0M7N8ndkqEjJlbFWtTVSWcJhPU2TmCL7BRWtcDjhta/o8QMnFn\npYUiMkiN/xxpR2OHOEtono4iPAIRd/8veKUS7W++DkNJsdgpETImblWsDUWHAADq7LnCxjXbUNei\nw+wIH6i9ZILGJmSm4XkOV507GwzA+7trXO4ObGVM7NBKXVIp2l7dBOORw2KnRMgZuU2xZk4nDCXF\n4NVqeCUkChr78LEeMAZkUhc4IYJIiwsYmoa0qR8HKlxvUQ2v+ARE3HkXwHFo3fQXmCrKxU6JkJ/l\nNsV6sP4YHLp+qLOywUmEnbCktHboenVmfKCgcQmZya5ZEQ+phMfWr2thsbreDGLeySkIv/1OgDG0\n5G2EqbpK7JQIOS23KdaGokIAgDo7R9C4docTR471IkCrQESgStDYhMxkwX7e+MWCKPTpLfjsPw1i\npzMqVVoGwm69HczhQMtLL8JcVyt2SoSMyi2KNWMMhqIicAolvFNSBI1d16KDyWJHRnyg4DetETLT\nXbwwFv5aBfIPNKKjzyR2OqNSZ2Uj7JbbwGxWtGx8AYP1rnUXOyGAmxRra0szbF2dUKVngJfJBY1d\nWtcDAMicTV3ghAhNIZfgquXxsDsYtuyuETud09LkzEPYzf8N5+Agmjf8mQo2cTluUawNxUUAAPVc\nYe8CB4auV8ulPJKiaZUtQqZCblIwkqJ9UVrXg7IT8xm4Is38BQi9+Zbhgm0+RgWbuA73KNZFheCk\nUqjSMwWN29lvRluPCSmx/rTKFiFThOM4XLcyETzH4f3dNbDZXe9ms5O0CxYNF+yWF6lgE9fh8sXa\n1tUFS1MTvJNTIPHyEjR22Ym7wDPiacgWIVMpMkiNFTmR6Owz49O9DWKn87OGCvZ/U8EmLsXli7Wh\n+OREKMLeBQ78cL06g2YtI2TKXbE0DgFaBb7Y14jmToPY6fws7YKFCP3tjwp2retebyczgxsU6yKA\n46DKyhY0rtliR1VjH6KD1fDXKgWNTQg5lVIuxfUXzIHDyfDOvyrhdLrWzGY/pZ2/EGG33AanxYLm\nF5+HqbJC7JTIDObSxdqu08FcWwOv+ARItVpBY5c39MHuYMigiVAImTYZswMxPzkYx1oH8FVRs9jp\nnJEmdz7Cb7sdzG5Hy0sbYDx6ROyUyAzl0sXaUFoMMDZFXeAnZi2jKUYJmVbXnpcIlVKKD7875lLL\naJ6OOjsH4bf/DmAMrXkbYSgtETslMgO5dLE2nlgRR5UtbBe4w+lESU03tCo54sKEPWMnhPw8H5Uc\nV50bD4vVgffyq1xuoY/RqDMyEf67uwGeR+vLedAXHhQ7JTLDSKf6BYKCNBN6nsNsRk1FObxjohGR\nMlvQnEqru2Aw23DhWbEICaFifToTbTviGly5/a44NxGHqrtRWtuNypYBLM2OFDulMwpathB+gVqU\nP/4U2l5/BSoZQ8h5K6bmtVy47Yg4prxYd3VNbD1b/aFCMJsNyrTMCcc4nd0HjgMA0mL8BI/tKYKC\nNPTZuDF3aL9rV8Sj8ngvXv5nKUJ9lPDTKMRO6cyCoxD5h/vRvPEF1Oa9jP72HvhfcKGgL+EObUdO\nb6r+0HLZbnBj6VAXuFrgu8CdToaiqk5ovGVIjPIRNDYhZOxC/Lxx9fJ4GAfteOeLSrfoDgcAZWwc\nou57EBJfX3Rv+we6d3zoNrkT9+WSxZo5HDCUlULi6wtFTKygsWua+zFgsmFuYhAkvEu+fUJmjHOy\nI5AW54/Dx3rwTUmr2OmMmSI8AtH3r4MsKBi9Oz9F5/t/B3M6xU6LeDCXrFbmulo4DQaoM7PBCVxQ\nCyu7AADz5gQLGpcQMn4cx+HGi5KhUkrxj69q0NHrmitzjUYWFISo+x+CPCISuq//jbbXX4XTZhM7\nLeKhXLJYG08u3CHwXeBOxlBY3Qm1lwxzaOEOQlyCn0aB6y+YA6vNib99Vg6HG52hSn19EXXfg/BK\nSISh8ABaXtoAh9ksdlrEA7lcsWaMwVBSDF6phNecZEFj1zbroDNYkZ0QCKnE5d46ITPW/OQQLEgJ\nQV3rAD7f1yh2OuMiUakQcfcfoMqeC3NlBZqfexp2Xb/YaREP43IVy9raCltXJ7zT0sHLZILGLqzq\nBADMS6IucEJcza9WJsJXLccn39ejtkUndjrjwsvlCL/tDvgsOweWpkY0Pf0UrO3tYqdFPIjLFWtD\nyYkucKHvAmcMh6q6oFJKkRzjJ2hsQsjkqb1kuOXSVDgZw6sfH4HB7F7XfzmeR/B/3YCAy1bB1t2F\nxmeehLmGFgAhwnC5Ym0sKQZ4XvC1q4+1DqBPb0EWdYET4rKSYvywakkcegcs+Ntn5XC62ZAojuMQ\ncNkqhNxwI5wmE5pfeBb6A/vFTot4AJeqWvb+PgzWH4NX4hxIVCpBYxdWnugCp7vACXFpF58Vi9Q4\nf5TV9eBf+93r+vVJPmcvQ8Tv7wEnlaLt9VfQ+8VOGotNJsWlivXJCfKF7gJnjOFQVSe8FBKkxPoL\nGpsQIiye4/DbS1Pgq5Zj+7fHUN3knjdrqVLTEPXAOkj9/NH94TZ0vvd/YHa72GkRN+VSxfrkwh1C\nF+tjrQPoGbAgKz4QMqlLvWVCyCi03nLcenkaAODVj49gwGQVOaOJUURGIXrdw1BEx0D33Tdo3vgC\nHAaD2GkRN+Qylcs5OAhTRTnkEZGQBQYJGrvgyNBdmQtTQwWNSwiZOolRvrhiaRz6DVa8suMI7A73\nGX/9Y1JfP0Td9+Dw0K7G9U/A2uY+s7UR1+AyxdpYfhTMbhf8rNpqc2B/eQd81XKkUhc4IW7lwoUx\nyEkMQlVTPzbvqnbb6768Uonw2+6A/0WXwNbZgcb1T8B45LDYaRE34jrF+sT1alWmsMW6qKYLZosd\nZ6WFgec5QWMTQqYWz3G4+ZIURAWr8W1JK74qahE7pQnjeB6Bq9cg9OZbwGw2tLy0AX1f5rvtHyBk\nerlEsWZOJ4xlJZD4+EAZGyto7IKyNgDAkowwQeMSQqaHQi7B767MgNZbhg921+Bofa/YKU2KduFZ\niLz3AUi0WnRt/QDtf3sNTotF7LSIi3OJYj1YfwwOvR6qjExBF+7o0Q2ivKEP8RE+CPX3FiwuIWR6\nBfgoccfqDPA88MpHR9DuRgt+jMZrdjxiHn4Mytnx0O/fh6ZnnoStq0vstIgLc4libTh5F7jAXeB7\nj7SBAVicTjeWEeLu4iN9cMMvkmCy2PHSP8ugd9M7xE+S+voh8g/3n5iitAnHn3iMrmOT03KJYm0s\nLQEnk8E7OUWwmIwxFBxuh1zKY35yiGBxCSHiWZwehgsXRqOj14SN28owaHXvccu8TIaQ69ci5Nc3\nglktaHlpAxq3bKW1sckpRC/W1q5OWFtb4J2SCl6hECxuTbMOnf1m5MwJgpdCKlhcQoi4rlw2G4vT\nQlHfNoBNbjyk68d8li5D5H0PQernj6YP/oGWjS/APjAgdlrEhYherH+4CzxL0Ljfn7yxLJ1uLCPE\nk/AchxsuTELm7AAcre/Fmzsr3G4O8dF4zZqFmEf+BL/cHJjKj+L444/AVF0ldlrERYherIevV2cI\nV6wHrXYcrOxEgFaJObTCFiEeRyrhceuqNMRH+mB/eQc+2F3jEUOgJGo1kh96AIFrroJjYADNzz+L\nnp2fUrc4EbdYO0xGmGuqoYiNg9TXV7C4hZVdsNgcWJweCp6jsdWEeCKFTILfr8lARJAK/z7UjI/2\n1HtEweZ4Hv6/uAhR9z4AqY8PenZ8iOYXnoOt172HrJHJEbVYG48cBhwOwWct+650aCq/s6gLnBCP\nplLKcM9VWQjyVeLTvQ3YseeYRxRsAPBKSETMo08MTVNaVYnjjz0M/aFCsdMiIhG3WJ9cZUvA69V1\nLTrUtuiQMTsAwb5egsUlhLgmP40C9183F8F+Xvhs73H889s6jynYErUa4f9zJ4KvXwtmt6Htlb+i\n49234RwcFDs1Ms1EK9bMbofxcBmk/gGQR0YJFjf/wND6txfkCheTEOLa/LVK3H/dXIT4e+OLfY3Y\n+nWtxxRsjuPgu+wcRP/xMSiioqD77lsc/9PDdPPZDCNasTbX1sBpMkGVmQVOoOvKnf1mHKruQnSI\nGkl0YxkhM8rQGXY2wgK8kX+gCR/srvGIu8RPUoSHI+qhR4YWA+nuRvOfn0HXPz6A0+rek8OQsRGt\nWBtOdoELeL1618EmMAZcMD9asD8ACCHuw1etwH3XzUV4oAq7DzXjjU/LYbN7zp3UvEyGwNVrEPXA\nOsiCg9G3Kx+Njz8K87E6sVMjU0yUYs0Yg7GkGLxSCa/EOYLENJht+L6sDX4aBXKTggWJSQhxPz4q\nOR741VzERwwN63pxawlMgzax0xKU1+x4xDzyOHxXrIS1vQ1NTz+Jzi2b6Vq2BxOlWFvbWmHr6oR3\nWjp4mUyQmN+WtMBic2DlvChIJaIPHyeEiEjtJcMfrslCTmIQKhv78fTfi9Cj86xCxisUCL72V4i8\n9wHIgoPRv3sXGh5dB+ORMrFTI1NAlKpmPDkRikBd4Da7E7sPNUMpl2BpZrggMQkh7k0uk+C2VWk4\nb14kWrqNeOq9Qhxv14udluC85yQh5rEn4H/RJbD396Nl4wa0vfEa7Dqd2KkRAYlSrA0lxQDPQ5WW\nIUi8/eUd0BmsWJYVDm8lzQNOCBnC8xyuOy8R15wbj36DFev/fggFh9vETktwvEyOwNVrEPPHR6GI\njYN+/3/Q8McH0Ld7F5jDIXZ6RADTXqztun4M1h+DV0IiJGr1pOMxxvDlwUbwHIfzcmi4FiHkVOfP\nj8bv1mRAKuHx5s4KvJdf5RELgPyUIioa0Q89jOBfXQ9wHLq2bMbxJx6DuaZa7NTIJE17sTaWlQKM\nCbZ2dUlNN5q7jMhNDkaAj1KQmIQQz5MVH4hH1s5DZJAaXxe34NnNRegd8Kzr2MDQdKW+y1cg9sln\noF18NqzNTWh6dj3a3ngNtt4esdMjEzTtxfrkkC2VANer7Q4ntn5dC57jcOlZsZOORwjxbCF+3lj3\n6xwsTA1BXesAHnv7IIqru8ROa0pItVqE3ngToh78IxTRMUNd4+seQPeOD+EcNIudHhmnaS3WTosF\npvKjkIeHQx48+eFVXxW1oKPPjHOywxEeqBIgQ0KIp1PIJPjtJSn41cpEDFodyNt+GG99XgGzxS52\nalPCa3Y8ov/4KEJuvBm8SoXenZ+i/qH70f/tN3Q9241Ma7E2VZSDWa1QCdAFbjDb8Mn39fBSSHH5\nkjgBsiOEzBQcx2FFTiQeXTsP0SFqfF/WhkffOoDqpn6xU5sSHM/DZ/ESxD31LAIuvwLOwUF0vvcO\nGh5Zh4ED+2gJTjcwrcXaIOCQrY+/r4fJYsdli2Oh8ZZPOh4hZOaJCFLjj7+eh0vOikHPwCCe3VyE\n93dXe+xZNq9QIODSyxG3/ln4LFsOW3cX2l9/FccffxSGkmKPmU/dE0kee+yxx6byBUymoXlrmdOJ\nznffAa9QIOjqayc1HWhbjxFv7axEkJ8Xbr4kBTxPU4sKTaVSDLcdcT/UfmPH8xySY/yRGuuP6qZ+\nHD7Wi4IjbfBTKxARqJr2qYuno+14pRfUmVnQLFwEh8kIc0U59Af2DS2upNFAFhJKUzZPkEqlmJK4\n01asB4/Vof/fu6CZPx+a7JxJxXxzZwXae0248aJkRARNfvgXORV92bs3ar/x89cqsSwrAjIJh6MN\nfThQ0YmaZh1mhWuntfduOttOolJBMzcH6pxcOPQDMFdWQH9gPwxFh8B7e0MeHk5Fe5zcvljrvvkK\n5ppqBFy6CvKwsAnHO1rfi4/21CMp2hdXLptN/yNNEfqyd2/UfhMj4TnMifbDgpQQdPaZcbS+F9+W\ntKLfYEV0iAZeiqmfdEmMtpNqtdDkzod6Xi6cZjPMVZUwHDoI/f594DgO8vAIcFKacGos3LpYM8bQ\n9f7f4bRYEHL92gk3umnQjrztZTAN2nHH6nT4qqfmQyH0Ze/uqP0mR6WUYUFKCGJCNKhv1+NofS++\nKW6B2WpHbKgGcqlk6l5bxLaTarTQzJ0HzcJFYDYbzNVVMJaWoP+br+AwGiEPDYXEy1uU3NyFWxdr\na3Mzend+AnVWNrSLzppQHMYY3visHLXNOly4MBpnpU387JycGX3Zuzdqv8njOA5hASoszw5HgFaJ\nY20DOHysF98Ut8JmdyA8SAWFTPii7QptJ1GpoM7Mgs/Zy8ApFLA0Hoep/Cj6/70bluYmSNRqSAMC\nqGdzFFNVrKelX0NfeAAAoMldMOEYuwubcaiqC4lRvli9dJZQqRFCyM+S8DyWZoZjYUoIvipqwef7\njuOTggZ8sb8RS9LDcP78KIT4eebZptTHB4GXXwH/iy6Gfv9+9O3+EoZDhTAcKoQsOAQ+S5dBu3gJ\npBqt2Kl6PI5N8b36nZ0DaFj3AOz9fZj9Yh54xfj/6qhr0eGZzUVQKaV49Mb58NNQ9/dUCwrSoKvL\n81Yomimo/aaOxerAnrJWfHmwCd26QXAAshODcE5WOFLi/MFP8mzTlduOMYbBulrovv0G+sIDYDYb\nIJFAlZ4B7aLFUGVkCrbssbsKCtJMSdwpP7O2NB6HrbMDmtz5EyrUBrMNr3x8BE4nwy2XpVKhJoSI\nSiGX4Lx5UVg+NwKFlV341/5GFFV3oai6CwFaJc7ODMOS9DD4az1vrQKO4+AVnwCv+AQEXXMdBv5T\nAN2e72AsKYaxpBi8twqa3FxoFiyCV3wCOF6UhR090pSfWZe/8ib6/vU5wv7nTmjmjm/IlpMx/OWf\nZSir68Gqs+Nw2WKaqWy6uPJf9+TMqP2mD2MMx1oH8F1pKw5UdMJic4DjgOQYP8xLCsbcxCBoxzH0\nyx3bztLUiIH/7MXA/n1w6IZmgZNotVBn50CdMw/ec5LASabupjxXMlVn1lNarBljOHDzrXAaDJj1\n4l/Ay8b+P6zN7sAbn1WgsLITaXH+uOuqzEl3L5Gxc8cvDPIDaj9xmC12HKjowJ6yNhxrHQAA8ByH\n5Bhf5MwJRsbsgDOecbtz2zGnE6aKchgOHYShqAgOw9D74FUqqNLSoUrPgCo1HRLN1BQ0V+CWxVpf\nVY2y+x6EZuEihN3832N+nsFsQ96HZahp1iEx0gd3rsmASjmzr4NMN3f+wiDUfq6gu9+MwqouHKzs\nRH3bwPD2iEAV0mb5I21WABIifCD/yR3lntJ2zOGAuaYa+kMHYSgugqP/xLzrHAflrNnwTkmFd1Iy\nlLNme9R1brcs1vVvvo3WTz5D+J13QZ2ZNabndPeb8eK2UrT1mJCbFIybL0mGbArHNJLRecoXxkxF\n7edauvvNKKntxpH6XlQe74PVPrRwhoTnEBuqQUKULxIifRAf4YNZMQEe13aMMVibm2E8XArj4TKY\n62qBE4uHcDIZlLPj4T0nCV7xCVDExkHi5SVyxhPnlsX64G9ugd1sxuwNfxnTRCh1LTr8dfth6IxW\nXDA/Cr9cHk9d3yKhL3v3Ru3numx2B6qbdDh8rAc1zf043m6A80dfw0F+XogMVCEmRIPoUA0iA1Xw\n91F61Hehw2iEuboKpqoKmCorYW1u+uEfT8yYppw1C8rYWVBERUMRETGhG5TF4JbFuuDyK6FdlTsS\nDAAADBJJREFUfDZCb7zpZ/c73q7HJwX1KK7pBgfgmvMSsHJe1FSlRcaAvuzdG7Wf+7BYHTjWqkN1\nsw51rTo0dxrRb7CM2Ecu4xHq743wABVC/b0R6KtEoI8Xgny94KOWu30hd+j1MNVUY/BY3dCjoR7M\n+qOJYTgO8tAwKKKiIA8LhzwkFPKwMMiCQ1yuiLvt0C1N7vxRtzPGcLxDj08LGlBc0w0AmB2hxeql\ns5Ec4zfVaRFCiEtQyCVIjvVHcqw/ACAwUI2a+h4c79CjsUOP1m4j2npMaOsxobHDcMrzpRIefho5\nfNUK+KoV8NMo4KOWQ+Mlh9pbBo23DBpvOdRKKZQKqUsWdolGA83cnOERQ8zhgKWlGZbGRliafnhY\n21pHPpHjIPX1gywwENKAAMgCgyALCIDU1w9SX19IfHwhUas9YgjZlBZriVoNfWgs+roMsNmd6B0Y\nREO7Hg1tA2ho18M4OLRm7OwILS5fEofUWH+avo4QMqNxHAc/zVDRzYoPHN7uZAw9ukF09JrQpRtE\nt86M7v6hn316C2pbdDhTPykHQKmQwlshhZdCCqVcAqVcAoVcAqVMArlMArmMh0wqgVzKQy7lIZXy\nkEp4SCUcpBIeEp6HRMJBynOQ8BwkEh48x4Hjh67B89zQg+OG3gvHYeTv+GH7j9/z0M+hHAEAAWHg\nAsKgzF4AJYZO8Jx9vbB3tg89OtrhaG+Do6cb5toaoKZ69DfNS8Cr1eBVavAq1fBPTukFXqkEp1CC\n81KClysAmRycTPbDQyIBJJKhn/yJn0NvBOD4E8lyP3y4cNMz60I+DPl/OzjqvwX7eiE1zh9LMsKo\nSBNCyBnwHIcg36Gu79E4nE4MGG3oN1igM1ihN1mhN9tgMNmgN1lhHLTDZLHDNGiH2WJDz4AZg1bH\nGQu8a1IAiBl6BAC8vxMauxE+NiN87Aao7WaoHaahn3YTvM0WeBk6oXTapjyz+I8/nJK4Uz4pCiGE\nEEImx/078gkhhBAPR8WaEEIIcXFUrAkhhBAXR8WaEEIIcXFUrAkhhBAXR8WaEEIIcXFUrAkhhBAX\nN+ZivXnzZqxYsQIZGRlYvXo1CgsLf3b/AwcOYPXq1cjIyMDKlSuxZcuWScckEzeez3rXrl246aab\nsGjRIsydOxdXXXUVvvrqqxH77NixA0lJSUhOTkZSUtLwf1t/PJ8vEcR42u7AgQPD7fHjdqmvrx+x\nX35+Pi6++GKkp6fjkksuwe7du6f6bcxY42m/Bx98cMRxdfJndnb28D5jbWMyOYWFhbjtttuwdOlS\nJCUl4aOPPjrjc6qrq3H99dcjMzMTy5Ytw6ZNm07ZZ8LHHhuDnTt3stTUVLZt2zZWV1fHnnjiCZaV\nlcXa2tpG3b+pqYllZWWxJ598ktXV1bGtW7ey1NRU9uWXX044Jpm48X7WTz75JHv99ddZWVkZa2xs\nZHl5eSw5OZkVFhYO77N9+3aWlZXFenp6WHd39/CDCGu8bbd//36WlJTE6urqRrSL0+kc3qeoqIil\npKSw1157jdXV1bFXXnmFpaSksNLS0ul6WzPGeNtPr9ePaLfu7m523nnnsYceemh4n7G0MZm8b775\nhm3YsIHl5+ezrKwstmPHjp/dX6/Xs8WLF7O7776b1dbWsi+//JJlZ2ezt99+e3ifyRx7YyrWv/zl\nL9nDDz88Ytv555/PNmzYMOr+zz33HDv//PNHbFu3bh27+uqrJxyTTJwQn/WaNWvYM888M/z79u3b\nWXZ2tmA5ktGNt+1OfpH39fWdNuZdd93FfvOb34zYtnbtWnbPPfdMPmEywmSPvcLCQjZnzhxWUlIy\nvG0sbUyENZZivXnzZpaTk8MsFsvwtpdffpktXbp0+PfJHHtn7Aa32Ww4evQoFi9ePGL74sWLUVRU\nNOpzSktLsWTJkhHblixZgiNHjsDhcEwoJpkYoT5ro9EIHx+fEdssFgvOPfdcLFu2DLfeeisqKioE\nyZkMmWjbMcZw5ZVXYsmSJVi7di32798/4t9LSkpOiblkyRIUFxcLlzwR5Njbtm0bEhISkJmZOWL7\nmdqYTL/S0lLMmzcPcrl8eNuSJUvQ2dmJlpYWAJM79s5YrPv6+uBwOBAQEDBie0BAALq7u0d9TldX\n1yn7BwYGwuFwoK+vb0IxycQI8