Skip to content

Instantly share code, notes, and snippets.

@tillahoffmann
Created February 16, 2017 13:49
Show Gist options
  • Save tillahoffmann/0113acd9e6843a9f05538b1b1beb2c39 to your computer and use it in GitHub Desktop.
Save tillahoffmann/0113acd9e6843a9f05538b1b1beb2c39 to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"# Regression using only conditional information about covariates\n",
"\n",
"We would like to infer the parameters $\\theta$ of a regression model given some observations $y_i$ for $i\\in\\{1,\\ldots,n\\}$ and the group $g_i$ that the $i^\\mathrm{th}$ observation belongs to. More formally, we are interested in the posterior\n",
"\n",
"$$\n",
"P(\\theta|y,g)\\propto P(y|\\theta,g)P(\\theta).\n",
"$$\n",
"\n",
"We assume that the observations $y$ are independent conditional on some covariates $x$ which are latent. However, we have access to the distribution of the covariates conditional on the group membership of the different observations. The likelihood can thus be expressed as\n",
"\n",
"\\begin{align}\n",
"P(y|\\theta,g) &= \\int dx\\,P(y|x,\\theta)P(x|g)\\\\\n",
"&= \\int dx\\,P(x|g)\\prod_{i=1}^nP(y_i|x_i,\\theta).\n",
"\\end{align}\n",
"\n",
"Performing the integral over $x$ is difficult in general and we would like to approximate using Monte Carlo integration."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Method 1\n",
"\n",
"Let's assume that the covariates $x$ are independent such that the product can be moved outside the integral and the likelihood becomes\n",
"\n",
"$$\n",
"P(y|\\theta,g)=\\prod_{i=1}^n \\int dx_i\\, P(y_i|x_i,\\theta) P(x_i|g_i).\n",
"$$\n",
"\n",
"Let $x_i^{(k)}$ be a sample drawn from $P(x_i|g_i)$ for $k\\in\\{1,\\ldots,m\\}$. Then an estimate of the $i^\\mathrm{th}$ term of the product is\n",
"\n",
"$$\n",
"\\hat{l}_i = \\frac{1}{m} \\sum_{k=1}^m P(y_i|x_i^{(k)},\\theta).\n",
"$$\n",
"\n",
"By the CLT, $\\hat{l}_i$ is an unbiased estimator of the true mean\n",
"\n",
"$$\n",
"\\bar{A}_i = \\int dx_i\\, P(y_i|x_i,\\theta) P(x_i|g_i)\n",
"$$\n",
"\n",
"and converges as $m\\rightarrow\\infty$.\n",
"\n",
"But the estimate\n",
"\n",
"$$\n",
"\\hat L_1 = \\sum_{i=1}^n \\log \\hat A_i\n",
"$$\n",
"\n",
"of the log-likelihood is biased because of the non-linear logarithm function. In particular, the expectation of $\\hat L_1$ is (using Taylor expansion to second order about $\\hat A_i=\\bar A_i$)\n",
"\n",
"$$\n",
"\\left\\langle \\hat L_1 \\right\\rangle \\approx \\sum_{i=1}^n\\left( \\log \\bar A_i - \\frac{\\mathrm{var} \\hat A_i}{2\\bar A_i}\\right).\n",
"$$\n",
"\n",
"Of course, $\\lim_{m\\rightarrow\\infty}\\mathrm{var}\\hat A_i=0$ such that $\\hat L_1$ is asymptotically unbiased."
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Method 2\n",
"\n",
"The method presented above makes the strong assumption that the covariates are independent. In contrast, suppose that only the observations are independent such that a Monte-Carlo estimate of the likelihood is\n",
"\n",
"$$\n",
"\\hat B = \\frac 1m \\sum_{k=1}^m \\prod_{i=1}^n P(y_i|x_i^{(k)},\\theta),\n",
"$$\n",
"\n",
"where $x^{(k)}$ are samples from $P(x|g)$ (with possible dependence amongst the elements of $x$).\n",
"\n",
"In practice, $\\hat B$ cannot be evaluated because it would underflow. So we consider the estimateor \n",
"\n",
"$$\n",
"\\hat L_2 = \\log \\hat B\n",
"$$\n",
"\n",
"of the log-likelihood. By analogy to the case considered above, the estimator is asymptotically unbiased:\n",
"\n",
"$$\n",
"\\left\\langle \\hat L_2 \\right\\rangle \\approx \\log \\bar B - \\frac{\\mathrm{var} \\hat B}{2\\bar B}.\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"## Summary\n",
"\n",
"In practice, the estimators have very high variance because (for exponential family distributions of $y$) they are dominated by just a few samples $x^{(k)}$. For illustration, consider the case of a Gaussian mixture model for $x$ such that \n",
"\n",
"$$\n",
"x_i|g_i\\sim N(\\mu_{g_i}, \\sigma^2),\n",
"$$\n",
"\n",
"where $\\mu_{g_i}$ denotes the mean of the group $g_i$. The covariates $x$ may have be multidimensional but we assume that the covariance matrix is spherical, i.e. proportional to the identity matrix.\n",
"\n",
"Assuming standard linear regression with Gaussian noise for $y$, we have\n",
"\n",
"$$\n",
"y_i|x_i,\\theta \\sim N(\\theta' x_i, \\lambda^2),\n",
"$$\n",
"\n",
"where $'$ denotes the transpose.\n",
"\n",
"Thus, \n",
"\n",
"$$\n",
"P(y|\\theta,g)\\propto\\prod_{i=1}^n\\int dx_i\\,\\exp\\left(-\\frac{(x_i-\\mu_i)^2}{2\\sigma^2}-\\frac{(y_i-\\theta x_i)^2}{2\\lambda^2}\\right).\n",
"$$\n",
"\n",
"Completing the square and integrating gives\n",
"\n",
"$$\n",
"P(y|\\theta,g)\\propto\\prod_{i=1}^n \\exp\\left(-\\frac{(y_i-\\theta \\mu_{g_i} )^2}{2 \\left(\\theta ^2 \\sigma_{g_i} ^2+\\lambda\n",
" ^2\\right)}\\right)\\left(\\theta ^2 \\sigma_{g_i} ^2+\\lambda ^2\\right)^{-1/2}.\n",
"$$\n",
"\n",
"Finally, the log-likelihood is (up to an additive constant)\n",
"\n",
"$$\n",
"\\log P(y|\\theta,g) = \\sum_{i=1}^n -\\frac{1}{2}\\left(\\frac{(y_i-\\theta \\mu_{g_i} )^2}{\\left(\\theta ^2 \\sigma_{g_i} ^2+\\lambda\n",
" ^2\\right)}+\\log \\left(\\theta ^2 \\sigma_{g_i} ^2+\\lambda ^2\\right)\\right).\n",
"$$\n",
"\n",
"So, in the standard linear regression case, we can evaluate the log-likelihood in closed form."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Simulation\n",
"\n",
"Let's simulate some data to ensure we haven't made any mistakes."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"from scipy.misc import logsumexp\n",
"import util # https://github.com/tillahoffmann/util\n",
"from tqdm import tqdm_notebook\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"class BaseModel:\n",
" \"\"\"\n",
" Base class for regression models.\n",
" \n",
" num_records - n above\n",
" num_groups\n",
" num_dims\n",
" intra_scale - \\sigma above\n",
" coefficients - \\theta above\n",
" num_samples - m above\n",
" method - method used to evaluate the likelihood\n",
" \"\"\"\n",
" def __init__(self, num_records, num_groups, num_dims, intra_scale=1, coefficients=None, \n",
" num_samples=100, method='analytic'):\n",
" \n",
" self.num_records = num_records\n",
" self.num_groups = num_groups\n",
" self.num_dims = num_dims\n",
" self.intra_scale = intra_scale\n",
" self.method = method\n",
" self.num_samples = num_samples\n",
" \n",
" if coefficients is None:\n",
" coefficients = np.random.normal(0, 1, self.num_dims)\n",
" self.coefficients = np.atleast_1d(coefficients)\n",
" \n",
" # Generate the group memberships\n",
" self.groups = np.random.choice(self.num_groups, self.num_records)\n",
" # Generate the group means\n",
" self.centers = np.random.normal(0, 1, (self.num_groups, self.num_dims))\n",
" # Sample coordinates\n",
" self.x = self.sample_x()\n",
" # Sample the observations\n",
" self.y = self.sample_y(self.x)\n",
" # Draw another sample of coordinates used to approximate the likelihood\n",
" self.sampled_x = None\n",
" self.resample()\n",
" \n",
" def sample_x(self, size=None):\n",
" \"\"\"\n",
" Sample coordinates given group membership with shape (*size, num_records, num_dims).\n",
" \"\"\"\n",
" if size is None:\n",
" size = tuple()\n",
" elif isinstance(size, int):\n",
" size = (size,)\n",
" \n",
" return np.random.normal(0, 1, (*size, self.num_records, self.num_dims)) * self.intra_scale \\\n",
" + self.centers[self.groups]\n",
" \n",
" def resample(self, *_):\n",
" \"\"\"\n",
" Draw a new sample of the sampled_x variable.\n",
" \"\"\"\n",
" if not self.method.startswith('analytic'):\n",
" self.sampled_x = self.sample_x(self.num_samples)\n",
" # Don't sample if we are using the analytic approach\n",
" \n",
" def evaluate_log_likelihood(self, coefficients=None, method=None):\n",
" if coefficients is None:\n",
" coefficients = self.coefficients\n",
" method = method or self.method\n",
" \n",
" if method.startswith('analytic'):\n",
" return self.evaluate_analytic_log_likelihood(coefficients, method)\n",
" \n",
" pll = self.evaluate_pointwise_log_likelihood(self.sampled_x, coefficients)\n",
" \n",
" # Method 1 above\n",
" if method == 'independent':\n",
" # Perform the average first to get the marginal log likelihood\n",
" mll = logsumexp(pll, axis=0) - np.log(self.num_samples)\n",
" # Add up the contributions\n",
" return np.sum(mll)\n",
" # Method 2 above\n",
" elif method == 'joint':\n",
" # Aggregate the contributions\n",
" aggll = np.sum(pll, axis=1)\n",
" # Then average\n",
" return logsumexp(aggll) - np.log(self.num_samples)\n",
" elif method == 'variational':\n",
" return np.mean(np.sum(pll, axis=1))\n",
" else:\n",
" raise KeyError(method)\n",
" \n",
" def sample_y(self, x):\n",
" \"\"\"\n",
" Sample observations given $x$.\n",
" \"\"\"\n",
" raise NotImplementedError\n",
" \n",
" def evaluate_pointwise_log_likelihood(self, x, coefficients):\n",
" \"\"\"\n",
" Evaluate the likelihood elementwise. Should return an array of shape (num_samples, num_records).\n",
" \"\"\"\n",
" raise NotImplementedError\n",
" \n",
" def evaluate_analytic_log_likelihood(self, coefficients, method):\n",
" \"\"\"\n",
" Evaluate the log likelihood analytically.\n",
" \"\"\"\n",
" raise NotImplementedError"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"class LinearModel(BaseModel):\n",
" \"\"\"\n",
" Standard linear regression model.\n",
" \"\"\"\n",
" def sample_y(self, x):\n",
" \"\"\"\n",
" Sample observations given $x$.\n",
" \"\"\"\n",
" predictor = np.dot(x, self.coefficients)\n",
" # Assume unit variance noise on the observations\n",
" return np.random.normal(0, 1, predictor.shape) + predictor\n",
" \n",
" def evaluate_pointwise_log_likelihood(self, x, coefficients):\n",
" \"\"\"\n",
" Evaluate the likelihood elementwise. Should return an array of shape (num_samples, num_records).\n",
" \"\"\"\n",
" predictor = np.dot(x, coefficients)\n",
" residuals = predictor - self.y\n",
" return -0.5 * residuals * residuals\n",
" \n",
" def evaluate_analytic_log_likelihood(self, coefficients, method):\n",
" \"\"\"\n",
" Evaluate the log likelihood analytically.\n",
" \"\"\"\n",
" predictor = np.dot(self.centers[self.groups], coefficients)\n",
" residuals = self.y - predictor\n",
" if method == 'analytic':\n",
" var = 1 + np.dot(coefficients, coefficients) * self.intra_scale ** 2\n",
" return -0.5 * np.sum(residuals * residuals / var + np.log(var))\n",
" elif method == 'analytic_variational':\n",
" return -0.5 * np.sum(residuals * residuals + self.intra_scale ** 2 * np.dot(coefficients, coefficients))\n",
" else:\n",
" raise KeyError(method)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x111cbdd30>"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYQAAAEKCAYAAAASByJ7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nNwFI8UuCAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111ca3278>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"np.random.seed(2) # For reproducibility\n",
"\n",
"# Create a model, generate data and plot the data (colour corresponds to groups)\n",
"model = LinearModel(1000, 10, 1)\n",
"plt.scatter(model.x[:, 0], model.y, c=model.groups, cmap='jet')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Analytical results"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"sampler = util.AdaptiveMetropolisSampler(model.evaluate_log_likelihood, mode='reevaluate')"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"text/plain": [
"array([-0.34732768])"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sampler.sample(sampler.samples[-1] if len(sampler.samples) else model.coefficients, 2000, \n",
" callback=model.resample, tqdm=tqdm_notebook)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:root:function values may not be interpretable in the 'reevaluate' mode\n"
]
},
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x111cda470>,\n",
" (<matplotlib.axes._subplots.AxesSubplot at 0x111d1ce80>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x111eb6860>))"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAakAAAEYCAYAAADmugmLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUmOXMEw5AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111cda470>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.trace_plot(values=model.coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x111f36400>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x111f26668>)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSQVKRESikgqUiIhEpf8P/obE9HHT1QcAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111f36400>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.grid_density_plot(burn_in=1000, values=model.coefficients)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Method 1\n",
"\n",
"Method 1 produces reasonable results."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"model.method = 'independent'\n",
"model.resample()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sampler = util.AdaptiveMetropolisSampler(model.evaluate_log_likelihood, mode='reevaluate')"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"text/plain": [
"array([-0.38485701])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sampler.sample(sampler.samples[-1] if len(sampler.samples) else model.coefficients, 2000, \n",
" callback=model.resample, tqdm=tqdm_notebook)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:root:function values may not be interpretable in the 'reevaluate' mode\n"
]
},
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x111ccc898>,\n",
" (<matplotlib.axes._subplots.AxesSubplot at 0x11218d4a8>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x1121ad160>))"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAakAAAEYCAYAAADmugmLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJztnXeYVOX1x79ntrCUpS8dXClKExAQBBU1YsXelRiiMdhN\n+anBlhiNisYSW1A09m6MgqCooIKJWADpIL1X6bDAtvP74967e2f29rltds7neeaZmVve98yd+77n\nvuc97znEzBAEQRCEOJKIWgBBEARBMEOUlCAIghBbREkJgiAIsUWUlCAIghBbREkJgiAIsUWUlCAI\nghBbREkJgiAIsUWUlCAIghBbREkJgiAIsSU3agHCpHnz5lxcXBy1GEKGMnPmzJ+ZuShqOaJE2pCQ\nDl7aUCRKioiaAngHQDGAVQAuZuYdKcf0ATAGQEMAFQDuZ+Z31H0vAzgewC718F8z82y7eouLizFj\nxgx/foSQdRDR6qhliBppQ0I6eGlDUZn7RgGYwsxdAExRv6dSAuBXzNwDwGkA/kFEjXX7b2XmPurL\nVkEJgiAImUdUSuocAK+on18BcG7qAcy8hJmXqp83ANgCIKtNLYIgCNlGVEqqJTNvBAD1vYXVwUQ0\nAEA+gOW6zfcT0VwiepyI6licO5KIZhDRjK1bt/ohuyAIghASgSkpIppMRPMNXue4LKc1gNcAXMnM\nlerm2wF0BXAUgKYA/mR2PjOPZeb+zNy/qEgGYoIgCJlEYI4TzDzUbB8RbSai1sy8UVVCW0yOawhg\nIoC7mPlbXdkb1Y8HieglALf4KLogCIIQE6Iy940HMEL9PALAuNQDiCgfwAcAXmXm91L2tVbfCcp8\n1vxApRUEQRAiISolNRrAyUS0FMDJ6ncQUX8iekE95mIAQwD8mohmq68+6r43iGgegHkAmgP4W7ji\nC4IgCGEQyTopZt4G4CSD7TMAXK1+fh3A6ybn/yJQAX1iw879qJefg8b18qMWRRCEgFm8aTcOa1GI\nRIKiFqVWIWGRAmTw6C8w6MEvohZDEISAmbl6B077x9d4/usVUYtS6xAlFTD7yyqiFkEQQuPdGWvx\n2vRVUYsROut2lAAA5m/YHbEktY+sit0nCFbsKilDnbwECvJyohYlY7nt33MBAFcMKo5WEKHWICMp\nQVDpfe9nuOS56VGLIQiCDlFSgqBjzrpd9gcJghAaoqQEQRCE2CJKShAAHBAHF0GIJaKkBAHA3oPl\nUYsgCIIBoqQEQRCE2CJKqhbBzGDmqMXISCRGgOCWbXsPonjURIyfsyFqUWo1oqRCZvrybTjl8amB\nzIFc9fIPuPLlH3wvVxCEmizfug8AsnLxcpjIYt6Q+etHC7Bk816s2LoP3ds09LXsL3+SpI6CkEnc\nM34BKplx7zk9oxYltshIKmS0EdSB8uC8yQ4GWLYgCP7x8jer8Or01VGLEWtESYXMqm1KjK93f1gb\nWB2H3zUpsLKFeEJE9xDRel1amzN0+3oR0XQiWkBE84ioIOXc8UQkOdlc4vf874GyCkyYu0HmlVMQ\nJRURZRVyI8aJWvJvPM7MfdTXxwBARLlQUt5cy8w9AJwAoEw7gYjOB7A3CmFrC+ST281Dkxbjxjd/\nxDfLtwEAflyzA33u/Qw79pX6Un6mIkpKEABU1t6n11MAzGXmOYCSy42ZKwCAiBoA+CMkaagtO/aV\n4sMf1xvuY58ecTbuPAAA2L1feYZ45svl2FlShh9WbU+r3JLSchSPmoh3fliTtoxRIEoqIihgn+cg\nTAaVlYzS8krfy40DXyzaErUIfnAjEc0loheJqIm67TAATESfEtEsIrpNd/x9AB4FUGJVKBGNJKIZ\nRDRj69bgnXO+Wf4zyiridZ/d8OYs/P6d2Vi7XblUs9bswNdLf06rTLPf6HfL3bz7IABgzFfLfS5Z\nWQT/4n9XBmqiFCUVMh2b1wcAHNeleaD1OL1nPvhxHf74zmxHx97xwTwcdtcnaUgVX0pj1ikaQUST\niWi+wescAGMAdALQB8BGKMoHUDx4jwUwXH0/j4hOIqI+ADoz8wd29TLzWGbuz8z9i4qKXMn8zbKf\nTUcgRvy4Zgcuf/47/P3Tn1zVEzSbdimjHO0+Of+f3+DpL5elVebjny9J+h70g2sQ3PvRAtw7YSG+\nWhLcw4u4oIdMx6L6WPHzPtQNOGeR0+eaP7wzBwBw57BuaNagjuWxbwfo7CHYw8xDnRxHRM8DmKB+\nXQdgKjP/rO77GEBfKPNQ/YhoFZR+oAURfcXMJ3iVz8ir9PIXvgMAnHtkW0dlbNurzL8s25I502Re\n56RWbdvn6Di7tnzsQ1+gb4cmePKyI9MqR2PO2p2ol5+DLi0LbY/dWaKYJg+WBfeQJyOp0Inn41Jl\nyFMyxaMm4ndv/xhupRbE819xDhG11n09D4DmrfcpgF5EVE91ojgewEJmHsPMbZi5GMoIa0k6CgoA\nXvrfqnROB5CZowmvmFk7tO1Or8W6Hft9jXpxzjP/w8mPT/OtvHQRJVVLyQQ31nGz/WtYM1dvR/Go\niVi6eY+3AjK/d3xYdS+fC+BEAH8AAGbeAeAxAD8AmA1gFjNPDEIAqygqAx+Y7MrsF9f7d39pBd74\nLnldk1+OE6nE9BKEjiipWkqQ93ccO5CP5mwEgLQnszMVZr6CmY9g5l7MfDYzb9Tte52ZezBzT2a+\nzeDcVczsa8iDVNPf5t0HcecH82zP054VorjDXvrfShSPmoh9RhHxVbke/GQR7vzA/yVlv311huk+\np49P789cl9b56SGOE7WOoBthkHokbNOgEzTF6XVAlPHjqJixZluJcWdvg19rjrzwr/+uBFA9L5aE\nes8b7Vuz3dI50hGfL9xseu86bW7/994cLNtS05IQw+bqClFSAgB3nbvfI6l3Z6xF8aiJ2Lz7QNpl\nibKJByc/Pg3Dnvw6ajFc4fUBR3Px9hsv8hwI0IEhlR/X7MD3aa7hcoIoqVpKUHZyAOh85ydYuGG3\n5/P3lyabgv6tmilWqFGlKysZE+ZuQKWLIZubX7vy5334SNIrBI4WAkzDzX8UpUU5yLaTVI+Z44SL\n+pdvtfeCDOrB7bx/flPl3RckoqRCJqz5+aAb+evfeQ+KuWhTsoLTLonWON/8fg1ufPNHvOVhhTw5\nuMCnPj4NN70VH8/CbGblz/swdppukWmEc1KaqdGw7fjYbs95+r+4YMw3pvW7Yf76Xcll1EJTgqyT\nEgC4V2rpKMHcRHJLSm1YW/Yo5pMtLswobuQxWrhbGxt32KSOkJ1w8XPTsXXPQVw+8BA0qJNb/cAS\nwVAqLKeNOesUxXJaj1aB1nOwvAKH3zUJF/ZrF2g9QSMjqYiIm4McM+OW9+ageJQz7+S3vvceByyR\n7gyxBaJsomHrnoN4btoK1+eVeHCuCAozBbmzpLTKFB139KOxkoPKQ4NmTo9bn+MUUVIBYfYkaNWH\nTlm0GY9+5k84GNcjI1TfzEGTkzqS0swsaZSZ7jxCm8Z10zo/29HCBrlF+9fW79iPDTv3V213u5Sg\ntLwysDxqv3cYNixuhPnAVlbBWK/7//xElFRAeHlq+c0rM/DUF+7igVVWsqFCdNtpp/uU9fy0FTj0\ndmejsBpKysfG5LWo5vWtQ0IJwXLqP6Zh8OgvkuYU7/xgHrY7TFNx9INT0PXuYPKo6RWwn6MRszaa\niSOev4xfgGNGf4Fd+/13pBAlFRBh3Wcd7/gYt/57bs36XQqQbnTz+z9e5LhOM3NfOo3T7NziURNx\n45uzvBcs+EpFJWP3AfOOTH9nvPHdGjzw8SJHZW7fV5p0D/x75rqqZQ33T1yIklJ7s6KmIL3chr7E\nrjOzglsIFBeFpj1MeFkbZ4coqYCwn/j17+7yw0w3edFmHyRxhtlISnuy9DIaqrqaBgpwwtyNNbbV\nPD8mrb2Wc8/4Beh1z2eOTXNO8ny9aeBp+vI3ysLceycsxPNfr8RzU+3ny6rnpFK2Oxjq3/a+8qDo\nJkHhpwuM21w6d2JtnJMVJRUQRjfangNl+GxhOMrA7Y0eZhedQyZzUpy+LGZtdNFGZ+u6Uj0PBX/R\n4vcdNBm5a56dbvjZIAqEdi+Vq56c5ZXWIx1mxoqfNecI73fgPosR254DZfh4nvkDk9mdZ6V4LPcZ\nlHjzWz/i3QzLZiBKKiD0T2NPf7EUM1dvx7NTnSUdY+a0bbthuPB6TUyX2rD8cP21+7mnP2Ed/SAu\nZpNMxclI1Mk1vuW9OUnf9x4Ix/tvmkNHDbvfqf+NB8srcPUrM6rSjvzp/bm4/g1/Tc81R336LzWP\nHz9nQ9WoL1MQJRUQ+pv5kc+W4IIx0x3P+7z0v1Xo/dfPMGvNjjTqt+efX6WXtG1PQB1IOmOZdM0d\ntdFckskYWR72l1Zgrw9zHxPnbqyK3H7QIoK7G/T3z4xVOzB50Wb8eZwSkHbdDm/eb349QBkp2CmL\nNrsyUUaBKKmAMLqxzAYeW/YcSMrSOWWx0jDP/2fNVel+se9gOR6eVO3u7qVvrmTGDW/Mwj3jF1Rt\nC2IE992KbSgeNTHJRbkmSr13fjAfize5D9kkA6nMYeADk9HzL586OrasQvlnf9pUHXi1spIxffk2\n3PDmLMPID74phTTLSW2T+0sr8MTkpZYWDDdRK3aVlOE3r8zA1a/OwPz1u7Dy5/TXggXRjkRJBYTR\nDWo0CbxlzwEMuH8KnpiytGpbTiL9v8Wugbi9maYZpIdmBibO24iXv1nlsjQTmUyEflNdOPz9SmfB\nLJ+aoowQ7WL/xTHlSKbipHMk8qcT2+1gBK/9tfPUsEGTF22p2nf+mG9w2fPfAgAWGMSg9OuuuPND\n+9QkRpjdl099sRSPT16Cd2dUzylZmh9tfogWeWXm6h0486n/4sRHvjLMCTZn7U4Uj5qIVT4oMS+I\nkgoIo5tnrS6kv3Yf/ryn5lDbl8l7n/vfX734vUEVBuuzPNSbjuuvUb2aXBU2wuh1mCis9PBrTsqI\ndTtKUDxqYo0HpaemLMW2vQcNa9a2GbWk2Wt3Wtbnl8v36m3uUnikehGmVlWihp1yGun8gI0HpdF0\ngmaa1Fi2ZQ/uUPOAffXTlhrHpxKEtTwyJUVETYnocyJaqr43MTjmECKaSUSziWgBEV2r29dPzUS6\njIieJCd+oiFidDPXzc9xdK5p2CA39dt0Gr5cLJ/69SpZNI8s1RNLm3DWsBqxJSkp9XOFjKRixcFy\nb3NJM1crnel7KUstHv18Cf5k4gRQqnbQTrwFd5aUJo2oGIxP5m3EN8sUZwo3bSXITshtt3D20/81\n3VdSWo5rXptZY/tPm5Pb3NDHplVdGyetpbaZ+0YBmMLMXQBMUb+nshHAYGbuA2AggFFE1EbdNwbA\nSABd1NdpwYvsHLs/a4ca4t5ImegHUm460jq51X+n2/7XS+I2qyfYF75egTUmT5JmHknatXjmS8UL\ncmKKu67dE3Bq+bZKyuSzEAz6v0Nb/OrkPtXWOBm1hRKToLZunBQufm56krkdAK57YxYuf+E7fDJv\nY9K9Yaf0jJ6VnSqXb1dsq/p8oKyixrVxkrpGq2vt9hLLPFdXvvSDbVleHLeOfegLbNzlb3ikKJXU\nOQBeUT+/AuDc1AOYuZSZtStdB6q8RNQaQENmns7Knfuq0flRYqdcHrGI0ae/qd1kwS0scB7UPrXh\neJlXMnYOYTw7dTn+NnFRld3fVhaL8gDgf8vs3YP1yt7pwlyj+qLMDJtNjHLhBr3QYo2bm9FF8aiJ\nhk4HSzab52S67o1ZSWvs7JaGGEVc2F9aUcMqYMRWVQHuL61A17sn1Vhg/8p0ZdHyz3urlc+qn40f\nBI97+EvLur4zm9/VNQozx60vf9qCJZtrZgDWTv/PrPWWdbslSiXVkpk3AoD63sLoICJqT0RzAawF\n8BAzbwDQFoB+7L9O3WZ0/kgimkFEM7ZurTn575X1O/fjkuemY5dJ0i+7btIqJpne3OdkxX1VnUnz\nMsFjJNv7s9Zh9CeLASiLF/3AaLGmFdZzCsbKTCx/4aKlq3CjZCbM3eg4Sr/Z3zl+tn2yy3TuhcWb\nanbes9bsxNDHpqK8wlnBdks79C7jqSNAq8u5drs/I5wrX/oBpzw+zZeynBCokiKiyUQ03+B1jtMy\nmHktM/cC0BnACCJqCeP/wvAOYOaxzNyfmfsXFRV5+yEGPP3FMny3cjsmzKt503+2YBN63fNZje1O\nwvMAyUrKTYNJMl+ZnLh2e4mjOGZu69PQK1+nslc5TqTRORgpaKPi3tatthfFFCXKxfflP9AVUlpe\niScmLzVdk2jnTOOXTEamZqfF1rQEuBMorTVkFk8NUbWXQJUUMw9l5p4Gr3EANqtmO818Z+k6oo6g\nFgA4DsrISZ/Jqx2A2OQDf/0777mWACSpYHcjKf0owZjjHv7SkT3abX0a+qdFMxn0jXDuup26zLz+\nYHXJzOfeRGPVBt74bjUen7zE/sCAcRq93Qij+TS90jtYXomHJi02dBcHgPsn2gflzSSizMw7HsAI\nAKPV93GpBxBROwDbmHm/6v13DIDHmHkjEe0hoqMBfAfgVwCeCk/0aow6RCfODh2b1zfdp3+WsZv8\nT6oX6loUm1O+W7ndl6ei3ftrPrFV6GKkObkO909cVDWXlo63HVt8Mz1H9JJvRHUtU+cQvYbq8pOZ\nq3egrUF+MqfxI1+dnhowl5I89T5Q4x/WzTP2Fk5rJBXDRhGlkhoN4F0i+g2ANQAuAgAi6g/gWma+\nGkA3AI8SEUPpux9hZm2F3HUAXgZQF8An6is0rGzpTv7nCyxSOuvNfTtKSlG/jguHCChddBj3mtEo\nL2ntkYMy9h4sR2FBnuPjzTByQU9VersPlBmup0o9X8gc/rvsZ/xX51hjtxA+3ZQ0TrhgzDe4oK+/\nKduNFh0/9nnNESMR8NEc70Ylba7QCIaztVJ+E5mSYuZtAE4y2D4DwNXq588B9DI5fwaAnkHK6BU3\naR+MOke9C7pN8OYaZSWIUMlsHwjTebGmGCkpJx2/qQu6T4rCrJhe93yGZvXzq75fOGY6LjmqPUYM\nLtYJ448MgjVBPRTk2Px/TztIKvrpgk1pyzFtqX9OWnExRd83YWEk9UrEiQBwolisTFv6tRZ2KQZS\ny0x4DCnuJciFnSnSyXwac7Ve+MnAM8opycrRvN5turmChRt34y9q3MF4dAOZi9uFpkFd74TNjby9\nxH6u6EeH6/Gs2Ooh5Yg/RP+U5XdYhSjNfRnNm6pzhJH9182fZHTsHF0jMVIEz05djvZN6mFYr9ZJ\n2xlwfI+mduReOg0jHeXFDV67Bo9PXoKurQuT9nlZGGjl3ScEg9uRETNj2JNfY79P0ced4sTcZxSn\nUogOUVJp8rPBE5MbJWXUuFfoAjkaucxq65CG9RqWUlj1iMhtB+3F/GI0YklSXGbmvpTv+snv1EWP\nT0xeCkekqZFkTipcGMbzLGmXWyv/R+cdSryCw/mDmPvSxOimcBJ7z2ljctvoUrPcmpbrrlhDjNeC\nVG9zZO6DPw3LrySRtbCNx5KdJovg0+UvurQxtYdaqXkdI0oqTbzGtX3UwDMnXRj6kVTwN7ZdDeUO\n3ee9pAxPZcriaq+jau++tIsVhMgpcxipAgAWb/Q+rxtXREmlye79Zdi060DStq8dpqJ2gquIE8yO\nlaYfHbhRGcss4qBVn5d8ohblOkpEnwlxZdte5w9xN7zpb3r6OCBKygP6IJJv/7AWRz84JbC6XLmz\nw393bsv6DCrRj2i8luEX8yzWfJhRG236QmaT7Q9QoqQ88Mt/fRe1CIZo66SA5Bt7064DNaMzp9z5\n+jQfjutzfYY/7D5QhunLlbQGW/YcMExhMHnhZlf/k5gGhbjyzJf2a7tqM6KkPPDjmvTXUTjFXYBZ\n1o2kqk88+sEpuGCMcdh9jeEDD3Etm5u4gnrS1QfXvT4Tlz3/LZZu3oMB90/B45OXoHWjgqTyV22L\nJtW1IPiN2ywAUeN3uhtRUrUMs9tj8aY9pmkqACDHw50Q1ehDmxzWAnF++dMWtGhYkHSMW4eWMBxN\ngoKI7iGi9WoG69lEdIZuXy8imq5mtp5HRAXq9nwiGktES4hoMRFdkI4Mr32bGm9OEPxB1knVIpLM\nfQZ97tDHpiYdq8fIEW9/aQUWbtyFfoc0NazP60hqtW6UY5R/R49hYkJKrt/oyS0Lp5YeZ+ZH9BuI\nKBfA6wCuYOY5RNQMgOb7fSeALcx8GBElABj/yQ75d0pqd0HwCxlJxRynCfwAzXHCvHtevrVaOaQm\nSzPi75/+hAvGTMf6ncZRH7yOPe6bYJ5KIPU3TVm82eAo5TdqijX1J3tyxsjcgZQVpwCYy8xzACVe\nJjNrIR6uAvCgur2Smf1zSRUEHxEllcHUWEyrizhhlz46NV38v/67sroYtZP/Wg2SudckU6hXz7z1\nBvlyzDCyx2tKyUlaebdkcPr4G4loLhG9qKa1AYDDADARfUpEs4joNgAgosbq/vvU7e+pyUQNCSq7\ntSA4QZRUzLGaK+n250k1jg3ChdqszCDmpJxEItDE0RStkXhxCXjqFzZZrscA6ASgD4CNAB5VT8sF\ncCyA4er7eUR0krq9HYD/MXNfANMBPAITgspuLQhOkDmpmGOlCIxWovsxEmB21sm7yMeYXL6FSnhB\nN6IzI1U2oxw4GTseMoGZhzo5joieBzBB/boOwFTNlEdEHwPoC+ALACUAPlCPew/Ab3wVWBB8QkZS\nEeN2NLL7gPFI44Ix36C8kj2l3DDDTjQvjhPb9h50FebFiCBMcpm8ToqI9OHwzwMwX/38KYBeRFRP\ndaI4HsBCVuy0HwE4QT3uJADRJAsSBBtkJBVzUvvOK1/6wfA4LbSQ11iCVnWalehlTmqWD2vMnPxE\nP65DBvEwEfWBukQMwDUAwMw7iOgxAD+o+z5m5onqOX8C8BoR/QPAVgBXhi61IDjAVkkRUScA65j5\nIBGdACVT7qvMHN6K1lqM277ULs6dH32zonzIVgl5GX3k+jDUC0L9ZPI6KWa+wmLf61Dc0FO3rwYw\nJEi5hOzE7+dDJ+a+9wFUEFFnAGMBtAfwpr9iZC+2KTVcagInaULcYlaklzkpu8ypTnAySvJ6GbJr\nACYI8ceJkqpk5nIotu6nmPlWAK1tzsk6bn1vDnY6SE3tFrd6wJeRlMO6vYw+/BhJ2eEtgaP/cgiC\nkD5OlFQZEV0GYASqvYbyghMpM3lv5jo8OcX/QJDjZ2/Ata/NrPpup4SCGEmZGdi8jKR8Mfc5mZNK\nuxZBEOKAE8eJKwFcC+B+Zl5JRIfCwMYtBEPqoluC9QjHj865pLQCCzfssB1K7djnfuSYmxOOknJL\nWAMpIqoPYD8zVxLRYQC6AviEmYNJVSsIGY6tkmLmhUT0JwAd1O8rAYwOWjDBG3504Lf/Zy4+nrcJ\neapCMSszqlTdjlzQPV6IEEZg0wAcp0aF+AyK590lUBbcCoKQgq25j4jOAjAbwCT1ex8iGh+0YII3\n/DD3aUFf013PZERYcz9ursKCDbsCTb6YAjFzCYDzAfyTmS8C0D2sygUh03AyJ3UPgAEAdgIAM88G\ncGiAMsWOXfvLsGSz0nE/N3W5r2U7dT5Yu73E0XF+KKm4z+fYTWu5dei49b25aUjjGiKiQVBGTtqa\nJVmvKAgmOFFS5cycGncmq3yhhr/wLU55fBoA4MFPFkcig13AWA0/zH1+O188+tlP+H7ldgD+3Dh2\nLujb9pbim+XOg8+WVVSGeUP/HsDtAD5g5gVE1BGAsz9XEDIAvx9ynSip+UR0OYAcIupCRE8BsE7z\nWsuYv343AO9Rv81gZvxn1npfy4ybYwIz46kvluHi56b7VqadeIs37cHH8zY5Li/MJy5mnsrMZwN4\nWv2+gplvDlEEQcgonCipmwD0AHAQwFsAdkN5Gsw6SisqfS3vo7kba3jv2WE3iqiXn77lKNUxIR3d\nvL+sIum7L3re50e1SubQNBURDSKihQAWqd97E9E/w6ldEDIPWyXFzCXMfCczH6WG67+TmQ+EIVzc\nuP39eb6Wt3SzdVZaI+z65/r5OUnfvYz+UvXg01/YJ0g0o6S0Wkmt3V7iy2g0yDmzEGL+/QPAqQC2\nAYCakFDCEwm1hhmrd6C03L8HeifefV8S0RepL98kyCD+86O1ac5tVPCnvvB/8W8qXhbcpnbUH87e\n4Ln+W9+bU/X5uIe/DGVOyi27Ssqw96BxYscgYOa1KZsqDA8UhAzk84WbsWu/f8v+nNiGbtF9LgBw\nAYDwWnQG8fI3q3DP2T0ileHLn5Izp3oaSfklDIzkSb9Mv8c62/aV4qa3fvS5VFPWEtFgKBlz8wHc\nDNX0Jwi1BT+jnzlZzDszZdP/iOh7/0QQnFJRySh3OTTyohOCtHj5Yu6Lu4+8NdcCeAJAWyhJCT8D\ncEOkEgmCz/hp7XCSqqOp7msCQD8AjXyTQHDM3oPlaFo/H9tdhCOKW+BUf/wmMldLqVlyJbqEUKsJ\ndSQFYCaUvoWgmPlWQlJNRwIzu1JQQPzyJHnJ5ptKJo+kiOglGOhqZr4qAnF84fOFm6MWQYgZfj5I\nOjH3ZVV0CY1tew9i1/4ydCxqELUoVTjp3xOU7CwRt5GUF0eOMAlB/03QfS6AkgLHu2dKDEhdZiAI\nfjYkUyVFROdbncjM//FPjPhx0mNTsbOkDKtGD4talCqcjEKIKG3NFP85qcwdSjHz+/rvRPQWgP9G\nJI4vZO6/IQRFWOa+syz2MYBaraR2lnhzoVy3w1mMPS84GYUkKNmf2YtOCHLOJ10dNWHuBizauNsf\nYeJBFwAtohZCEPwkFMcJZr7St1pSUJ0x3gFQDGAVgIuZeUfKMYdAUYQ5UJIsPsXMz6r7voKSHXi/\nevgpzLwlKHndcOxDwYVhczIKUW6O6uPiNieVrjyvTV/tkyQmBDwsIKI9qJ7jZQCbAPwp2FqDJYMH\ntkJAhO04ASIaBiU0UoG2jZnvTaPeUQCmMPNoIhqlfk9tqBsBDGbmg0TUAEoMwfHMrNnvhzPzjDRk\nyDi8zOfEbk4qzYXoMfs5rmHmwqhl8JtM9rYUgiFUxwkiehZAPQAnAngBwIUA0l0ndQ6AE9TPrwD4\nCilKipliETwhAAAgAElEQVT1bmx14CzOoO9Uxmim39GclO7zsi17MfSxqa7r8TOkSSrxuZrhQkR9\nrfYz86ywZBGEoPFzdO1kJDWYmXsR0Vxm/isRPQrgkzTrbcnMGwGAmTcSkaFNnojaQ8m50xnArbpR\nFAC8REQVAN4H8Dc2sYUR0UgAIwGgQ4cOjoTTKya/g8qmgzPHierPny10Hglcz08eYgo6Zc+B9MKl\naCk/MpBHLfYxgF+EJYjfiLlPSCVsJaXN+5QQURsogTFb251ERJMBtDLYdadT4dQYZ73Uej8kon8z\n82Yopr71RFQIRUldAeBVkzLGAhgLAP3793f0IF+ic6kNM6abHW5Nd3Ez9QHADo8OKZkOM58YtQxB\nITpKSCVUcx+ACUTUGMDfAcyC8tT3vN1JzDzUbB8RbSai1uooqjUAS6cHZt5ARAsAHAfg38y8Xt2+\nh4jehJI52FBJeUEfFHX1tn1+FZs2fiyEjZo4mU+jgoh6QkkZr5/j9e3+FYSoyfHRc8JJqo77mHmn\nur7jEABdmfnPadY7HsAI9fMIAONSDyCidkRUV/3cBMAxAH4iolwiaq5uzwNwJoD5acqTxCfzq81k\nMbL24ekQoqYHTUXMFW3QowIi+guAp9TXiQAeBnB2wNUGys97D0YtghAz/PTuc5KqYw4R3UFEnZj5\noEEqeS+MBnAyES0FcLL6HUTUn4heUI/pBuA7IpoDYCqAR5h5HhQnik+JaC6A2QDWw8HIzimvf5vs\n4vz3T6NJF2/EezPX2R6jH2b7nUnYDypkJHUhgJMAbFKXefRGhsfC9DMtg1A7CDXALJSnvEsAvEtE\nlVDWN73LzGu8VsrM26A01NTtMwBcrX7+HEAvg2P2QQlyGwh3fZg8KPth1Q6TI+NPDHWUmPuA/cxc\nSUTlRNQQiqm7fdRCCUJccWLuW83MDzNzPwCXQ1EcKwOXTPBE3D2tREdhhjrH+zyU4M2zAEyPVqT0\nyOQwVUL8cbqYtxjAxVBGVBUAbgtOpOiIo3nMLfqfEMdfE/s5qYA7XGa+Xv34LBFNAtCQmecGWqkg\nZDBOFvN+ByUs0bsALmLmFYFLFREHdYtYe7ZtiPnra1WMuFiQ7eY+IhoHxWQ+jplXRSyOIMQeJ1Ec\nRjBzX2YeXZsVFAB0vXtS1Wc7BdW2cd2gxfFEbo7ecSJCQUyI+0gqBB4DcCyAhUT0HhFdSEQFdicJ\nQrbiZE4qPu5tMSIRSZAme5rVz6/6HLfgsoCMpJh5qmry6whlkfnFsFknKAjZTEy72nhwSX9zp6sR\ng4rDE8QFehUQx0GLuKAD6vq/CwBcC+AoKPEr0y3zHiJaT0Sz1dcZun29iGg6ES0gonnayI2ILlO/\nzyWiSdr6w3QY2q1lukUIQhKWSoqIEkQ0OCxh4kazBvnIy6k5kd6kXh6uPq5jBBK5I47qINvNfUT0\nDoBFUGL1PQOgEzPf5FPxjzNzH/X1sVpfLoDXAVzLzD2gBHYuU7c/AeBEZu4FYC6AG71UKs59QpBY\nOk6o6zmeAXBkSPLEiopKRllFzU41zi63UekApwmB466jQvhrXwJwOTOHlXP9FABzmXkOULVGUYvW\nQgDqE9E2AA0BeAppIqk6hCBxYu6bQkQXUJx75gD448mHma6kj/OFSPqXQtQITq9Jtpv7mHlSgArq\nRtV096IaSgwADgPARPQpEc0iottUOcoAXAdgHoANUGIJ/suoUCIaSUQziGjG1q1bLQU4ubskGRb8\nxYmSugbAewBKiWg3Ee0holrvm11Ryfh66c+G++Ksr389uLjqc5jqwOk1Kc9yJZUORDSZiOYbvM4B\nMAZAJwB9oCQM1VKD5ELxJhyuvp9HRCepI6nroFhJ2kAx991uVC8zj2Xm/szcv6ioyFLGosI6Sd9v\nP72rx18rCAq266RqYyZRIw6WJz/cVlQy1u/cb3is0TxVXKifX/2Xhmlac3pFasOC6aiwyiygh4ie\nBzBB/boOwFRm/lnd9zGAvgB2q2UuV7e/CyVDtq8c0TajwxIKMcBJgFkiol8S0d3q9/ZENCB40cIl\nde6pfh1z/Z0bYyWldzsPM7WH08Fltpv7AICI2hLRYCIaor18KFOf4+08VGcG+BRKTrZ6qrPE8QAW\nQgnM3J2ItKHRyVAcOjzUrfsca2O4kIk4CYv0TwCVULyR7gOwF4pX0lEByhU6ZbpoEzef1AVXHlOM\nhyYZLxHLi+siqRTiqA/Eu48eghJebCGUEGOAYpmdlmbRDxNRH7WsVVDM9GDmHUT0GIAf1H0fM/NE\nVZa/AphGRGUAVgP4dZoyCILvOFFSA5m5LxH9CFTd9Pl2J2UaZbrEUX88+TDLY2M8JZUcuy9UxwmC\nk1mwuC/mDeGvPRfA4czsaxImZr7CYt/rUNzQU7c/C+DZdOvOiXODEAKlsCAXew4Em73cyZCgjIhy\noPZAqnkgRqkA/WF7SSkA4Nw+bSKWxD9CzeTr1NwXbx0VBiugxMKsNSRlYRV9lVUkQnhAcTKSehLA\nBwBaENH9UJK23R2oVBFw2j++BgBs21dqe2ycvfuiijjh9IqEqjjjSQmA2UQ0BUDVaIqZb45OpPSw\nmqPN+n+7lhNGV+jEu+8NIpoJJUkhATiXmT1NsGYCR3ds5vhYpwtYwySqVB1Ob9a4m/tCYLz6qjXo\nn6ab169jcaRQ2zimU3NMnLcx0DqcpOp4TbV3LzbYVusYoVtnZIbWJHOIUB43LaUjTNH0aU6s+GT+\npoAlSY8Q8km9os7pahOfP6kLazOWXJ25r2fbhkn7Ytw8BB/44ymHRa+kAPTQf1HnpwJL3x41DSxc\nz1PJSVDsFqdG5YIunZEziOgEKAFlV0F53mlPRCOYOV3vvshImpMSsoownGZMHSeI6HYi2gNljYUW\naWIPlLQC4wKXLMZo/0tuDBtnVN59cSZmC0ofBXAKMx/PzEMAnArg8YhlSgurOakYT98KPhBGD2Oq\npJj5QTXaxN+ZuSEzF6qvZsxsGD4l20jEUEnpmbNuV9QixIJjOqedgcJP8pj5J+0LMy9Bhnv71c2r\ntj6kmkvlOal2U14RvKO3E9vWnUT0SwCHMvN9RNQeQGtm/j5g2UKlbeO6jp0mtFX1YbhfukXfJ+w2\nCZArRMoMIvoXgNfU78MBzIxQnrQ5rkusHgKEEAnjQd3JOqlnAAwCcLn6XYs4Uasoq6hEfq6zC67p\nphjqqKRHV6cPsWf3rj1rw4xwk6E4hL/0OgALANwM4HdQIk9cG3y1wZHaDibefGzV5zhmh9a4Zkhw\nOeEa18vowbFj2jepF3gdTpTUQGa+AcABQIk4AaBWRpzIy3EW7kjTA3HUUXqcOk6cU4sWMBviop90\nsk4uHZj5IDM/xsznM/N5zPy439EnoqZHm1jNAZrSpH5w3Vi2mDkTBHQqqh9oHU7MfVkRcaKsgpGb\nEpOvQ9N6WLO9pMaxcX46jHv6+GyFiN5l5ouJaB4M1KaaHTcjkaCy2UsYgQ28Rpy4K1CpIqCsohJ5\nKea+FoV1DJWU5nUex8gTyYt5nWmpGP4Mf3H5+yorOQhb++/U9zP9LjiO5Ock0K1NQ/sDdYwc0hFj\np61Iu+6ORfWxYuu+tMtJh/r5OaZJU2sTziJ2poetfYuZ3wBwG4AHoSRTO5eZ3wtYrtApq6hEfoq5\nz6zz1sxocezbmRlPX34kAKDS4XjXy5PwHWdkUDI7l61oX6n/ATOZWVvxeD0zr9a/AFzve4UhorUT\nfZ61JfefjnE3HOOqnIv6tbPcf8XRh+BfI/rbllPcLFjzEwC0b1rXdF9OgmL5ABsEYfxMpzknNgP4\nGsA3AOoSUd/gRAqfikpGJaOGuc+s89ae0uJ6H3Zs3sDdCR5+x8ghndyflCGk3gc+c7LBttODrDBK\n9CP71o0K8Ieh5hkG7NrTfef2xEndWqYlT9vG5srFDVYPdv0PaeJLHX7RsXlwSjsMZewk6eF9UFJL\nPwllIeKjAB4JWK5Q0dJ0pJr77Dvv+GkpRnVjd7qYN36/IlqC0FFEdJ06H9WViObqXisBzPO/xvjR\npF4+fje0S2T15+cm0KZxQWT123HrqYcHUu5F/dtjzl9O8b3cXw06xPcyjXAyJ3UxgE7MHKzbU4Ro\nSqqGuc/mvDiOpJir5XIasSk1K3Ftw+2vC2gk9SaAT6CYzfVp2vcw8/YgKow7vds1Sllw7k+DMi0l\n5UZw61g0/fZfYNCDX3gRyREN6wbntt4ogLLvPacngOAfcp20xvkAGgcsR6RonXRqmKN6+TmW58VQ\nRyXh1HGiVcP4Pl1GQRDrE5l5FzOvAvAEgO26+agyIhrof40ZQByf8ixo3cgfU2HYpHOZUx/cjYjc\ncQLKk9+PRPQpEY3XXgHLFSrV5r7ky/H3i3pbnhfHBXuManu50yfFYKdgMo+A7exjoCyI19inbstY\ngrpcvzy6g6fznMrjRe4LbZw74kg6f0/nFi7ntwPASff0CoCHAIxG9ZzUo0EKFTZLNu8BAGzdk7ym\nsnkD69w4L185AD0s3GzD8ID77XGHJn1nDxEn3Eax/r+TzSe/44ibQLtOvMfShFgnEDNXwpnZPfYY\nORO4ecrWK41Vo4ehfr7/l0Uvo5d1hI9c1BurRg+zrsOjVgjq0chMnuJm3qNFWDnA+I0TJVXCzE8y\n85fMPFV7BS5ZiLzyzSoAwKcLNrs6r03juphw07Gm+389+FDTfX7QtVUhTj+idY3t2k2ZqnTNcBtu\n/6aT/J/8TjW1OjEzOMVNNpXuLtf2eGAFEd1MRHnq63dQUspnPOkucvevk84sM2LQtCg0NufbPYRb\nYTcV4idOeoKviehBIhpERH21V+CShcjXS38G4O3CW5mG3D5RRRWoMw7R3Bffd1ryBh9F2mET6qiw\nQBfFO/gO7loAgwGsB7AOwEAAI4OuNCqchMx58Pwj8MKvAh/BhhYphhk4uXt6rvJ+MlSVZdLvj0va\n7uRqOOrDAr6sTpTUkQCOBvAAaqkLupZV1u+nA7fd3eBOzV3Pc6XWwey+3jASl+np3b4x3r1mUGj1\nVcQoPhQzb2HmS5m5BTO3ZObLmXlL1HL5gZGCb9ekHj5UF/Wa/QtdWxViaPeWoS+AHdqtRSDlJohw\n17Bu+P7Ok2yPDSJh5GUDkufytBq6tgrcShAITiJOnGjw+kUYwoXN7wIwY7mBwa5tvakN+7BWha5H\ncGFnViUAAw5tmrQtSDXixtwXdD9JREVEdAcRjSWiF7VXsLVGS55FUsQg0P+H4288Bjf9orPhcV1a\nFtrOL2nMuGuo7TG92imBdYsK6yA3J2FqZktFr1R+78M6siYpD7qB6/6Ay3dk+CeiYUR0GxH9WXul\nWzERNSWiz4loqfpuukybiBoS0Xoielq3rR8RzSOiZUT0JPnwGNattbcnDbP5Ey8iOUlH/+vBxQBq\njpq+uuUEHH9Ykes6a3v6b9to8OEOtMYBaARgMoCJuletxY+B7MX97b3qUjtnAOjVrjF+efQhNeR4\n+AJ38XxT52+ONTDNt2+aXtoKIqCZLjL7+9eFZ21wS5hBtp1EnHgWwCUAboLSJ14EwI+lxqMATGHm\nLgCmIHmBYyr3AUh11hgDxZbfRX2dlnqSU7q3bojcBKF+nWidrJir3eGtKCpUGkzqjVJcFf7EndIJ\nfSTloDo/JXLj3RfClajHzH9i5neZ+X3tFXy10WO7OF5972DQ2T98ofVyEAB48HxjxUMGXzqk4dkG\nAH89uwem3Xqi7XFaHE2nXDqgA/7v5MOw+L7T0O+QpvYnGOD0bnfTLqLEyUhqMDP/CsAOZv4rlASI\nfvgfngPFvR3q+7lGBxFRPwAtAXym29YaQENmnq66875qdr4T8nMTGBxAinEvHV6FG9sU/BnKxyHD\ncGouLz9FchpoNyQmENEZUQsRBXZ3thYVwXcHIv295FO/nJeTMFV0+nv3zF5t0NQib1WqosjLSeCm\nk7qgIM+/+fF0nIEyxXHigPpeQkRtAJQBqOn37J6WWmRo9b3GLCYRJaA4atyasqstFM8ojXXqNk8c\nLK8ZAd0P3Ha0zIxyByGKNKWimPtqVpLOnNRpPVq5O9kDduJZufV7wZXjRPD6+ndQFNV+ItpNRHuI\naHfgtUaI2f04Qo39pkUtb1I/H1/fdiLuObuHr/WEhsltdsOJxnNitid6JIjLMPBQb6M6P3DSM39E\nRI0B/B3ALACroMQhs4WIJhPRfIPXOQ7lux7Ax8y8NrVog2MN/2kiGklEM4hoxtatWw0rKS2vQJ3c\nNJSUgTReF8o56VA1naIPJmsjjiV6775mDaJPutyzbSNfXcHDSHHtFGYuZOYEM9dl5obq98x0u1LJ\nSyTQplEBRl9whKvzzu/bDqtGD0vKkNu+aT3HGbKdor+XTuvZqqoevzGbp7nIwXwa4M/yhycu7VOz\nXJNinarGZfefjrd+e3TyuSFaCi0nYdSRzBRm3gngfSKaAKCAmXdZnafBzKYuMUS0mYhaM/NG1Xxn\n5IY7CMBxRHQ9gAYA8oloL5T4Z/p/vh2ADSYyjAUwFgD69+9veGlLKyqRn46SMuDUHq2SHCfycxMo\nLbe2OzEDFapt6pZTDsPF/dtjwANTahznNsq5HfqwSGE8jYbtanxo83qYeddQ9PvbZBOB9B+DlY2I\nhhhtZ+ZpgVYcIIkE4Zvb7d2to0J/u115TDEuPqo9Gujmn8/t0wYfzjbsPmx595pBGPHi99hfVhGL\nDMW5iYTv1rdcg4eGpHnsKL371JAtz+i+H3SqoBwwHsAI9fMIKF5PqfUPZ+YOzFwM4BYArzLzKNU8\nuIeIjla9+n5ldL5TSgMy9+lx4sLKqPbuSyTI9M+3awxulYD+hotDQ0uHgjzj/7FZGqvrfeZW3etu\nAB8BuCdKgcIi7In65qpVQLujFcsDJSkoADirdxvLcl69aoDpvgGHNsXgTs2StkXZgtw0/e4OvJnN\n+gPNYzIMnPTMU4joAj9cvFMYDeBkIloKJRHcaAAgov5E9IKD868D8AKAZQCWQ0mD4InScv9HUl6p\nVJVUDpHpDUI25j4rPjTIlqp3nPD6L4863XmcQidV7C+rcC3D3Wd2N1ywaNc16uUJepDHzGfpXicD\n6AlgR7C1RksUDz7/HN4X425U5jbT7bqGeFjWoceudj91txtH3U5FDbDkb+7zbZ7Zq3WyY0fAzx5O\nfK6vAfBHAOVEdADKNed07ejMvA1ADRsBM88AcLXB9pcBvJxyXM90ZNA4GISSIsuvhijmPuWzkoLa\n+LiETksZOk5Y1NGuSc10A3549/mV8TQdzH5FzD1t1wHoFrUQQeJ1TY3ZWTef1AVPTllqfh4DZ+hi\nWlaNpFzeCI3r5WFnSZnj47Xf6UYp6iXy4wGpa6uGWLRxj+O64/JwboWtkmLmwjAEiQpmdjSSuvSo\n9sjLSeC1b1cHKo82J5WTIFNnDu1mNhttWN3sBGUitPOd1QNP/W8P45k3qNFKgkwcSWzqS+oofJWo\nJkT0lK7KBIA+UBySaj1+GWN+c+yhWL51LybO3Zhcvmm91uWZPaR99vshWL9zv2O5vIwYCdVrtloU\nujdJt2tSF+t2KDIuf+AM5CQI1x7fCQfLK/Hs1OWW59amdVIgoiZENICIhmivoAULi70Hy1FeyWhs\nk7mSyHwobbTZyw3L4Ko5qdwEobAgDw9fWHOBojaHtGt/mesOn4hCDrAQHkSEH9fsrLE9Zm1xBoCZ\n6ms6gD8x8y/TLZSI7lGjssxWX2eo24frts0mokoi6qPu8z1qSxg0qpuHZy6vGeO6udrJm+VAMvt5\ng1LmlDRaNCzAkR1MA+HUwMuIkQFcM6QTXr1qAE7q5j4orf4naf1C3fwcjDq9a9X3zPhXzbEdSRHR\n1VDWdrQDMBtKsNnpAGpF/D5t8ayd26uSlt343za6NVMjR+jPfeC8I3DHB/MM69BC+OSoLnc92zSq\ncVzDAkWhFuTlmLigm9+VhGBGC24aQlBzFF4bY5N6+dhzoFwtIyjZqAMzr2HmV+yP9szjzJwU/JmZ\n3wDwhirDEQDGMfNsdbcWteVbAB9DidrieW7XjqCf3Pt2aIK3Rx6NfockK5bqJKDG9WudeYLcxXl0\nit09lZOgtOe9gsLYMhGu1nMykvodgKMArGbmE6FERa/5uJqhVI1cHATBdPPf/Ou/K033XT6wA9o0\nMg4+WW6Syt5IDi+NPkGE3JwExgyvVdlWAHhrPMvuPz3JrBpg8/uwqg6iqMIgXQbgLVUGX6O2WBGm\n48TRHZvVfOAMeSRhVZ3WrrWgu11ikPnWikEdjUeZYeIo4gQzHwAAIqrDzIsBHB6sWOFR5U3nwC0m\nrfAiDo5hVI/sEhZDdX1n7DrihLrPKFkiUD2CA4ATDo/n050ZBOAQg0XUlnN04T0V6ivqGFAdNxLR\nXDWyupGd6hKoSgouorY4WRAfBD3b1rQieMHuLzbafc9Z3R2X7/RRsX5+TtXD8DvXDEJOgvDv6wZb\nnmOXusdJn+S137prWDfcemrNrj5s66ETJbVOjTjxIYDPiWgcgGC9B0KkXOfybQWzua3bC4adIzPa\nqSvhW5uMtAD7iBPW9Rpv1xSSfr9fidtOSSln7Y4SX8pNxY2X4nUndAKguqrqtgeos9jks2NsIriM\nAdAJiiPGRijhxPTnDoSSZXu+tslGxuqNzGOZuT8z9y8qCu/B5Wyb9UtO0a+TMtxv8Kc3tJmjdoOR\nxaNbq4ZY/sAZVaZ7M7665QRf63VD+6b1DBfyho0T777