Vlv3rwZHR0duPzyy4e3xcXF4amnnsLLL7+MDRs2QC6X49prr0Vj\nY6Og+c9kE2m7oKAg/OlPf0JeXh42bdqEuLg4rF27dsR10tGOTzr2hDfZY89gMCA/Px9XX331iO1j\naWMy/bq7u0ete4yx4faezLE35lW3froqFmPsZ1fKGm3/n24fb0wycRP9rPPz8/H888/jxRdfRFhY\n2PD2rKwsZGVlDf+enZ2Nyy+/HO+99x7WrVsnXOJkXG0XFxeHuLi44d8zMzPR0tKCt956C/PmzTtt\nzNNtI5M30WPv448/htPpxGWXXTZi+1jbmEy/idS90237qTOeWfv5+UEikZxS+Xt7e0/5C+GkoKCg\nU/bv6emBRCKBr6/vhGKSiZnMZ52fn4/7778fzz33HM4555yf3ZfneaSlpeH48eOTTZmcINRxkpGR\nMaJdTnd80rEnrMm237Zt23DBBRdAq9Wecd+ftjGZfoGBgaMeVxzHITBwaF3yyRx7ZyzWMpkMqamp\nKCgoGLG9oKAAc+fOHfU5WVlZ2Lt37yn7p6WlQSKRTCgmmZiJftaff/457r//fjz77LNYuXLlmF6r\nqqoKQUFBk8qX/ECo46SiomJEu2RlZZ0Sc+/evSOGB5HJm0z7lZWVobKyElddddWYXuunbUymX1ZW\nFgoLC0cMXy0oKEBwcDDCw8OH95nwsTeWO+F27tzJ0tLS2NatW1ltbS174oknWHZ29vDwg3vvvZfd\nd999w/ufHLr11FNPsdraWrZ161aWlpbGdu3adcaYra2tY0mJjMN42++zzz5jqamp7N1332VdXV3D\nj/7+/uF98vLy2J49e1hjYyOrqKhgDzzwAEtNTWWHDx+e9vfnycbbdu+88w7btWsXa2hoYDU1Nez5\n559nSUlJI469oqIilpqaOjx85NVXX2WpqamsrKxs2t+fpxtv+5300EMPsQsuuGDUmGNpYzJ5RqOR\nVVRUsPLycpaZmck2bdrEKioqhmvU888/z2644Ybh/U8O3brnnntYdXU1y8/PZ3Pnzj1l6NZEj70x\nXbO+6KKLoNPp8Oqrr6KrqwsJCQl44403EBoaCgBoa2sDz/9wkh4ZGYk33ngD69evx5YtWxAcHIyH\nH34Y55133hlj/vi6KBHGeNtvy5YtcDgcWL9+PdavXz+8PTc3F++++y4AQK/X45FHHkF3dzc0Gg2S\nk5Px/vvvIy0tbXrfnIcbb9vZbDb8+c9/RkdHBxQKBRISEvD666/j7LPPHt4nOzsbGzZswMaNG5GX\nl4fo6Ghs3LgR6enp0/7+PN142w8YGnnxxRdf4I477hg15ljamEzekSNH8Otf/3r4enJeXh7y8vKw\natUqPP300+ju7kZzc/Pw/mq1Gm+//TYef/xxrFmzBlqtFjfddBPWrl07vM9kjj2OsRNXwAkhhBDi\nkmhucEIIIcTFUbEmhBBCXBwVa0IIIcTFUbEmhBBCXBwVa0IIIcTFUbEmhBBCXBwVa0IIIcTFUbEm\nhBBCXBwVa0IIIcTFUbEmhBBCXNyY17MmhLgus9mMDz74AMXFxVizZg36+vpQXl6O5cuXY9GiRWKn\nRwiZJDqzJsQD7N69G9dccw26u7thtVqxatUqXHPNNXj66afFTo0QIgAq1oR4gOXLl0MqlaKpqQkr\nVqwAALS3t6O/v1/kzAghQqBiTYgHUKvVKCsrQ3p6+vCSi3v27MHixYtFzowQIgS6Zk2Ih9i/fz8S\nExMBAL29vfj666/x1ltviZwVIUQItJ41IR5i7dq1yMzMREJCAsrKynDllVdizpw5YqdFCBEAFWtC\nPIDNZsOyZctQUFAAjuPETocQIjC6Zk2IBygtLUVCQgIVakI8FBVrQtxcdXU1Nm3ahP7+fhQUFIid\nDiFkClA3OCGEEOLi6MyaEEIIcXFUrAkhhBAXR8WaEEIIcXFUrAkhhBAXR8WaEEIIcXFUrAkhhBAX\nR8WaEEIIcXFUrAkhhBAX9/+wt8Pxp+dicwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc60ff4c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot edward's approximation to the true beta-binomial posterior\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ed_posterior = sp.stats.beta(beta_binomial_inference.latent_vars[p].distribution.a.eval(),\n",
    "                             beta_binomial_inference.latent_vars[p].distribution.b.eval())\n",
    "\n",
    "plot_x = np.linspace(0, 1, 100)\n",
    "ax.plot(plot_x, prior.pdf(plot_x),\n",
    "        '--', c='k', label='Prior');\n",
    "\n",
    "ax.plot(plot_x, posterior.pdf(plot_x),\n",
    "        c=blue, label='Posterior');\n",
    "ax.plot(plot_x, ed_posterior.pdf(plot_x),\n",
    "        c=red, label='Edward posterior');\n",
    "\n",
    "\n",
    "ax.set_xticks(np.linspace(0, 1, 5));\n",
    "ax.set_xlabel(r'$p$');\n",
    "\n",
    "ax.set_yticklabels([]);\n",
    "\n",
    "ax.legend(loc=1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EvUlYewCT2creYxXEhPsREeLr7HI8UsroaAB+SpfNPYQQPU/C2gPsO1qB2WKT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\nR8WaEEIIcXFUrAkhhBAX9/+wt8Pxp+dicwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc60ff4c50>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from edward.models import PyMC3Model\n",
    "\n",
    "# probability model\n",
    "x_beta_binomial_obs = shared(np.zeros(1))\n",
    "\n",
    "with pm.Model() as beta_binomial_model_untransformed:\n",
    "    p = pm.Uniform('p', 0., 1., transform=None)\n",
    "    x_beta_binomial_ = pm.Bernoulli('x', p, observed=x_beta_binomial_obs)\n",
    "    \n",
    "pymc3_data = {x_beta_binomial_obs: x_beta_binomial}\n",
    "pymc3_beta_binomial_model = PyMC3Model(beta_binomial_model_untransformed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 29.3 s, sys: 5.54 s, total: 34.8 s\n",
      "Wall time: 22.4 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# variational distribution\n",
    "pymc3_q_p = Beta(a=tf_positive_variable(),\n",
    "                 b=tf_positive_variable())\n",
    "pymc3_q = {'p': pymc3_q_p}\n",
    "\n",
    "pymc3_beta_binomial_inference = ed.MFVI(pymc3_q, pymc3_data,\n",
    "                                        pymc3_beta_binomial_model)\n",
    "pymc3_beta_binomial_inference.run(n_iter=30000, n_print=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oqALrPH/+PMOHD8fNzY02bdowceJE7W8GISoqSVRFuXHnzh0GDRpEjRo1WLVq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\n0KemkrRyNfaly7AtXpywe1qlUdVO69Mv0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VFXV+e7OBwOX5/s7Gxx7tw5UVZWJoqLi8VH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\nRFL5f4yiFuVgX8QEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc609b8710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot a comparison of the variational approximations calculating using\n",
    "# using the tensorflow and pymc3 models\n",
    "fig, (tf_ax, pymc3_ax) = plt.subplots(ncols=2, sharex=True, sharey=True, figsize=(16, 6))\n",
    "\n",
    "tf_ax.plot(plot_x, prior.pdf(plot_x),\n",
    "           '--', c='k', label='Prior');\n",
    "\n",
    "tf_ax.plot(plot_x, posterior.pdf(plot_x),\n",
    "           c=blue, label='Posterior');\n",
    "tf_ax.plot(plot_x, ed_posterior.pdf(plot_x),\n",
    "           c=red, label='Edward posterior');\n",
    "\n",
    "\n",
    "tf_ax.set_xticks(np.linspace(0, 1, 5));\n",
    "tf_ax.set_xlabel(r'$p$');\n",
    "\n",
    "tf_ax.set_yticklabels([]);\n",
    "\n",
    "tf_ax.legend(loc=1);\n",
    "tf_ax.set_title('TensorFlow Model');\n",
    "\n",
    "pymc3_posterior = sp.stats.beta(pymc3_beta_binomial_inference.latent_vars['p'].distribution.a.eval(),\n",
    "                                pymc3_beta_binomial_inference.latent_vars['p'].distribution.b.eval())\n",
    "\n",
    "pymc3_ax.plot(plot_x, prior.pdf(plot_x),\n",
    "              '--', c='k', label='Prior');\n",
    "\n",
    "pymc3_ax.plot(plot_x, posterior.pdf(plot_x),\n",
    "              c=blue, label='Posterior');\n",
    "pymc3_ax.plot(plot_x, pymc3_posterior.pdf(plot_x),\n",
    "              c=red, label='Edward posterior');\n",
    "\n",
    "\n",
    "pymc3_ax.set_xticks(np.linspace(0, 1, 5));\n",
    "pymc3_ax.set_xlabel(r'$p$');\n",
    "\n",
    "pymc3_ax.set_yticklabels([]);\n",
    "pymc3_ax.set_title('PyMC3 Model');\n",
    "\n",
    "fig.suptitle('Beta-Binomial Mean Field Variational Inference with Edward');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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oqALrPH/+PMOHD8fNzY02bdowceJE7W8GISoqSVRFuXHnzh0GDRpEjRo1WLVq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\n0KemkrRyNfaly7AtXpywe1qlUdVO69Mv0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VFXV+e7OBwOX5/s7Gxx7tw5UVZWJoqLi8VH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\nRFL5f4yiFuVgX8QEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc609b8710>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Edward-supported modeling \"languages\"\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <th><center>Joint Distribution</center></th>\n",
    "        <th><center>Variational Distribution</center></th>\n",
    "    <tr>\n",
    "    <tr>\n",
    "        <td><center><a href='https://github.com/tensorflow/tensorflow/blob/master/tensorflow/g3doc/api_docs/python/contrib.distributions.md'>TensorFlow Distributions</a></center></td>\n",
    "        <td rowspan='4'><center>TensorFlow</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center>PyMC3</center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td><center><a href='http://mc-stan.org/'>Stan</a></center></td>\n",
    "    </tr>\n",
    "    <tr>\n",
    "        <td>Direction density calculations<br>\n",
    "            <ul>\n",
    "                <li>TensorFlow\n",
    "                <li><a href='http://www.numpy.org/'>Numpy</a>\n",
    "                <li>Pure Python\n",
    "            </ul>\n",
    "        </td>    \n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Congressional Ideal Points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The congressional ideal point model uses the [1984 congressional voting records data set](https://archive.ics.uci.edu/ml/datasets/Congressional+Voting+Records) from the [UCI Machine Learning Repository](https://archive.ics.uci.edu/ml/index.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%%bash\n",
    "# download the data set, if we have not already\n",
    "if [ ! -e /tmp/house-votes-84.data ]\n",
    "then\n",
    "    wget -O /tmp/house-votes-84.data \\\n",
    "        http://archive.ics.uci.edu/ml/machine-learning-databases/voting-records/house-votes-84.data\n",
    "fi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Load and code the congressional voting data.\n",
    "\n",
    "\"No\" votes (`'n'`) are coded as zero, \"yes\" (`'y'`) votes are coded as one, and skipped/unknown votes (`'?'`) are coded as `np.nan`.  The skipped/unknown votes will be dropped later.\n",
    "\n",
    "Also, code the representative's parties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "N_BILLS = 16\n",
    "\n",
    "vote_df = pd.read_csv('/tmp/house-votes-84.data',\n",
    "                      names=['party'] + list(range(N_BILLS)))\n",
    "\n",
    "vote_df.index.name = 'rep'\n",
    "\n",
    "vote_df[vote_df == 'n'] = 0\n",
    "vote_df[vote_df == 'y'] = 1\n",
    "vote_df[vote_df == '?'] = np.nan\n",
    "\n",
    "vote_df.party, parties = vote_df.party.factorize()\n",
    "republican = (parties == 'republican').argmax()\n",
    "\n",
    "n_reps = vote_df.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Republicans (`'republican'`) are coded as zero and democrats (`'democrat'`) are coded as one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['republican', 'democrat'], dtype='object')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parties"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     party    0  1  2    3    4  5  6  7  8  9   10   11 12 13 14   15\n",