z1I/3ENGXUNIMTApUqhCpcDGSGtarteFc\nkl8wgBtO6IQuLRrgaHWYbTfn5LZPDaoPNnpau/+8nli9rQQtCuvgs4Wbq7Zv3KWEg2zVsACbdh+o\ncZ4RrRsVVJ1nKoOLH/eHoYfhT6cpa7vWbAtGaabQW43RRwDq6uL1OV7SYRXBRQ8RPQ9gQsrmS1E9\nigKUkZOjqC3pokXtPzWEuJBGeBkt+zWKS5Wjbm4CB8oqHTtZNK6Xfpgy07BIqgjN6udjm0326igx\nVZNEVEBEvyeip4noGiLKZeapzDyemeP7i1ziRkmZ/dlOmkDquWZlFeTl4Kzebao9cwxKrxpJmdzn\n6Zi3/FRiwwcegjvO6IaSUmNX+U//kOwkOqxXa9P1VuMMFiGnkiBvnnz6KBVBzZ8wc44uVl+u+tm3\n2H3qHJPGeQDm6/YloKTYeVsnj69RW6woKqyDOX8+JbKkol7+0cNaprHyxqLC964dhFtPPRz18v1J\nC5ROW9cU5YSb3QV0Ti02aKcPq7HcKwD6A5gH4HSkmA9qC+UOlRSDTe+9ywd2MNljjom1z9W5zByo\ne2ldn9IFmK3/aJRiUnn6siMx9dYTDI/VhzVq3agAVxiEZSGQ4ROq0XXVX7dbT3MeLSPGPKy6k88F\ncCKAP+j2DQGwjplXpJzjW9QWOxrVy6uaZ40bmlQndWuJXu0aoWXD4EJodW5R6CAqejL3ntOjKplp\nq4bJ0wBWV9Spua91I+MHQ6f/1l3DuuGbUdXO3n73SVbqvDszH6FUSv8C8L2/VYfPiq37cMlz0/HA\n+UegU1EDjJ22HBPUBYG5iQSWb92LO/6jmPPeuSY5K+bqFJPQ7f+ZW5VkbeGG3TiibSPMW58c1nDs\ntOrFdCNe/B4dmtar8pbZbjC8/s+P67Bt38Gqci95brrhgt3PVdNZRSXjj+/OqSHXYpsV55c8N72G\nnEbri976fg0u6NsO789aV2PfZJ35zoyx05ZjyqItjhr95IWbMbR7S3z10xY8/3VqXwpc/vy3VZ8v\n6tcO363cjjvO6IoHPl5ctf3ZqctNFb2RvNp1eOD86ujdv3nlB5zSoyVGDulkeT/EDWa+wmLfV1CW\njqRu9y1qS5yxXcybIPxv1C/QrH6+r3mcNNL1av/VoGIQEaYu2YoWDeskmchHDC7GXz9aaHm+2c+3\n02FmAQ5GDkn2+8nNSaCNzgLi90oDq5FUVTwQZi73t9r4oF1Qu/nB71Zutxw+O3lIbN2oAA+pi3ON\nDs9NOJukJJPPbs81IvX+Sr0hTcsN0YOunlkGZVPbe81WE89neiEIqtdJmR/TtnHdtBWUXeeczj1n\ndO6q0cNw5TGHmp9j0+6s1obeeUa3qtFbKmmZQj1g1Sv2VpOy7SaiPQB6ZXqSto5F9fHONYPQqUjx\n0hs5pBMeVJ+icxIJdCpqgHeuGeToqVmfqvqdawbhH5fWTBM9ckinqs+vXjUwqdzUqNz3nNUdX95y\nQo1yH72oZtrs03oq0w8JIjx2SXL+mAfP74VnLNZAEaHGbxw5pBOO7NC4xrGvXz3QVPkMNfD8u+b4\nZIU2ckgnvHPNIAx1sJJeK29o95aG11+fz2bkcR3xzjWDkq4vANxwQmfDjmLn/jJDebXroN0PAPDi\nlUdVlevmfhDckerxGSQhBA1Ori8mj0BW5r4bTuyE4UfXnKZoWj8ffz27B347pGPoi3bNMDX3MbP/\n494YopnOSkrtB4tpPQmlOk6k7L+of3vDeTGj+0QbcLGJTFb3lt1oLZ3faOYC7kcAW30RpoF3TX6a\nUf1xaYDZyKJ7T6tazJoN+GH+SqcIo3v91lON52GvP6ETRgwuti4vDVm84I+LSQajhcPZ7NAV2i9S\nbxwvYYUUxwlnJzaqm4fP/zjE1M5s6inoXCzTY/2eLzf7zQQyfHqMV/Z4oW5+uM+/sXkeiYscAWOV\nf8sL0a/Uipi6+colOFBmnTUXsJl3cVlv6vHmJoKa2zWPxLzchOPgti+M6I8WheYLhM1w2sDJ4lg/\nRi1OyiAyfuI08vjLkv6iVlBk4h0aG+UTAlULkk0euOqFrPit8NslPetHUqf3bI1nvlyOX3RtYXus\np1D8Jmt3KlPt2KYdfM1tDQty0aReHu49x9gxy4t7ux8N3uz6hOV5rFdkj13cGyu27sPTXy5zN5LK\npp4vA1h476mm5uLUaCFmBD1H1Fr1bNMy/tYQ10dvN6NL8dGNx/rmNu/sYTDcNpL1Sqpn20ZYNXpY\n2jrGzboAABLUSURBVOWY/W85RCg36CV37XeeTC2VvNwEfvzzKQCA1dv2eS7n69tOrFq7YriWyCZm\n+uk9W+GT+Zuqjze7BmloqTOOaIVRpznLCaiEblA+dyxqgDXblWUDht59oosyAqeLXu8+0zzWXtD/\n9Z/P7I6BhzZFp6IGeG/mOhzXpbmxHD7UZdROj2hnHB3jsJaFWLzJWQLEOJP1SsoNXm72hEn8/45F\nDTBzdXXWcKunxVT0N6rTzLz169Q0B7RvWjMYa1I9Bo+AXVtVu5+O+WU/XPvaTExasMm0XiA9x4nH\nLu7j2DU4QdWLeROkm7tzUZ/orsyBdGaK3xxr4YodsBwFeTk4p48Sm3fOX06psUi9sCAXJx5ehKuP\nCyqusDFvXD0QizftSesh0Qiz0q49vhMWbvTf8VuUlE/YmbpqmPdMjnOCviyn/X8Pg7xUSfKYmAhT\nt5/WMzn+mpMYZHbK0C/0ptUEkS4yh9Gxoo6yhTD/61QFBSgPqi9d6a8zgROaNaiDYzoHFz0jlVGn\nBxO5JesdJ4Kmdztl/VHqaCK13ZhFGzZqYJV2mdk8tEmjjtx4Ls2qXuOKO7dogO/vOAk92rgPUeem\nf0lV9B2L6gMADm1eP5D6hGhx+lfJX5rZyEjKIUd3bOqpA3t+RH8s3bynhsnK6dOd0VF2w/e08l6l\nrEeqMXdm4YVgVWuLhgWerp+730LYsudg1bdhR7RG2+vrok/7mguVhczHsedpLdJSXlLUu8HJpQr7\nespIyiF2naXZH9ewIA/9DmlqUJ539IE6/b5h9DqoIC8Hu0qSlZR5Th5/Fu0alevmWC3zaVFhHRAR\njuzQxJW5Jy7RAgR7svG/Svc3H39Yke9zVEEjIykX+Nko0unPc5OUlFE0Be9lawzuZJw2OnVuTf/V\n7t7fttd9hhc3PyVBhApVoNwMa4hCcGht5PaA5kwyiVd8WGgb9nyujKQc4vcwOx2FF8SIRaNG0Snf\nrdYc2Ym194D7OMXuRkHV8hmFf5p5l33OwNpkGqr1uPivVo0ehmuO72R/YMwJ2twXR0RJucCqAytP\n8SgoNIvU7aAsPUa3pH64bhxxIhl9Uj/b+mzagJH3klNKK+yjeqTiaiSl+5m5BrHhUoP6CplNNj1P\nZPPDkygpnygtT+6An7uin+XxTkdDqQtRcxKE4mbV3mpOihmti6zuFr2c9fJzcFXKepS2TZTV9o3q\n5tuOesq8KCk3c1K6bivT7O6CYIXfOZoyCZmTckivdo2ts2CmjHlMcx6peBlJ/ebYQ3HXsG5JysBw\nMW9K4ece2dZZZQZy6eemLhvQoUYOmlGnd8WA4qYY1KkZZq3ZASvq18mtCuirJ98ir40rc5/uUKtc\nOULtIBtHF9noLCIt2SG3nXq4ZYeZ+qTj162kL/fuM7s7i63lU32A0tnfNcw8LFGd3BycfkRr9Vzr\nx72/X1hzRPfcFf3w+R+HuBfUACKqMkd6HUllY8cnZA6Bu6DH8P6XkZQND1/YCyu27kNuTgIVFitZ\n3Q7HnY4Q7Dp+rZjCAn/+yv7FTbBky17cbaGYzLCLs3aSQfLDU3u0MjjSGwRg3A3HYMZq6xGdUDvI\nplGFVfQUP9FPJcQFGUnZcHH/9lXhPqyahNOo5lX7XcrRuUUDw+2GjhNptN06eTl49aoB6OIhRfSI\nwcWWKQOC6FK+vOWEqs8JIhQ3r48L+7XzXF42dXyZThyf+oNC616C+s2a5eFYk+C4USJKKiC8Lv5N\nRVN9poeTzf4QyUkQFt57Gh69qDdeuvKoUOrUhzzSop5bcX5f5/NzgpAtjDpNeRDPiaHmF3OfC6z+\nP7fDcL3XXG+TUPtA9QjNdmSmOyBqz7YLTEYyQS8C3LnffrHwIxf2xoPnH2G6P4ZtVDAhm/6qoM19\nvx3SEb8dEm6UdqfISMonvJr7Tu7eEu9dO9j0uKphvkmTNNpeWJCHJy7tYy2AB9JtIOl2KpcP7IBe\nFgrdCYkEoU5uuCZJIRiy2Cs7qxAl5QJL7z7XZSnv+TkJ5Oea/w12tmiz7Vp+G6c0qad4xdWxkCVq\n7j+3Jz68/pioxRBiQjauHcrGkX58e6QMQ+vkWzUsQIem9dBOXeRqjj93m1/37L3n9sQ9Z3XHoI41\nY/YVFSqRGlo1Si9iQ7oNjIiSgusGgeSZyhyyKURQr7ZKJP9jOxdFJsMZR/jniesGmZPyiUOa1ceE\nm47FYS0LLUdGGlV9oU2fqDVEu84z3b61YUEefn3MoYb7zu7dBvk5CZySpru4GwVw6VHt8fYPa12V\nP6C4ZrR5QagNHNGuEeb/9VQs37IXz05dHokMT1x6JB44z338zXSRkZSP9GzbyJGCAqojhtt129Vz\nUsaE8eRPRDj9iNahOmQ8eP4RWPHAGa7O6e+DkpJxVOaQbea+BjZRbIImLyeBxvXyQ69XRlIRoTk8\n2CkZ2zkpP4WKEaRL/y4IRmSZjspaIhlJEVFTIvqciJaq700sjm1IROuJ6Gndtq+I6Ccimq2+WoQj\nuX847YC7ti7EaT1a4ZGLehvul4bqL6IYMwi5+bOCqMx9owBMYeYuAKao3824D8BUg+3DmbmP+toS\nhJBBQg7NfXk5CTx7RT90a93Qujx/xMpamjcI34whCII9USmpcwC8on5+BcC5RgcRUT8ALQF8FpJc\njkgnp5JGtbkvvXLsYvtlA0MNYgK65bXfDMSY4X3Fu0+INd3bWD+s1kaimpNqycwbAYCZNxqZ64go\nAeBRAFcAOMmgjJeIqALA+wD+xia9NRGNBDASADp06JC24P8c3jftBaWA85GU8/Kyt3P95/C+2Hcw\nPa+jbq0b2o5WhXhx91ndcfeH86MWI1SyMQVNYEqKiCYDMPJZvtNhEdcD+JiZ1xp0wMOZeT0RFUJR\nUlcAeNWoEGYeC2AsAPTv3z/tYccZalqKdPFLqcg4CsjPTSA/V8x12YbRmj6h9hGYkmLmoWb7iGgz\nEbVWR1GtARjNKQ0CcBwRXQ+gAYB8ItrLzKOYeb1axx4iehPAAJgoqbhStUzKJ2WVveMoQRBqM1GN\nHccDGKF+HgFgXOoBzDycmTswczGAWwC8ysyjiCiXiJoDABHlATgTQMaN+f029wnZCxHdo3rAat6u\nZ6jbh+u2zSaiSiLqQ0T1iGgiES0mogVENDrq3+ANxY7QsSh+OZAE/4hKSY0GcDIRLQVwsvodRNSf\niF6wObcOgE+JaC6A2QDWA3g+SGGDgGp8EIS0eFzn7foxADDzG9o2KCbxVcw8Wz3+EWbuCuBIAMcQ\n0ekRye0Zu4XuQu0gEscJZt4GA2cIZp4B4GqD7S8DeFn9vA9Av2AlDB7f5qRkUkpwxmUA3gIAZi4B\n8KX6uZSIZgHwnikyYrLZaSgbyD5XkZhQbe5Lr4E1rKs8Z9xwYud0RRIymxuJaC4RvWiyOP4SqEpK\nDxE1BnAWlPWKhhDRSCKaQUQztm7d6p/EaSLPZ9mBhEWKCL/WSdXJzcGq0cN8kEiIMzbesmOgLHpn\n9f1RAFfpzh0IoISZk+ZuiSgXiuJ6kplXmNXtt4esX3RoWg9tG9fF3Wd2j1oUIUBESUVEGI4Tlw3o\ngLUOUqoL8cfKW1YPET0PYELK5kthMIqConiWMvM/0hQvEgrycvC/Ub+IWgwhYERJRUQYVnSrNOlC\n7UFbzqF+PQ86b1d1UfxFAIaknPM3AI1gMAcsCHFClFREVI2kZM5XSJ+HiagPFHPfKgDX6PYNAbBO\nb84jonZQzISLAcxSHQ+eZmY7z1pBCB1RUhGRULVTuo4TgsDMV1js+wrA0Snb1kE8t4UMQbz7IkJG\nUoIgCPaIkooM0U6CIAh2iLkvIrJ1JFVYkIurjjk0ajEEQcgQRElFhBYpItsiRsy759SoRRAEIYMQ\nc19EvPPDGgDA2z+sjVgSQRCE+CJKKiIqs2wEJQiC4AVRUoIgCEJsESUlCIIgxBZRUoIgCEJsESUl\nCIIgxBZRUhFRLz8HANCisE7EkgiCIMQXUVIR0byBopweuah3xJIIgiDEF1FSEVGpruItkpFU6Eya\nNAmHH344OnfujNGjR0ctjiAIFoiSiggt0kROIsviIkVMRUUFbrjhBnzyySdYuHAh3nrrLSxcuDBq\nsQRBMEHCIkVMNuuov360AAs37Pa1zO5tGuIvZ/Uw3f/999+jc+fO6NixIwDg0ksvxbhx49C9u6Qg\nF4Q4IiOpiKFsizAbMevXr0f79u2rvrdr1w7r16+PUCJBEKyQkVREsGrvS2SxkrIa8QQFG0T0lQcF\nQYgvMpKKCC12X450kKHSrl07rF1bHdR33bp1aNOmTYQSCYJghSipiMjWfFJRc9RRR2Hp0qVYuXIl\nSktL8fbbb+Pss8+OWixBEEwQJRURN/2iCwoLctGkfn7UomQVubm5ePrpp3HqqaeiW7duuPjii9Gj\nR/hmR0HwSmFBLkYMOiRqMUKDjGz0tZX+/fvzjBkzohajCmaW+ZAMgohmMnP/qOWIkri1ISGz8NKG\nZCQVIaKgBEEQrBElJQiCIMQWUVKCIAhCbBElJQiCIMQWUVKCIAhCbBElJQiCIMQWUVKCIAhCbBEl\nJQiCIMQWUVKCIAhCbMmqiBNEtBXAaoNdzQH8HLI4cUSug/U1OISZi8IUJm5IG7JFroPPbSirlJQZ\nRDQj28PdAHIdALkGXpHrpiDXwf9rIOY+QRAEIbaIkhIEQRBiiygphbFRCxAT5DrINfCKXDcFuQ4+\nXwOZkxIEQRBii4ykBEEQhNgiSkoQBEGILVmvpIjoNCL6iYiWEdGoqOXxEyJ6kYi2ENF83bamRPQ5\nES1V35uo24mInlSvw1wi6qs7Z4R6/FIiGhHFb0kHImpPRF8S0SIiWkBEv1O3Z921CAJpQ7X/vom0\nDTFz1r4A5ABYDqAjgHwAcwB0j1ouH3/fEAB9AczXbXsYwCj18ygAD6mfzwDwCQACcDSA79TtTQGs\nUN+bqJ+bRP3bXF6H1gD6qp8LASwB0D0br0UA11baUBbcN1G2oWwfSQ0AsIyZVzBzKYC3AZwTsUy+\nwczTAGxP2XwOgFfUz68AOFe3/VVW+BZAYyJqDeBUAJ8z83Zm3gHgcwCnBS+9fzDzRmaepX7eA2AR\ngLbIwmsRANKGsuC+ibINZbuSagtgre77OnVbbaYlM28ElBsPQAt1u9m1qFXXiIiKARwJ4Dtk+bXw\niWy8Jll934TdhrJdSZHBtmz1yTe7FrXmGhFRAwDvA/g9M++2OtRgW626Fj4i16SaWn/fRNGGsl1J\nrQPQXve9HYANEckSFpvVYTfU9y3qdrNrUSuuERHlQWlcbzDzf9TNWXktfCYbr0lW3jdRtaFsV1I/\nAOhCRIcSUT6ASwGMj1imoBkPQPOoGQFgnG77r1SvnKMB7FKH758COIWImqieO6eo2zIGIiIA/wKw\niJkf0+3KumsRANKGsuC+ibQNRe01EvULihfKEigeSndGLY/Pv+0tABsBlEF5gvkNgGYApgBYqr43\nVY8lAM+o12EegP66cq4CsEx9XRn17/JwHY6FYlKYC2C2+jojG69FQNdX2lAtv2+ibEMSFkkQBEGI\nLdlu7hMEQRBijCgpQRAEIbaIkhIEQRBiiygpQRAEIbaIkhIEQRBiiyipDIOI9qrvxUR0uc9l35Hy\n/Rs/yxeEOCBtKLMQJZW5FANw1cCIKMfmkKQGxsyDXcokCJlEMaQNxR5RUpnLaADHEdFsIvoDEeUQ\n0d+J6Ac1f8s1AEBEJxDR10Q0HkrkYhDRh0Q0U80LM1LdNhpAXbW8N9Rt2hMnqWXPJ6J5RHSJruyv\niOjfRLSYiN5QV6aDiEYT0UJVlkdCvzqCYI+0oUwg6pXM8nK98nuv+n4CgAm67SMB3KV+rgNgBoBD\n1eP2AThUd6y2KrwugPkAmunLNqjrAigh9XMAtASwBkp+mRMA7IISfysBYDqUlelNAfwEVC0Wbxz1\ndZOXvLSXtKHMeslIqvZwCpRYWbOhhNBvBqCLuu97Zl6pO/ZmIpoD4FsowR67wJpjAbzFzBXMvBnA\nVABH6cpex8yVUEKlFAPYDeAAgBeI6HwAJWn/OkEIHmlDMUSUVO2BANzEzH3U16HM/Jm6b1/VQUQn\nABgKYBAz9wbwI4ACB2WbcVD3uQJALjOXQ0mG9z6AMwFMcvVLBCEapA3FEFFSmcseKGmcNT4FcB0p\n4fRBRIcRUX2D8xoB2MHMJUTUFUpqZ40y7fwUpgG4RLXZF0FJqf29mWCk5JxpxMwfA/gDgN5ufpgg\nhIS0oQwgN2oBBM/MBVCumhxeBvAEFDPBLHXidSuqUznrmQTgWiJaBMXm/a1u31gAc4loFjMP123/\nAMAgAHOgREK+jZk3qQ3UiEIA44ioAMoT5B+9/URBCBRpQxmAREEXBEEQYouY+wRBEITYIkpKEARB\niC2ipARBEITYIkpKEARBiC2ipARBEITYIkpKEARBiC2ipARBEITY8v89A4bHQXPkjQAAAABJRU5E\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111ccc898>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.trace_plot(values=model.coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x111d06e10>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x112627518>)"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIpIKlIiIRKT/Bw3NX5t7lJWCAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x111d06e10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.grid_density_plot(burn_in=1000, values=model.coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false,
"scrolled": true
},
"outputs": [],
"source": [
"def plot_likelihoods(model, list_num_samples=None, num_runs=50, ref='analytic', ax=None):\n",
" \"\"\"\n",
" Plot likelihoods as a function of the number of samples\n",
" \"\"\"\n",
" _num_samples = model.num_samples\n",
" \n",
" if list_num_samples is None:\n",
" list_num_samples = np.logspace(1, 3, 20).astype(int)\n",
" values = []\n",
"\n",
" for num_samples in tqdm_notebook(list_num_samples):\n",
" model.num_samples = int(num_samples)\n",
" for _ in range(num_runs):\n",
" model.resample()\n",
" values.append(model.evaluate_log_likelihood())\n",
"\n",
" values = np.reshape(values, (-1, num_runs))\n",
" \n",
" # Reset the number of samples\n",
" model.num_samples = _num_samples\n",
" model.resample()\n",
"\n",
" ax = ax or plt.gca()\n",
"\n",
" ax.errorbar(list_num_samples, np.mean(values, axis=1), np.std(values, axis=1) / np.sqrt(num_runs - 1), \n",
" label=model.method)\n",
" \n",
" if isinstance(ref, str):\n",
" ref = [ref]\n",
" for i, _ref in enumerate(ref, 1):\n",
" ax.axhline(model.evaluate_log_likelihood(method=_ref), color='C%d' % i, ls='--', label=_ref)\n",
" \n",
" ax.set_xscale('log')\n",
" ax.set_xlabel('num samples')\n",
" ax.set_ylabel('log likelihood')\n",
" ax.legend(loc=0)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEOCAYAAABIESrBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\np423igNLa1kAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x112192d68>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_likelihoods(model)"
]
},
{
"cell_type": "markdown",
"metadata": {
"deletable": true,
"editable": true
},
"source": [
"### Method 2\n",
"\n",
"Method 2 performs badly."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"model.method = 'joint'\n",
"model.resample()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"sampler = util.AdaptiveMetropolisSampler(model.evaluate_log_likelihood, mode='reevaluate')"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"text/plain": [
"array([-0.14907828])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sampler.sample(sampler.samples[-1] if len(sampler.samples) else model.coefficients, 2000, \n",
" callback=model.resample, tqdm=tqdm_notebook)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:root:function values may not be interpretable in the 'reevaluate' mode\n"
]
},
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x10837e080>,\n",
" (<matplotlib.axes._subplots.AxesSubplot at 0x10837c320>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x1129164a8>))"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAakAAAEYCAYAAADmugmLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10837e080>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.trace_plot(values=model.coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x112ac1518>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x112aacd30>)"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/w/0DT3hCbtsHgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x112ac1518>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.grid_density_plot(burn_in=1000, values=model.coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEOCAYAAABIESrBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1083b0780>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_likelihoods(model)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This problem arises because the variance of the estimator is large due to the exponential that is applied in the calculation. Let's have a look at the intermediate results: the distribution of the aggregate log-likelihood samples is well behaved (looks approximately Gaussian) but the variance of the standard deviation of the samples is about 13. That means the contributions to the mean vary by a factor of at least $\\exp(13)\\approx 4.4\\times10^5$ and the mean is dominated by the samples that happen to be large."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(array([ 1., 3., 11., 17., 16., 18., 16., 7., 7., 4.]),\n",
" array([-691.16769989, -684.82602491, -678.48434993, -672.14267495,\n",
" -665.80099997, -659.45932499, -653.11765002, -646.77597504,\n",
" -640.43430006, -634.09262508, -627.7509501 ]),\n",
" <a list of 10 Patch objects>)"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD8CAYAAABw1c+bAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x112ad6c88>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"pll = model.evaluate_pointwise_log_likelihood(model.sampled_x, model.coefficients)\n",
"aggll = np.sum(pll, axis=1)\n",
"plt.hist(aggll)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Variational approximation\n",
"\n",
"Variational inference approaches generally lower-bound the integral by exchanging the order of integration and taking the logarithm. Let's see whether that approximation is any good:\n",
"\n",
"\\begin{align}\n",
"\\log P(y|\\theta,g) &\\geq \\int dx\\,\\log P(y|x,\\theta)P(x|g)\\\\\n",
"&= \\int dx\\,\\sum_{i=1}^n\\log P(y_i|x_i,\\theta)P(x|g)\\\\\n",
"&\\approx \\frac 1m \\sum_{k=1}^m \\sum_{i=1}^n\\log P(y_i|x_i,\\theta)\n",
"\\end{align}\n",
"\n",
"Again, in the case of the linear regression problem, we can evaluate the lower bound analytically:\n",
"\n",
"$$\n",
"\\log P(y|\\theta,g) \\geq -\\frac{(y-\\theta\\mu)^2+\\theta^2\\sigma^2}{2}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Analytic variational approximation"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"model.method = 'analytic_variational'"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"sampler = util.AdaptiveMetropolisSampler(model.evaluate_log_likelihood, mode='reevaluate')"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"text/plain": [
"array([-0.14844975])"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sampler.sample(sampler.samples[-1] if len(sampler.samples) else model.coefficients, 2000, \n",
" callback=model.resample, tqdm=tqdm_notebook)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:root:function values may not be interpretable in the 'reevaluate' mode\n"
]
},
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x1121c8e80>,\n",
" (<matplotlib.axes._subplots.AxesSubplot at 0x1134b0588>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x112f01ba8>))"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAakAAAEYCAYAAADmugmLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nASCNK1VxV/DkAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1121c8e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.trace_plot(values=model.coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x1128d2978>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x112f7f9e8>)"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3Xl8XWd95/HPT5t1JXmRbXmVtyS2YhOSEIRJCIkNaVjt\nBGZChxRoWDryAO0wjA1NX6Uzr5aZebUdG0qhFKssKTSQIYECdlpICpFDIThxQhbbibzHuyUvsrVc\nLZae+eNcJYqizbrLc56r7/v1el5XOvf4nu/r2NZPz3Oe8xxzziEiIhI3Bb4DiIiIDEUFSkREYkkF\nSkREYkkFSkREYkkFSkREYkkFSkREYkkFSkREYkkFSkREYkkFSkREYqkolwebOXOmW7x4cS4PKSIi\nMfPkk0+eds5VjbZfTgvU4sWL2bFjR3ofsnp19NrQkG4cERHxwMxeHMt+GuITEZFYymkPKiM2b/ad\nQEREciC8AlVT4zuBiIjkQHhDfBs3Rk1ERPJaeAVq69aoiYhIXgtviG/NGt8JREQkB8IrUBs2+E4g\nIiI5EN4QX2Nj1EREJK+F14Naty561Y26IpIpB7bBtr+GWVfC3GthyU1Qudh3qgkvvAIlIpJpv/oS\nHP8tnHgGnvg6lE6FzxyAQv2I9Cm8Ib6GBvWeRCRz2k/DgQZ4Yx3cfRje/QXoPA9Nu3wnm/DCK1Ai\nIpm065/B9cJr3wcFBbD01mj7kcf95pIAC1RdXdRERDLhuQegajnMfk30/dQFUDFHBSoGwhtg3bPH\ndwIRyRctR+DIb+Ctn3t5mxksWAlHVaB8G7UHZWbfNLMmM9s5aPsfmVmjme0