       "rep                                                                   \n",
       "0        0    0  1  0    1    1  1  0  0  0  1  NaN    1  1  1  0    1\n",
       "1        0    0  1  0    1    1  1  0  0  0  0    0    1  1  1  0  NaN\n",
       "2        1  NaN  1  1  NaN    1  1  0  0  0  0    1    0  1  1  0    0\n",
       "3        1    0  1  1    0  NaN  1  0  0  0  0    1    0  1  0  0    1\n",
       "4        1    1  1  1    0    1  1  0  0  0  0    1  NaN  1  1  1    1"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vote_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Transform the voting data from wide form to \"tidy\" form; that is, one row per representative and bill combination.\n",
    "\n",
    "If you haven't already, go read [Hadley Wickham](http://vita.had.co.nz/papers/tidy-data.pdf)'s [_Tidy Data_](http://vita.had.co.nz/papers/tidy-data.pdf) paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "long_vote_df = (pd.melt(vote_df.reset_index(),\n",
    "                        id_vars=['rep', 'party'], value_vars=list(range(N_BILLS)),\n",
    "                        var_name='bill', value_name='vote')\n",
    "                  .dropna()\n",
    "                  .astype(np.int64))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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AAICBCOIAAAAAABiIIA4AAAAAgIEI4gAAAAAAGIggDgAAAACAgQjiAAAAAAAY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\nf6Q55wCQE6WbzTp+/A+79lmxYmWm8AA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc600e2048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = sns.factorplot('bill', 'vote', 'party', long_vote_df,\n",
    "                      kind='bar', ci=None, size=8, aspect=1.5, legend=False,\n",
    "                      palette=[red, blue]);\n",
    "grid.set_axis_labels('Bill', 'Percent of party\\'s\\nrepresentatives voting for bill');\n",
    "grid.add_legend(legend_data={parties[int(key)].capitalize(): artist\n",
    "                             for key, artist in grid._legend_data.items()});\n",
    "grid.fig.suptitle('Key 1984 Congressional Votes');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAICBCOIAAAAAABiIIA4AAAAAgIEI4gAAAAAAGIggDgAAAACAgQjiAAAAAAAY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\nf6Q55wCQE6WbzTp+/A+79lmxYmWm8AA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc600e2048>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid.fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "*Idea*:\n",
    "\n",
    "* Representatives ($\\color{blue}{\\alpha_i}$) and bills ($\\color{green}{\\beta_j}$) each have an _ideal point_ on a spectrum of conservativity\n",
    "    * If a representative's and bill's ideal points are the same, the representative has a 50% chance of voting for the bill"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "* Bills also have an ability to _discriminate_ ($\\color{red}{\\gamma_j}$) between conservative and liberal representatives\n",
    "    * Some bills have broad bipartisan support, while some provoke votes along party lines"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Representative ideal points\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\color{blue}{\\alpha_1}, \\ldots, \\color{blue}{\\alpha_N}\n",
    "    & \\sim N(0, 1)\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normal_log_prior(value, loc=0., scale=1.):\n",
    "    return tf.reduce_sum(normal.log_pdf(value, loc, scale))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "#### Bill ideal points and discriminative abilities\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\mu_{\\beta}\n",
    "    & \\sim N(0, 1) \\\\\n",
    "\\sigma_{\\beta}\n",
    "    & \\sim U(0, 1) \\\\\n",
    "\\color{green}{\\beta_1}, \\ldots, \\color{green}{\\beta_K}\n",
    "    & \\sim N(\\mu_{\\beta}, \\sigma_{\\beta}^2)\n",
    "\\end{align*}\n",
    "$$\n",
    "<br>\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\mu_{\\gamma}\n",
    "    & \\sim N(0, 1) \\\\\n",
    "\\sigma_{\\gamma}\n",
    "    & \\sim U(0, 1) \\\\\n",
    "\\color{red}{\\gamma_1}, \\ldots, \\color{red}{\\gamma_K}\n",
    "    & \\sim N(\\mu_{\\gamma}, \\sigma_{\\gamma}^2)\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def hierarchical_log_prior(value, mu, sigma):\n",
    "    log_hyperprior = normal_log_prior(mu) + uniform.log_pdf(sigma, 0., 1.)\n",
    "\n",
    "    return log_hyperprior + normal_log_prior(value, loc=mu, scale=sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def log_prior(alpha,\n",
    "              beta, mu_beta, sigma_beta,\n",
    "              gamma, mu_gamma, sigma_gamma):\n",
    "    \"\"\"\n",
    "    Combine the log priors for alpha, beta, and gamma into the\n",
    "    overall prior\n",
    "    \"\"\"\n",
    "    return normal_log_prior(alpha) \\\n",
    "            + hierarchical_log_prior(beta, mu_beta, sigma_beta) \\\n",
    "            + hierarchical_log_prior(gamma, mu_gamma, sigma_gamma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Note that we do not specify a hierarchical prior on $\\alpha_1, \\ldots, \\alpha_K$ in order to ensure that the model is identifiable.  See [_Practical issues in implementing and understanding Bayesian ideal point estimation_](http://www.stat.columbia.edu/~gelman/research/published/171.pdf) for an in-depth discussion of identification issues in Bayesian ideal point models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Observation model\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\mathbb{P}(\\textrm{Representative }i \\textrm{ votes for bill }j\\ |\\ \\color{blue}{\\alpha_i}, \\color{green}{\\beta_j}, \\color{red}{\\gamma_j})\n",
    "    & = \\frac{1}{1 + \\exp(-\\color{red}{\\gamma_j} \\left(\\color{blue}{\\alpha_i} - \\color{green}{\\beta_j}\\right))}\n",
    "\\end{align*}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def long_from_indices(short, indices):\n",
    "    return tf.gather(short, tf.cast(indices, tf.int64))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "def log_like(vote, rep, bill, alpha, beta, gamma):\n",
    "    # alpha, beta, and gamma have one entry for representative/bill,\n",
    "    # index them to have one entry per representative/bill combination\n",
    "    alpha_long = long_from_indices(alpha, rep)\n",
    "    beta_long = long_from_indices(beta, bill)\n",
    "    gamma_long = long_from_indices(gamma, bill)\n",
    "\n",
    "    p = tf.sigmoid(gamma_long * (alpha_long - beta_long))\n",
    "\n",
    "    return tf.reduce_sum(bernoulli.logpmf(vote, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### Edward model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "class IdealPoint:\n",
    "    def log_prob(self, xs, zs):\n",
    "        \"\"\"\n",
    "        xs is a dictionary of observed data\n",
    "        zs is a dictionary of parameters\n",
    "        \n",
    "        Calculates the model's log joint distribution\n",
    "        \"\"\"\n",
    "        # parameters\n",
    "        alpha, beta, gamma = zs['alpha'], zs['beta'], zs['gamma']\n",
    "        mu_beta, mu_gamma = zs['mu_beta'], zs['mu_gamma']\n",
    "        sigma_beta, sigma_gamma = zs['sigma_beta'], zs['sigma_gamma']\n",
    "        \n",
    "        # observed data\n",
    "        vote, bill, rep = xs['vote'], xs['bill'], xs['rep']\n",
    "\n",
    "        # log joint distribution\n",
    "        log_prior_ = log_prior(alpha,\n",
    "                               beta, mu_beta, sigma_beta,\n",
    "                               gamma, mu_gamma, sigma_gamma)\n",
    "        log_like_ = log_like(vote, rep, bill,\n",
    "                             alpha, beta, gamma)\n",
    "        \n",
    "        return log_prior_ + log_like_\n",
    "\n",
    "ideal_point_model = IdealPoint()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "ideal_point_data = {\n",
    "    'vote': long_vote_df.vote.values,\n",
    "    'bill': long_vote_df.bill.values,\n",
    "    'rep': long_vote_df.rep.values\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def tf_normal(shape=None):\n",
    "    \"\"\"\n",
    "    Create a TensorFlow normal distribution with the given shape\n",
    "    \"\"\"\n",
    "    return Normal(mu=tf_variable(shape),\n",
    "                  sigma=tf_positive_variable(shape))\n",
    "\n",
    "def tf_uniform(shape=None):\n",
    "    \"\"\"\n",
    "    Create a TensorFlow uniform distribution with the given shape\n",
    "    \"\"\"\n",
    "    a = tf_positive_variable(shape)\n",
    "    \n",
    "    return Uniform(a=a,\n",
    "                   b=a + tf_positive_variable(shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### BBVI inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "# variational distribution\n",
    "q_alpha = tf_normal((n_reps,))\n",
    "\n",
    "q_mu_beta = tf_normal()\n",
    "q_sigma_beta = tf_uniform()\n",
    "q_beta = tf_normal((N_BILLS,))\n",
    "\n",
    "q_mu_gamma = tf_normal()\n",
    "q_sigma_gamma = tf_uniform()\n",
    "q_gamma = tf_normal((N_BILLS,))\n",
    "\n",
    "q = {\n",
    "    'alpha': q_alpha,\n",
    "    'beta': q_beta, 'mu_beta': q_mu_beta, 'sigma_beta': q_sigma_beta,\n",
    "    'gamma': q_gamma, 'mu_gamma': q_mu_gamma, 'sigma_gamma': q_sigma_gamma,\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 33s, sys: 30.2 s, total: 2min 4s\n",
      "Wall time: 52.8 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "inference = ed.MFVI(q, ideal_point_data, ideal_point_model)\n",
    "inference.run(n_iter=20000, n_print=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "ideal_point_alpha_mean = inference.latent_vars['alpha'].mean().eval()\n",
    "ideal_point_alpha_std = inference.latent_vars['alpha'].std().eval()\n",
    "\n",
    "N_IDEAL_POINT_SAMPLES = 10000\n",
    "\n",
    "ideal_point_alpha_samples = np.random.normal(ideal_point_alpha_mean[:, np.newaxis],\n",
    "                                             ideal_point_alpha_std[:, np.newaxis],\n",
    "                                             size=(n_reps, N_IDEAL_POINT_SAMPLES))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
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HBt4IsYoVK9ksO3/+vCQpJSVZZ84kWcP5pgceqKXvvtsqSTp48IAqVapiDdrsmM1BNkEr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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc5942c390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "bins = np.linspace(-3, 3, 100)\n",
    "\n",
    "is_republican = (vote_df.party == republican).values\n",
    "ax.hist(ideal_point_alpha_samples[~is_republican].ravel(), bins=bins,\n",
    "        color=blue, alpha=0.5, lw=0,\n",
    "        label='Democrat');\n",
    "ax.hist(ideal_point_alpha_samples[is_republican].ravel(), bins=bins,\n",
    "        color=red, alpha=0.5, lw=0,\n",
    "        label='Republican',);\n",
    "\n",
    "ax.set_xlabel('Conservativity');\n",
    "ax.set_yticklabels([]);\n",
    "\n",
    "ax.legend(loc=1);\n",
    "ax.set_title('Posterior Ideal Points');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HBt4IsYoVK9ksO3/+vCQpJSVZZ84kWcP5pgceqKXvvtsqSTp48IAqVapiDdrsmM1BNkEr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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc5942c390>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "*Fun project:* Recreate the [Martin-Quinn](http://mqscores.berkeley.edu/) dynamic ideal point model for ideology of U.S. Supreme Court justices with Edward\n",
    "\n",
    "<img src='http://mqscores.berkeley.edu/images/ipAnim1937_2006.gif'>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Variational Inference with PyMC3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "### Automatic Differentiation Variational Inference (ADVI)\n",
    "\n",
    "* Only applicable to differentiable probability models\n",
    "* Transform constrained parameters to be unconstrained\n",
    "* Approximate the posterior for unconstrained parameters with mean field Gaussian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Beta-binomial model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UmrEgIjKGkJCQBuvxVSoV4uLiANQvVairq8OgQYOafG5ycjLCwsKgUCj0j0VGRkIqlSIx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vfu3ZKk9vZ2vfXWW2ppaVFUVJRmzJihzz77TDNnzhzakwti/R2Xrq4ubd26Vc3NzbrvvvsUHx+v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\nAAAAgF+RaAIAAAAA/IpEEwAAAADgV/8Dh0jP68T4NcsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc593d2518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the transformed (unconstrained) parameters\n",
    "fig, (const_ax, trans_ax) = plt.subplots(ncols=2, figsize=(16, 6))\n",
    "\n",
    "prior = sp.stats.uniform(0, 1)\n",
    "posterior = sp.stats.beta(1 + x_beta_binomial.sum(),\n",
    "                          1 + (1 - x_beta_binomial).sum())\n",
    "\n",
    "# constrained distribution plots\n",
    "const_x = np.linspace(0, 1, 100)\n",
    "const_ax.plot(const_x, prior.pdf(const_x),\n",
    "              '--', c='k', label='Prior');\n",
    "\n",
    "def logit_trans_pdf(pdf, x):\n",
    "    x_logit = sp.special.logit(x)\n",
    "    return pdf(x_logit) / (x * (1 - x))\n",
    "\n",
    "const_ax.plot(const_x, posterior.pdf(const_x),\n",
    "              c=blue, label='Posterior');\n",
    "\n",
    "const_ax.set_xticks(np.linspace(0, 1, 5));\n",
    "const_ax.set_xlabel(r'$p$');\n",
    "const_ax.set_yticklabels([]);\n",
    "const_ax.set_title('Constrained Parameter Space');\n",
    "const_ax.legend(loc=1);\n",
    "\n",
    "# unconstrained distribution plots\n",
    "def expit_trans_pdf(pdf, x):\n",
    "    x_expit = sp.special.expit(x)\n",
    "    return pdf(x_expit) * x_expit * (1 - x_expit)\n",
    "\n",
    "trans_x = np.linspace(-5, 5, 100)\n",
    "trans_ax.plot(trans_x, expit_trans_pdf(prior.pdf, trans_x),\n",
    "              '--', c='k');\n",
    "trans_ax.plot(trans_x, expit_trans_pdf(posterior.pdf, trans_x),\n",
    "              c=blue);\n",
    "\n",
    "trans_ax.set_xlim(trans_x.min(), trans_x.max());\n",
    "trans_ax.set_xlabel(r'$\\log\\left(\\frac{p}{1 - p}\\right)$');\n",
    "trans_ax.set_yticklabels([]);\n",
    "trans_ax.set_title('Unconstrained Parameter Space');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "#### Transformed distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UmrEgIjKGkJCQBuvxVSoV4uLiANQvVairq8OgQYOafG5ycjLCwsKgUCj0j0VGRkIqlSIx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\nAAAAgF+RaAIAAAAA/IpEEwAAAADgV/8Dh0jP68T4NcsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc593d2518>"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0 [0%]: ELBO = -10.91\n",
      "Iteration 2000 [10%]: Average ELBO = -7.76\n",
      "Iteration 4000 [20%]: Average ELBO = -7.37\n",
      "Iteration 6000 [30%]: Average ELBO = -7.24\n",
      "Iteration 8000 [40%]: Average ELBO = -7.22\n",
      "Iteration 10000 [50%]: Average ELBO = -7.17\n",
      "Iteration 12000 [60%]: Average ELBO = -7.15\n",
      "Iteration 14000 [70%]: Average ELBO = -7.19\n",
      "Iteration 16000 [80%]: Average ELBO = -7.18\n",
      "Iteration 18000 [90%]: Average ELBO = -7.19\n",
      "Finished [100%]: Average ELBO = -7.2\n",
      "CPU times: user 3.12 s, sys: 0 ns, total: 3.12 s\n",
      "Wall time: 3.1 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "with beta_binomial_model:\n",
    "    advi_fit = pm.advi(n=20000, random_seed=SEED)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "advi_bb_mu = advi_fit.means['p_interval_']\n",
    "advi_bb_std = advi_fit.stds['p_interval_']\n",
    "advi_bb_dist = sp.stats.norm(advi_bb_mu, advi_bb_std)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# plot the ADVI gaussian approximation to the unconstrained posterior\n",
    "trans_ax.plot(trans_x, advi_bb_dist.pdf(trans_x),\n",
    "              c=red, label='Variational approximation');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### ADVI approxiation to transformed posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UgDNxOdh95KbRk1sic6VUKuv0OH788QY88cQyeHv7wMrKCseOHYFEItG//vvv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XBszvjx4xEREWFS9vrrryMoKAjPP/+8zSSZQBunzsbHx2PBggWIiIjA4MGDsWXLFpSV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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc593d2518>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# plot the ADVI approximation to the true posterior\n",
    "const_ax.plot(const_x, logit_trans_pdf(advi_bb_dist.pdf, const_x),\n",
    "              c=red, label='Variational approximation');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "#### ADVI approximation to posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZunXrwf79e3jrrX/h6upG7959DeWWL/+MRx6ZxRNP/L3S+UIIIYQQDUUSzdtY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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc593d2518>"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "### Dependent Density Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "The depdendent density regression uses LIDAR data from Larry Wasserman's book [_All of Nonparametric Statistics_](http://www.stat.cmu.edu/~larry/all-of-nonpar/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "%%bash\n",
    "# download the LIDAR data file, it is not already present\n",
    "if [ ! -e /tmp/lidar.dat ]\n",
    "then\n",
    "    wget -O /tmp/lidar.dat http://www.stat.cmu.edu/~larry/all-of-nonpar/=data/lidar.dat\n",
    "fi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "scrolled": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# read and standardize the LIDAR data\n",
    "lidar_df = (pd.read_csv('/tmp/lidar.dat',\n",
    "                        sep=' *', engine='python')\n",
    "              .assign(std_range=lambda df: (df.range - df.range.mean()) / df.range.std(),\n",
    "                      std_logratio=lambda df: (df.logratio - df.logratio.mean()) / df.logratio.std()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DR3Bfe5UPU1vQ8YvUZyvfHy0w2nmDC4/Hc+JibWTMn2+1JoC5aMB9MnooO9zwtJeV4cHg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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc58f4fc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the LIDAR dataset\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "ax.scatter(lidar_df.std_range, lidar_df.std_logratio,\n",
    "           c=blue, zorder=10);\n",
    "\n",
    "ax.set_xticklabels([]);\n",
    "ax.set_xlabel('Range');\n",
    "\n",
    "ax.set_yticklabels([]);\n",
    "ax.set_ylabel('Log ratio');\n",
    "\n",
    "ax.set_title('LIDAR Data');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DR3Bfe5UPU1vQ8YvUZyvfHy0w2nmDC4/Hc+JibWTMn2+1JoC5aMB9MnooO9zwtJeV4cHg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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fcc58f4fc88>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "_Idea_: A mixture of linear models, where the _unknown number_ of mixture weights depend on $x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# fit and plot a few linear models on different intervals\n",
    "# of the LIDAR data\n",
    "LIDAR_KNOTS = np.array([-1.75, 0., 0.5, 1.75])\n",
    "\n",
    "for left_knot, right_knot in zip(LIDAR_KNOTS[:-1], LIDAR_KNOTS[1:]):\n",
    "    between_knots = lidar_df.std_range.between(left_knot, right_knot)\n",
    "    slope, intercept, *_ = sp.stats.linregress(lidar_df.std_range[between_knots].values,\n",
    "                                               lidar_df.std_logratio[between_knots].values)\n",
    "\n",
    "    knot_plot_x = np.linspace(left_knot - 0.25, right_knot + 0.25, 100)\n",
    "    ax.plot(knot_plot_x, intercept + slope * knot_plot_x, \n",
    "            c=red, lw=2, zorder=100);\n",
    "    \n",
    "ax.set_xlim(-2.1, 2.1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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