ys7/OXsRB1q+PmohI\nunb+IHq96o5Xbl+wEs4dgramnEeSl42lB3UP8BXg2/0bzOwtwO3A1c65LjOblZ14Q1i7NmeHEpE8\n99wDML8Wpi955fbqldHrkcdhuVav8WXUHpRz7lHg7KDNHwf+0jnXldond79mbNkSNRGRdDQ3wqnn\n4LV3vPq9uddAYYmG+Twb7ySJZcBNZrbdzLaZ2RsyGWpEmzZFTUQkHc+nftFd8Z5Xv1dcGhUpTZTw\narwFqgioBK4HPgN838xsqB3NrM7MdpjZjubm5nEeboBly6ImIpKOg4/CrNfAlLlDv1+9Mrp592J3\nbnPJS8ZboI4CP3SRx4E+YOZQOzrn6p1ztc652qqqqvHmfFl9fdRERMarpxOObIfLVg2/z4KVcLET\nTj6Xu1zyCuMtUD8C3gpgZsuAEuB0pkKJiGTVke1R8VkySoECXYfyaCzTzL8HPAbUmNlRM/sY8E3g\nstTU8/uAu5xzLrtRU1avjpqIyHgdfBSsEBa9afh9psyDKdW6DuXRqNPMnXN3DvPWBzOcRUQkNw5u\ng/nXQemUV721bdu2l75eXrqYyfv/nccHbBts1aoRemGSlvBWkti82XcCEQlZ5wU49hS8+dOj7tpR\nVk1V06+wvh5cQXEOwslA4RWomhrfCUQkINsG9X5mnH6cq1wvz7ROo2WEnhFAZ2IOhqO08xTJsups\nxpQhhLdY7MaNURMRGYdp556lt6CE81OuHHXfZOkcABLJU9mOJUMIr0Bt3Ro1EZFxmHbuGS5MXY4r\nLBl132QiukeqNHki27FkCOEN8a3RulgiMj7F3S1UtL/Igdk3j2n/npJp9BaWkkiezHIyGUp4BWrD\nBt8JRCRQ085FN922TLt6bH/AjGTpbEpVoLwIb4ivsTFqIiKXaNq5Z7hYWEbr5CvG/Gc6E3NJaIjP\ni/B6UOvWRa8NDV5jiEh4KluepaXyKigoHPOfSSbmUHn2KXB9YOH9Th8ynW0RmRAmdTaRSJ4c+/Be\nSjIxh8K+bkq6z2UpmQwnvB6Uek4iMg7Tzj0LwLnKay7pz3WmZvIlkifonjQj47lkeOpBiciEUHnu\nGbqLp9JRvvCS/lwyEd0LpYkSuRdegaqri5qIyFg5x7Rzz9FSeTUM/ei6YXVNqsJZgaaaexDeEN+e\nPb4TiEhgyjqOMqn77CUP7wG4giI6J1WpB+VBeAVq/XrfCUQkMP3Xn1oqL22CRL/OxBz1oDwIr0Ct\nXes7gYgEZtq5Z0iWzqIzdT3pUiUTc6lq/lWGU8lowrsGtWVL1ERExsL1Mq1l57h7TxBNlCjuaaXw\nYnsGg8lowutBbdoUvaonJSJjUNF2kOKLbbSM4/pTv/6eVyJ5krbJl2cqmowivAK1bJnvBCISkMqz\nTwNw7hJv0B1o4KrmKlC5M+oQn5l908yazGznEO9tMDNnZjOzE28I9fVRExEZg8qzT9NWvoieSZXj\n/ozO0tkAmiiRY2O5BnUP8I7BG81sAXArcDjDmUREMqO7g6nnd3Nu+rVpfUxvURndxVNVoHJs1ALl\nnHsUODvEW18EPgu4TIca0erVURMRGc3hxyhwFzlXmV6BgmiYTw8uzK1xzeIzs9uAY865Z8awb52Z\n7TCzHc3NzeM5nIjI+Bx4hD4r4vy0q9L+qM7EHBKdevR7Ll3yJAkzKwP+FHjbWPZ3ztUD9QC1tbXp\n97Y2b077I0RkgtjfwPmpy+krnJT2RyUTc5h16lGsrwdXUJyBcDKa8fSgLgeWAM+Y2SGgGnjKzMZ3\nB9ylqqmJmojISNqa4NRzaV9/6tdZOhujj0mdGgnKlUvuQTnnngNm9X+fKlK1zrnTGcw1vI0bo1c9\n+l1ERnJgGwAtGbj+BAPuheo8RWfZvIx8poxsLNPMvwc8BtSY2VEz+1j2Y41g69aoiYiM5MAjUDqN\n1smXZeTj9NiN3Bu1B+Wcu3OU9xdnLM1YrFmT08OJSICcg/2PwGWrwMb+ePeRdJdU0ltQoqnmORTe\nShIa2hOR0TQ3QutxuOwtkKnl86yAztLZlHaqQOVKeIvFNjZGTURkOI3/Er0uvTWjH9uZmK0hvhwK\nrwe1bl302tDgNYaIxNgLD8K818HUamB/xj42WTqHqS27oyHES3wyr1y68HpQIiIjaT0Jx3bAle/O\n+Ed3JmZT1NtB0cXWjH+2vFp4PSj1nERkJP3DezXZKFD9j904RWvxlIx/vrySelAikl9eeBAql8Cs\n5Rn/6GRp/1RzrcmXC+EVqLq6qImIDNZ5IbpB98p3Z+UaUWdCj93IpfCG+Pbs8Z1AROJq379BXw9c\nmZ37JfsKS+kumUapFo3NifAK1Pr1vhOISFy98CCUzYQFK7N2iGTpHE01z5HwCtTatb4TiEgcXeyG\nvQ/BitugIDOrRwylMzGHqed3Z+3z5WXhXYPasiVqIiIDPf8T6LoAK96b1cMkE3OY1Hka6+vJ6nEk\nxB7Upk3Rq3pSIjLQ9s0w/TK4/K1ZPczAx25oVfPsCq8HtWxZ1ERE+h17Eo4+DivXQUF2f6y9fC+U\nrkNlW3g9qPp63wlEJG6210NJBVz7e1k/1EuP3dCisVkXXg9KRGSg1lOw8wdw7QegNPurO3SXVNJX\nUEwiqanm2RZegVq9OmoiIgBP3hPd+7QyRzfwWwHJ0tlaTSIHwitQIiL9ejphxzfgilth5hU5O2yy\nbB5lyeM5O95ENeo1KDP7JrAGaHLOXZXa9n+BtUA30Vr2H3HOtWQz6Es2b87JYUQknrZt2/bS19WH\nf8jlbad4pmIVLQO2Z1tH2QKmn3kK67uYs2NORGPpQd0DvGPQtoeBq5xzVwN7gD/JcK7h1dRETUQm\ntKKeCyx68X7OTK+lpfLqnB67vXwhBe4iCQ3zZdWoBco59yhwdtC2h5xz/b86/AaozkK2oW3cGDUR\nmdAWHbqfwotJDlx+V86P3VG+EICy9sM5P/ZEkolrUB8F/jUDnzM2W7dGTUQmrNLkSeYde5CTc2+h\no2JRzo/fUVaNwyhvP5LzY08kad0HZWZ/ClwE7h1hnzqgDmDhwoXpHC6yJjurFItIOJYc+A7OCjm0\nJPv3PQ2lr3ASnaWzKetQDyqbxl2gzOwuoskTtzjn3HD7OefqgXqA2traYfcbsw0b0v4IEQlXouMY\ns5p+yYuL3kf3pBnecrSXL6RcQ3xZNa4hPjN7B/DHwG3OuY7MRhpFY2PURGRCmnf0QfqsiGPVfkdT\nOsoXkOg4Dr1aNDZbRi1QZvY94DGgxsyOmtnHgK8Ak4GHzexpM/talnO+bN26qInIxNN5njknf07T\n7JvoKan0GqV/Jh9nD3jNkc9GHeJzzt05xOZvZCGLiMjIfnsvRb1JjlX7f5pBR/mC6IvmF6BKt75k\nQ3iLxTY0+E4gIj709cLjmzk/dTltk3O3asRwOsoW4DCs6QVYcbvvOHlJSx2JSBj2/AzOHeJoDHpP\n0D+Tb1bUg5KsCK9A1dVFTUQmlu1fgynzOTPzet9JXtJRvlAFKovCK1B79kRNRCaO5Dk4+Chc+3u4\ngvhcmWgvXwin92omX5bE5296rNav951ARHLt4C8BB5ffAoe6fad5SUf5guhRH2cPQpWe9J1p4RWo\ntfEYfxaRHDq4LXpibnUtHPq17zQvaU+tyUfz8ypQWRDeEN+WLVETkYnjQAMsuhEKi30neYWOstQ6\n2c1aPCAbwutBbdoUvaonJTIxtByBM/ug9qO+k7xKX2EpTFsEp3b5jpKXwitQy9SNFplQDqYeRHjZ\nap8phjf/9XBku+8UeSm8AlVf7zuBiOTSgQYor4JZK3wnGdqCN8KuH8L5ozA1d4/GmwjCuwYlIhOH\nc3BgW9R7MvOdZmgL3xi9Hv6N3xx5KLwCtXp11EQk/zU9D+1N8R3eA5j9Wigu1zBfFoRXoERk4jjQ\nEL0uWeU1xogKi6Ba16GyIbxrUJs3+04gIrlyoAFmXAHTFvhOMrIFb4RffgG62mBShe80eSO8HlRN\nTdREJL85B0efgIU3+E4yugXXg+uFYzt8J8kr4RWojRujJiL5re0UJM/CnNf6TjK6BW8ADA5rmC+T\nwitQW7dGTUTy26md0evs1/jNMRalU6Np8LoOlVHhXYNas8Z3AhHJhf7VGeJ6/9NgC1bCzh9ED1Ys\nKPSdJi+M2oMys2+aWZOZ7RywbbqZPWxme1OvldmNOcCGDVETkfx2ahdMmQ9l030nGZuF10PXhWhq\nvGTEWIb47gHeMWjb3cDPnXNLgZ+nvs+NxsaoiUh+O7U7nN4TRDP5QMN8GTRqgXLOPQqcHbT5duAf\nU1//I/CeDOca3rp1UROR/NXbEz2pNoTrT/0qF8PkuS+vHShpG+8kidnOuRMAqddZw+1oZnVmtsPM\ndjQ3N4/zcCIyoZzeGz0IcPZVvpOMnRnUvBP2PgzdHb7T5IWsz+JzztU752qdc7VVVVXpf2BDQ9RE\nJH/1T5AIqQcFsOI90NMB+x72nSQvjLdAnTKzuQCp16bMRRKRCe/UTigohplLfSe5NItuhLIZsPvH\nvpPkhfEWqJ8Ad6W+vgvI3d9GXV3URCR/ndoFVVfG7gm6oyosguVrofGn0JP0nSZ4Y5lm/j3gMaDG\nzI6a2ceAvwRuNbO9wK2p73Njz56oiUj+atoNswOawTfQituhpx32/dx3kuCNeqOuc+7OYd66JcNZ\nxmb9ei+HFZEc6TgLF46Fd/2p3+KbIDEddv8IlmthgXSEt5LE2rW+E4hINjXtjl5DLVCFxXDlu2HX\nj6CnE4pLfScKVnhr8W3ZEjURyU8vzeALaIr5YCveA92tsP8XvpMELbwCtWlT1EQkP53aGc2Eq5jt\nO8n4XbYqGuZ7+l7fSYIW3hDfsmW+E4hIBm3b9sqVF163bzt9JfN45tFHPSXKgMJieP2H4Vd/A+de\nhMpFvhMFKbweVH191EQkLyU6jtNRNt93jPS94WOAwRP/4DtJsMIrUCKSt4p6Wim+2EoyMdd3lPRN\nrY7uiXrq29Dd7jtNkMIrUKtXR01E8k6i4zgAyXzoQQFc/3HoPA/P3Oc7SZDCuwYlInkrkYwKVEdi\nnuckYzf4GtorOMd1FZdT8MgX2dF+OZixatWq3IULXHg9qM2boyYieaes4ziOAjoTAc/gG8iMYwvW\nUt5xhMpzT/tOE5zwClRNTdREJO8kksfpLK3CFQS2Bt8ImmbdRE/RZGaf1D1Rlyq8ArVxY9REJO8k\nOo6TLAtneG8sXEExzbPexMzT2yno7fIdJyjhFaitW6MmIvnFORLJ4yQDuv40Vk2zbqawt5MZpx/3\nHSUo4U2SWKPFF0XyUXFPC0W9ybzrQQGcn7aCrpLpzGraBnzOd5xghFegNmzwnUBEsiDRcQIgL3tQ\nWCHNs25i3rEHIXkOEpW+EwUhvCG+xsaoiUheKUseA6AjD3tQAE2zb6bAXYTntdj1WIVXoNati5qI\n5JVEx3H6rJDOSbN8R8mK1slX0JGYC8894DtKMMIrUCKSlxLJE3SWzoGCQt9RssOM5lk3w8FHofWk\n7zRBSKtAmdmnzWyXme00s++ZWfafzNXQEDURySuJjmMky/JgDb4RNM2+CXDQ+C++owRh3AXKzOYD\n/xWodc5dBRQC789UMBGZQFwfieQJkok8WYNvGB1lC6C8Cg5v9x0lCOkO8RUBCTMrAsqA4+lHGkVd\nXdREJG+UdJ2lsK+bjjzvQWEG1SvhqO6HGotxFyjn3DFgI3AYOAGcd849lKlgw9qzJ2oikjfKUovE\n5uUU88EWrISzB6D9tO8ksZfOEF8lcDuwBJgHlJvZB4fYr87MdpjZjubm5vEn7bd+fdREJG+8/JiN\nCVKgAI4+4TdHANIZ4vsd4KBzrtk51wP8EHjT4J2cc/XOuVrnXG1VVVUah0tZuzZqIpI3Esnj9BUU\n0zVppu8o2TfvdVBQBEd0HWo06RSow8D1ZlZmZgbcAjyfmVgj2LIlaiKSNxLJ4yRL54BNgDtfihMw\n52o4oh7UaNK5BrUdeAB4Cngu9Vn1Gco1vE2boiYieSPRcWJiDO/1W7ASjj8FvT2+k8RaWr+uOOf+\np3PuSufcVc65Dznnsr+W/LJlUROR/OD6SHSeJJnI8xl8Ay1YCT0dcGqn7ySxFt5isfXZ76SJSO5M\n6jpDQV/PxCpQ1amJEkeeiK5JyZAmwICviMRZaTJa9mdCFaip1TB5ru6HGkV4BWr16qiJSF5IJPsf\nszGBCpRZNMynmXwjCq9AiUheSSRP0GdFdJVOgCnmA1WvhJbD0HrKd5LYCu8a1ObNvhOISAZFq5jP\nBsvTVcyHM/CG3eV6UvhQwitQNTW+E4hIBkWLxE6c4b1t27YBUNDbyZsxXtz+IC82TR52/1WrVuUq\nWuyEN8S3cWPURCR8zkUFKt8XiR1CX2EpycQcytsP+Y4SW+EVqK1boyYi4WtvprC3c0L1oAZqL19E\neduLvmPEVnhDfGs0ViuSN84eAKBzohaoisXMPP04Bb1d9BVO8h0ndsIrUBs2+E4gIpmSKlATtwe1\nGKOPsvbDtE1Z6jtO7IQ3xNfYGDURCd/ZAzgroLM0A086CFB7xWIAyts1zDeU8HpQ69ZFrw0NXmOI\nSAacPUDnpFm4gmLfSbxIJmbTW1BCRdshdDfUq4XXgxKR/HH2wIQd3gPACqOJEupBDSm8HpR6TiL5\n4+xBktNv8J3Cq/aKRcw4rWdDDUU9KBHxo+MsdLZM2Bl8/drLF1HSc57i7nO+o8ROeAWqri5qIhK2\nswcBJuRNugO9NFFC90O9SngFas+eqIlI2Cb4FPN+7eWLAahoO+Q1RxyFdw1q/XrfCUQkE84eAIxk\n6RzfSbzqKZlKV0mlJkoMIa0CZWbTgK8DVwEO+Khz7rFMBBvW2rVZ/XgRyZGzB2DKPFxhie8k3kVL\nHh3yHSN20h3i+xLwU+fclcA1wPPpRxrFli1RE5GwndkLM67wnSIW2isWU9ZxBPp6fUeJlXEXKDOb\nAtwMfAPAOdftnGvJVLBhbdoUNREJl3NwZp8KVEp7+SIK+7pferqwRNLpQV0GNAPfMrPfmtnXzax8\n8E5mVmdmO8xsR3NzcxqHS1m2LGoiEq7209B5HmZq/Tl4eSZfhR698QrpFKgi4Drg751zrwPagbsH\n7+Scq3fO1TrnaquqMrDeVn191EQkXGf2Ra8zVKAA2ssX0meFVLQe8B0lVtIpUEeBo8657anvHyAq\nWCIiIzuzN3qdcbnfHDHhCorpKKvWRIlBxl2gnHMngSNm1v8M9luA3RlJNZLVq6MmIuE6vRcKS2Da\nQt9JYqO9YgkV7Qd9x4iVdGfx/RFwr5k9C1wL/J/0I4lI3juzH6ZfBgWFvpPERlvFEiZ1naGo54Lv\nKLGR1n1QzrmngdoMZRmbzZtzejgRyYIze2GmJjsN9NJEibaDtFRe4zdMTIS31FFNTdREJEy9F6N1\n+DTF/BXaKpYAUNGqYb5+4RWojRujJiJhankR+no0xXyQnpJpqSWPVKD6hVegtm6NmoiE6cz+6FVT\nzF+lvWKJFo0dILzFYtes8Z1ARNLx0hRzDfEN1laxhOojz2J9PbiCYt9xvAuvQG3Y4DuBiKTjzD5I\nVEL5DN9JYqetYjEF7iJlHUdpT12TmsjCG+JrbIyaiITptBaJHU5/UdINu5HwCtS6dVETkTCd2afr\nT8PoSMynt6CEijYteQQhFigRCVdXG7Se0BJHwykopL18oSZKpIR3DaqhwXcCERmv/kViNcV8WO0V\nS5hxenv0SBIz33G8Ug9KRHJHq5iPqq1iCSU9FyjpPus7infhFai6uqiJSHjO7AMMpmuG2nDaJkcT\nSCZf2OM5iX/hFag9e6ImIuFpfgEqF0FxwneS2GqdfDl9VsTU8y/4juJdeNeg1q/3nUBExqvpeZj1\nGt8pYs0VFNM6+QqmnH/edxTvwitQa9f6TiAi43GxK7oH6kqtBjOaC1OXM//oFqyvx3cUr8Ib4tuy\nJWoiEpbTe8H1wqzlvpPE3vmpyylwF5ncus93FK/C60Ft2hS9qiclEpam1JDVbA3xjebC1OiRQlMm\n+HWo8ArUMj3kTCRITbugoBim6ybd0fSUVNKRmDvhr0OFV6Dq630nEJHxaHo+ukG3qMR3kiBcmHol\n0888NaFv2E37GpSZFZrZb81MD2kSkeE17YZZK3ynCMaFKcsp6TkP5ybuAwwzMUniU0Du+qGrV0dN\nRMLR1QothzVB4hKcn5o6V0ce9xvEo7QKlJlVA+8Gvp6ZOCKSl5pSF/s1QWLMOsoXcLGwDI5s9x3F\nm3SvQf0N8Flg8nA7mFkdUAewcOHCNA8HbN6c/meISG417Y5e1YMaOyvgwtQaph+euAVq3D0oM1sD\nNDnnnhxpP+dcvXOu1jlXW1VVNd7DvaymJmoiEo6m3VBcDlMz8EvqBHJ+6vLo3CVbfEfxIp0hvhuB\n28zsEHAf8FYz+6eMpBrJxo1RE5FwNO2Oek8F4a0N4FPLtKsBBwce8R3Fi3H/a3HO/Ylzrto5txh4\nP/AL59wHM5ZsOFu3Rk1EwtH0vIb3xuHC1BpIVMKeh3xH8SK8+6DWaB0vkTjbtm3bK74v7m7hTe3N\n7GudxLFB78korBCu+B3Y+xD09U24HmhGCpRzrgFoyMRnjWrDhpwcRkQyo7z9RQDayxd5ThKopW+H\n5+6H409Bda3vNDkVXjlubIyaiAShvC1VoCo0QWJcrrgFrAD2/Mx3kpwLr0CtWxc1EQnC5Na9dE2a\nQU9Jpe8oYSqbDtUrYa8KlIhIRk0538iFKbo1JC3L3gYnnoELJ3wnyanwClRDQ9REJPaKu1tIdJ5U\ngUrX0rdHr3sn1my+8AqUiARjyoXoerEKVJpmvwamzFeBir26uqiJSOxNOf8CfVZE22Q9AyotZrDs\n7bD/EehJ+k6TM+EVqD17oiYisTflQiNtFUvoK5zkO0r4VrwHetrhhQd9J8mZ8G7UXb/edwIRGYu+\nXiZf2MuJeW/znSQ/LL4Jpi6Ap78Lr73Dd5qcCK9ArV3rO4GIjEFF+yEK+7q4MGWZ7yj5oaAArrkT\nfrkRLhyHKfN8J8q68Ib4tmyJmojE2uSXJkhc6TlJHrnm/eD64Jn7fCfJifAK1KZNURORWJtyvpHu\nkml0lc7yHSV/zLgcFt4QDfM55ztN1oVXoJYti5qIxNqUCy9EvScz31Hyy7W/B2f2wtEdvpNkXXgF\nqr4+aiISW0XdFyhLntD9T9mw4j1QlICn7/WdJOvCK1AiEnsv3aA7VQUq40qnwIrbYOcPoPO87zRZ\nFV6BWr06aiISW9PP7KC3YBKtk5f6jpKfrv8EdF2Ax/N7NCm8AiUi8dbXS1Xzrzkz8w26QTdb5l0b\nrc/32Fehq813mqwJr0Bt3hw1EYmlaed3UtJznuaqN/uOkt9WfRaSZ2HHN3wnyZpxFygzW2Bmj5jZ\n82a2y8w+lclgw6qpiZqIxFJV06/oLSzl7IzX+46S36pr4fK3wq+/DN0dvtNkRTo9qIvAeufccuB6\n4JNmtiIzsUawcWPURCR+ei8ys/nXnJmh4b2cuPmz0N4MT/2j7yRZMe4C5Zw74Zx7KvV1K/A8MD9T\nwYa1dWvURCR+Dv2Skp4LNM3S8F5OLLohWqPvl1/Iyxl9GVmLz8wWA68Dtg/xXh1QB7Bw4cL0D7Zm\nTfqfISLZseufuViY4Nz063wnyRvbtm0b8f2Kme/lukMbOP6dj7Nv2TpWrVqVo2TZl3aBMrMK4AfA\nf3POXRj8vnOuHqgHqK2tTX9tjg0b0v4IEcmC3h54fgtnZq7U8F4OtU2+gmPz38X8Yw9ycs5bgfwp\nUGnN4jOzYqLidK9z7oeZiTSKxsaoiUi87PkZJM/SXHWj7yQTzqHLPkB3SSXLGr8Kfb2+42RMOrP4\nDPgG8Lxz7guZizSKdeuiJiLx0dUKP70bZi7T7D0PeovK2b/0D5jcth8e/wffcTImnR7UjcCHgLea\n2dOp9q4M5RKRkPz883D+KNz2ZVxBse80E1Jz1Y2cnf46+MXnoeWI7zgZMe5rUM65fwdyv0xxQ0PO\nDykykY12kX7K+Re49ql6js9/J/sOduUolbyKGXuWfYLrn/xvsPXT8IH7g19JPryVJEQkNgp6u1j2\nwpfpmjSDg5f9vu84E15XYjbc8mew72F47n7fcdIWXoGqq4uaiHhV1n6Y1z25gfKOI+yt+SS9RWW+\nIwnAyjqofgP86x9D+2nfadISXoHasydqIuKHc8w5/hDX7fjvlHS38NzV/0MTI+KkoBBu+wp0t0UT\nVwKWkRunUQKtAAAJg0lEQVR1c2r9et8JRCas0uRJljb+PdPP/ZZzldfwwvJP0z1puu9YMkD/NcNF\nC/4Di5+7j2cKr6al8pph94/zjb3hFai1a30nEJl4XB/VR37E4oPfxVkhe5fWcXz+u8DCG4SZKI4s\n/I/MPtnAFXs28+QbvhTk7Mrw/nVt2RI1EckN18fSPV/j8v33cG76dTzxxq9yvHqNilPM9RVOYt+y\nOso7jlJ95Me+44xLeD2oTZuiV/WkRLKvr4+ljV9l3omHOLzwDg5e9qHgpy5PJGdn1NI883oWHbqP\nptk301U6y3ekSxLer0DLlkVNRLLLOdj6KeadeIgXF/2uilOg9i/9z4Bxxd7wHg8fXg+qPryTLBKk\n7V+Dp77Ni4vex6ElH1BxClRXaRWHltzJ5fvvYUbzY5ypusF3pDELrwclItl39El46M+g5l0cWvJB\nFafAHau+jbbyxSzdW0/hxXCevhtegVq9Omoikh3Jc3D/h2HyXLj971Sc8oArKGJPzScp6TrL4gP/\n5DvOmIVXoEQke5yDH30SWo/D+74FZbrHKV+0Tq3h+Px3Mv/Yg0y+EMZiB+EVqM2boyYimffrv4XG\nB+HWv4DqWt9pJMMOXvb7dE+azpW7N1HY0+Y7zqjCK1A1NVETkcw69Cv4tz+H5bfB9Z/wnUayoLeo\njN0rPkNpZxPLn/8iuD7fkUYUXoHauDFqIpI5rSfhgY/A9CW67pTnLkxbwf4r/oAZZ55g0aHv+44z\novAK1NatURORzOhqhe/fFb3+7negdIrvRJJlx+e/i5Nz3sKiQ9+DnT/0HWdY4d0HtWaN7wQi+aP9\nNNx7B5x4Fu74Bsxe4TuR5IIZe5d9gkTHCaY+8BE4sx9u3hC7nnN4BWrDBt8JRPJDyxH4znvh/BF4\n/3eh5h2+E0kO9RVO4tlrP89NLQ/AI/8LTu2E274cqx50WkN8ZvYOM2s0s31mlpsHjzQ2Rk1Exqf9\nNPz88/D3N0JbE3zoRypOE1Rf4SR47+Zo1ubuH8MXr4pu0D5/zHc0II0elJkVAn8H3AocBZ4ws584\n53ZnKtyQ1q2LXhsasnoYkbzjHDz8Z/DEN6AnCStug7d8Dqq0tuWEZgY3fgoW3xTdZvDYV+Cxv4O5\n10S3Gsy7DqZWQ3kVVMyC0mlQkJvpC+kM8a0E9jnnDgCY2X3A7UB2C5SIjI8ZdJyFFbfDmz8NVbpd\nQwaYfx287x449yI89W04sh1+ey88Pmj90w/+EK64JSeR0ilQ84EjA74/Crxx8E5mVgfUpb5tM7PM\njM+N/2LeTOB0RjLkXqjZQ80N4WYfJXdsb3YP9XxDuNkvLfef/04mjrloLDulU6CGqhDuVRucqwdi\nswS5me1wzgV5i3yo2UPNDeFmV+7cCzV7nHOnM5B4FFgw4Ptq4Hh6cURERCLpFKgngKVmtsTMSoD3\nAz/JTCwREZnoxj3E55y7aGZ/CPwMKAS+6ZzblbFk2ROb4cZxCDV7qLkh3OzKnXuhZo9tbnPuVZeN\nREREvAtvLT4REZkQVKBERCSW8rJAmdl0M3vYzPamXitH2HeKmR0zs68M2PZ6M3sutYTT35rlZgXF\nseQ2s0Vm9qSZPW1mu8zsvwx4ryG19NTTqTYrF7kzlD3O5/xaM3sslflZM/tPA967x8wODjjn1+Yi\nd4ayLzGz7ak///9Sk51ikTu130/NrMXMtg7aHutzntpvuOxxP+d3pfbZa2Z3Ddju52eLcy7vGvDX\nwN2pr+8G/mqEfb8EfBf4yoBtjwM3EN3r9a/AO+OSGygBJqW+rgAOAfNS3zcAtXE956Nkj/M5XwYs\nTX09DzgBTEt9fw9wR4zP+UjZvw+8P/X114CPxyV36r1bgLXA1kHbY33OR8ke23MOTAcOpF4rU19X\npt7z8rMl53/BOfrLaATmpr6eCzQOs9/rgfuAD5MqUKn9Xxiwz53A5jjlHrD/DOAw8ShQ484e0jlP\n7ffMgB/6Pn9Yjjs70S8Cp4Gi1PYbgJ/FLTewOmYFatzZ437OB/+/I1pu5M7U115+tuTlEB8w2zl3\nAiD1+qruqJkVAJuAzwx6az7RTcj9jqa25cKouQHMbIGZPUu01NRfOecG3iD9rVQX/M9yNUyWkk72\n2J/zfma2kqgnuH/A5v+dGj77oplNyl7UV0kn+wygxTl3MfV2bM/5MII454PE/ZwPtXzdwHw5/9kS\n3vOgUszs34A5Q7z1p2P8iE8A/+KcOzLoXI9pCafxykBunHNHgKvNbB7wIzN7wDl3CviAc+6YmU0G\nfgB8CPh2JnJD9rITwDlPfc5c4DvAXc65vtTmPwFOEv3grwf+GPiL8ad91TGzkn2YHzCxO+fDCOKc\nD/XRQ2yL0zkfKV9Wf7YMJ9gC5ZwbdsVCMztlZnOdcydS/zGbhtjtBuAmM/sE0fWQEjNrI7omVT1g\nv4wu4ZSB3AM/67iZ7QJuAh5wzh1LbW81s+8SrTifsX9EWcz+K2J+zs1sCvAg8Dnn3G8GfPaJ1Jdd\nZvYtIKNP1Mxi9tPANDMrSv1GH7tzPsJnx/6cDyPu5/wo0bBkv2qioT2y/bNlOPk6xPcToH8Gyl3A\njwfv4Jz7gHNuoXNuMdE/8G875+5O/eNvNbPrU79l/v5Qf95XbjOrNrNE6utK4Eag0cyKzGxmansx\nsAbYmZPUkXFnD+CclwD/TPRv5P5B781NvRrwHuJ3zofM7qILC48Ad4z057Nk1Nwjifs5H04A5/xn\nwNvMrDL1//NtwM+8/mzJ9UWvXDSisd6fA3tTr9NT22uBrw+x/4d55Sy+2tRfwH7gK6RW3IhDbqIH\nRD5LdLH7WaAutb0ceDK1bRdRT7AwTud8uOwBnPMPAj3A0wPatan3fgE8l8r+T0BFzM75SNkvI5o9\nuQ+4n9QMyzjkTn3/S6AZSBL9dv/2EM75KNnjfs4/msq2D/hIapu3ny1a6khERGIpX4f4REQkcCpQ\nIiISSypQIiISSypQIiISSypQIiISSypQIjliZu9IrQi9z8zu9p1HJO40zVwkB8ysENhDdC/YUeAJ\nooU4d3sNJhJj6kGJ5MZKYJ9z7oBzrptoFf3bPWcSiTUVKJHcGG2laBEZRAVKJDeyupK1SD5SgRLJ\njaPAggHfZ3Qla5F8pAIlkhtPAEvNbElqhfH3E60wLSLDCPZ5UCIhcc5dNLM/JHqkQSHwTefcLs+x\nRGJN08xFRCSWNMQnIiKxpAIlIiKxpAIlIiKxpAIlIiKxpAIlIiKxpAIlIiKxpAIlIiKx9P8BdhEY\nkO9IVb0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1128d2978>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.grid_density_plot(burn_in=1000, values=model.coefficients)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sampled variational approximation"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"model.method = 'variational'\n",
"model.resample()"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true,
"deletable": true,
"editable": true
},
"outputs": [],
"source": [
"sampler = util.AdaptiveMetropolisSampler(model.evaluate_log_likelihood, mode='reevaluate')"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"text/plain": [
"array([-0.11797807])"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sampler.sample(sampler.samples[-1] if len(sampler.samples) else model.coefficients, 2000, \n",
" callback=model.resample, tqdm=tqdm_notebook)"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING:root:function values may not be interpretable in the 'reevaluate' mode\n"
]
},
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x10837eb00>,\n",
" (<matplotlib.axes._subplots.AxesSubplot at 0x11305fcf8>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x1130cba90>))"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAakAAAEYCAYAAADmugmLAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmZlZsZykzMysWN8AOHLgsUTRdmoAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10837eb00>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.trace_plot(values=model.coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false,
"deletable": true,
"editable": true,
"scrolled": true
},
"outputs": [
{
"data": {
"text/plain": [
"(<matplotlib.figure.Figure at 0x113d2add8>,\n",
" <matplotlib.axes._subplots.AxesSubplot at 0x113d118d0>)"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEYCAYAAAAJeGK1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n3awSPYTdAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x113d2add8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sampler.grid_density_plot(burn_in=1000, values=model.coefficients)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEOCAYAAABIESrBAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x112ab33c8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_likelihoods(model, ref=['analytic_variational', 'analytic'])"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.3"
},
"widgets": {
"state": {
"11a3a5dcae9b4c0bbea4f9eed5383b5e": {
"views": [
{
"cell_index": 25
}
]
},
"7debe4616f704fc3805fe0371e280066": {
"views": [
{
"cell_index": 17
}
]
},
"8de3e335572d4b768fff1c8137b806f8": {
"views": [
{
"cell_index": 35
}
]
},
"9ff9382793ba4747a986fd351bc98b12": {
"views": [
{
"cell_index": 28
}
]
},
"ac569744021944e89c491f223cd818c4": {
"views": [
{
"cell_index": 41
}
]
},
"cfdf18234daf4d0bb9331ca781eddddd": {
"views": [
{
"cell_index": 11
}
]
},
"df1e60786c3c48e780f1f4e11ea05d0c": {
"views": [
{
"cell_index": 44
}
]
},
"f4b81903f7d94c6abcefca2fd29f80a6": {
"views": [
{
"cell_index": 21
}
]
}
},
"version": "1.2.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment