{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Dirichlet process mixtures for density estimation\n", "Author: [Austin Rochford](https://github.com/AustinRochford/)\n", "\n", "## Dirichlet processes\n", "\n", "The [Dirichlet process](https://en.wikipedia.org/wiki/Dirichlet_process) is a flexible probability distribution over the space of distributions. Most generally, a probability distribution, $P$, on a set $\\Omega$ is a [measure](https://en.wikipedia.org/wiki/Measure_(mathematics%29) that assigns measure one to the entire space ($P(\\Omega) = 1$). A Dirichlet process $P \\sim \\textrm{DP}(\\alpha, P_0)$ is a measure that has the property that, for every finite [disjoint](https://en.wikipedia.org/wiki/Disjoint_sets) partition $S_1, \\ldots, S_n$ of $\\Omega$,\n", "\n", "$$(P(S_1), \\ldots, P(S_n)) \\sim \\textrm{Dir}(\\alpha P_0(S_1), \\ldots, \\alpha P_0(S_n)).$$\n", "\n", "Here $P_0$ is the base probability measure on the space $\\Omega$. The precision parameter $\\alpha > 0$ controls how close samples from the Dirichlet process are to the base measure, $P_0$. As $\\alpha \\to \\infty$, samples from the Dirichlet process approach the base measure $P_0$.\n", "\n", "Dirichlet processes have several properties that make then quite suitable to [MCMC](https://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo) simulation.\n", "\n", "1. The posterior given [i.i.d.](https://en.wikipedia.org/wiki/Independent_and_identically_distributed_random_variables) observations $\\omega_1, \\ldots, \\omega_n$ from a Dirichlet process $P \\sim \\textrm{DP}(\\alpha, P_0)$ is also a Dirichlet process with\n", "\n", " $$P\\ |\\ \\omega_1, \\ldots, \\omega_n \\sim \\textrm{DP}\\left(\\alpha + n, \\frac{\\alpha}{\\alpha + n} P_0 + \\frac{1}{\\alpha + n} \\sum_{i = 1}^n \\delta_{\\omega_i}\\right),$$\n", " \n", " where $\\delta$ is the [Dirac delta measure](https://en.wikipedia.org/wiki/Dirac_delta_function)\n", " \n", " $$\\begin{align*}\n", " \\delta_{\\omega}(S)\n", " & = \\begin{cases}\n", " 1 & \\textrm{if } \\omega \\in S \\\\\n", " 0 & \\textrm{if } \\omega \\not \\in S\n", " \\end{cases}\n", " \\end{align*}.$$\n", "\n", "2. The posterior predictive distribution of a new observation is a compromise between the base measure and the observations,\n", "\n", " $$\\omega\\ |\\ \\omega_1, \\ldots, \\omega_n \\sim \\frac{\\alpha}{\\alpha + n} P_0 + \\frac{1}{\\alpha + n} \\sum_{i = 1}^n \\delta_{\\omega_i}.$$\n", "\n", " We see that the prior precision $\\alpha$ can naturally be interpreted as a prior sample size. The form of this posterior predictive distribution also lends itself to Gibbs sampling.\n", " \n", "2. Samples, $P \\sim \\textrm{DP}(\\alpha, P_0)$, from a Dirichlet process are discrete with probability one. That is, there are elements $\\omega_1, \\omega_2, \\ldots$ in $\\Omega$ and weights $w_1, w_2, \\ldots$ with $\\sum_{i = 1}^{\\infty} w_i = 1$ such that\n", "\n", " $$P = \\sum_{i = 1}^\\infty w_i \\delta_{\\omega_i}.$$\n", "\n", "3. The [stick-breaking process](https://en.wikipedia.org/wiki/Dirichlet_process#The_stick-breaking_process) gives an explicit construction of the weights $w_i$ and samples $\\omega_i$ above that is straightforward to sample from. If $\\beta_1, \\beta_2, \\ldots \\sim \\textrm{Beta}(1, \\alpha)$, then $w_i = \\beta_i \\prod_{j = 1}^{j - 1} (1 - \\beta_j)$. The relationship between this representation and stick breaking may be illustrated as follows:\n", " 1. Start with a stick of length one.\n", " 2. Break the stick into two portions, the first of proportion $w_1 = \\beta_1$ and the second of proportion $1 - w_1$.\n", " 3. Further break the second portion into two portions, the first of proportion $\\beta_2$ and the second of proportion $1 - \\beta_2$. The length of the first portion of this stick is $\\beta_2 (1 - \\beta_1)$; the length of the second portion is $(1 - \\beta_1) (1 - \\beta_2)$.\n", " 4. Continue breaking the second portion from the previous break in this manner forever. If $\\omega_1, \\omega_2, \\ldots \\sim P_0$, then\n", "\n", " $$P = \\sum_{i = 1}^\\infty w_i \\delta_{\\omega_i} \\sim \\textrm{DP}(\\alpha, P_0).$$\n", "\n", "We can use the stick-breaking process above to easily sample from a Dirichlet process in Python. For this example, $\\alpha = 2$ and the base distribution is $N(0, 1)$." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "from __future__ import division" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from matplotlib import pyplot as plt\n", "import numpy as np\n", "import pymc3 as pm\n", "import scipy as sp\n", "import seaborn as sns\n", "from statsmodels.datasets import get_rdataset\n", "from theano import tensor as tt" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "blue, *_ = sns.color_palette()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "SEED = 5132290 # from random.org\n", "\n", "np.random.seed(SEED)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "N = 20\n", "K = 30\n", "\n", "alpha = 2.\n", "P0 = sp.stats.norm" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We draw and plot samples from the stick-breaking process." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n", "w = np.empty_like(beta)\n", "w[:, 0] = beta[:, 0]\n", "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n", "\n", "omega = P0.rvs(size=(N, K))\n", "\n", "x_plot = np.linspace(-3, 3, 200)\n", "\n", "sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAecAAAF1CAYAAADSoyIcAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n", " label='DP sample CDFs');\n", "ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n", "ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n", "\n", "ax.set_title(r'$\\alpha = {}$'.format(alpha));\n", "ax.legend(loc=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As stated above, as $\\alpha \\to \\infty$, samples from the Dirichlet process converge to the base distribution." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA6UAAAF1CAYAAAAQgExAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\napkmMQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (l_ax, r_ax) = plt.subplots(ncols=2, sharex=True, sharey=True, figsize=(16, 6))\n", "\n", "K = 50\n", "alpha = 10.\n", "\n", "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n", "w = np.empty_like(beta)\n", "w[:, 0] = beta[:, 0]\n", "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n", "\n", "omega = P0.rvs(size=(N, K))\n", "\n", "sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)\n", "\n", "l_ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n", " label='DP sample CDFs');\n", "l_ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n", "l_ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n", "\n", "l_ax.set_title(r'$\\alpha = {}$'.format(alpha));\n", "l_ax.legend(loc=2);\n", "\n", "K = 200\n", "alpha = 50.\n", "\n", "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n", "w = np.empty_like(beta)\n", "w[:, 0] = beta[:, 0]\n", "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n", "\n", "omega = P0.rvs(size=(N, K))\n", "\n", "sample_cdfs = (w[..., np.newaxis] * np.less.outer(omega, x_plot)).sum(axis=1)\n", "\n", "r_ax.plot(x_plot, sample_cdfs[0], c='gray', alpha=0.75,\n", " label='DP sample CDFs');\n", "r_ax.plot(x_plot, sample_cdfs[1:].T, c='gray', alpha=0.75);\n", "r_ax.plot(x_plot, P0.cdf(x_plot), c='k', label='Base CDF');\n", "\n", "r_ax.set_title(r'$\\alpha = {}$'.format(alpha));\n", "r_ax.legend(loc=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dirichlet process mixtures\n", "\n", "For the task of density estimation, the (almost sure) discreteness of samples from the Dirichlet process is a significant drawback. This problem can be solved with another level of indirection by using Dirichlet process mixtures for density estimation. A Dirichlet process mixture uses component densities from a parametric family $\\mathcal{F} = \\{f_{\\theta}\\ |\\ \\theta \\in \\Theta\\}$ and represents the mixture weights as a Dirichlet process. If $P_0$ is a probability measure on the parameter space $\\Theta$, a Dirichlet process mixture is the hierarchical model\n", "\n", "$$\n", "\\begin{align*}\n", " x_i\\ |\\ \\theta_i\n", " & \\sim f_{\\theta_i} \\\\\n", " \\theta_1, \\ldots, \\theta_n\n", " & \\sim P \\\\\n", " P\n", " & \\sim \\textrm{DP}(\\alpha, P_0).\n", "\\end{align*}\n", "$$\n", "\n", "To illustrate this model, we simulate draws from a Dirichlet process mixture with $\\alpha = 2$, $\\theta \\sim N(0, 1)$, $x\\ |\\ \\theta \\sim N(\\theta, (0.3)^2)$." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "N = 5\n", "K = 30\n", "\n", "alpha = 2\n", "P0 = sp.stats.norm\n", "f = lambda x, theta: sp.stats.norm.pdf(x, theta, 0.3)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "beta = sp.stats.beta.rvs(1, alpha, size=(N, K))\n", "w = np.empty_like(beta)\n", "w[:, 0] = beta[:, 0]\n", "w[:, 1:] = beta[:, 1:] * (1 - beta[:, :-1]).cumprod(axis=1)\n", "\n", "theta = P0.rvs(size=(N, K))\n", "\n", "dpm_pdf_components = f(x_plot[np.newaxis, np.newaxis, :], theta[..., np.newaxis])\n", "dpm_pdfs = (w[..., np.newaxis] * dpm_pdf_components).sum(axis=1)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdMAAAFpCAYAAADHr8K+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.plot(x_plot, dpm_pdfs.T, c='gray');\n", "\n", "ax.set_yticklabels([]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now focus on a single mixture and decompose it into its individual (weighted) mixture components." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdMAAAFpCAYAAADHr8K+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlY1NX+B/D3dxhWEREEFUkFZEdEQHPPJTU1NVNL065L\nWVl2bbNdzaW0RaOyRW8lWWlWVm5ZWWoquaEiyq6IKwq4sS8zc35/+BsSZwYGmBlmeb+ep+e5fs+Z\ncz6DVz+e8z2LJIQAERERNZysqQMgIiKydEymREREjcRkSkRE1EhMpkRERI3EZEpERNRITKZERESN\nxGRKRETUSEymREREjcRkSkRE1EhMpkRERI0kr0/lVq1aiY4dOxopFCIiIvNy+PDhAiGEV1316pVM\nO3bsiMTExIZHRUREZEEkSTqjT706p3klSXpMkqRESZIS8/PzGx8ZERGRlakzmQohVgkhYoUQsV5e\ndY50iYiIbA4XIBERETVSvd6ZEpH1qaqqwvnz51FeXt7UoRA1GScnJ/j6+sLe3r5Bn2cyJbJx58+f\nR/PmzdGxY0dIktTU4RCZnBACV65cwfnz5+Hn59egNjjNS2TjysvL4enpyURKNkuSJHh6ejZqdobJ\nlIiYSMnmNfbPAJMpETU5Ozs7REVFITw8HF26dMHy5cuhUqkM2sdnn32GNWvWAADi4+Nx8eJFg7ZP\nto3vTImoyTk7OyMpKQkAkJeXh4ceegg3btzAggULDNbHE088Uf2/4+PjERERAR8fH4O1T7aNI1Mi\nMive3t5YtWoVVqxYASEElEol5syZg27duiEyMhIrV64EAOzatQv9+/fHuHHjEBISgkmTJkEIAQB4\n+eWXERYWhsjISLzwwgsAgDfeeAPvvfcefvzxRyQmJmLSpEmIiorC1q1bMWbMmOr+t2/fjvvvv9/0\nX5wsGkemRFTtmWeeqR4hGkpUVBTi4uLq9Rl/f3+oVCrk5eVh48aNaNGiBQ4dOoSKigr07t0bQ4YM\nAQAcPXoUKSkp8PHxQe/evZGQkICwsDD8/PPPSE9PhyRJuH79eo22x40bhxUrVuC9995DbGwshBB4\n/vnnkZ+fDy8vL6xevRrTpk0z2Pcn28CRKZGNE0KgvLwcpaWlTR1KDepR5h9//IE1a9YgKioKd955\nJ65cuYKsrCwAQPfu3eHr6wuZTIaoqCjk5OTAzc0NTk5OePTRR/HTTz/BxcWl1n4kScLDDz+Mb775\nBtevX8e+ffswbNgwo38/si4cmRLZsA0bNsDV1bU6kb744otm8R4xOzsbdnZ28Pb2hhACH330EYYO\nHVqjzq5du+Do6Fj9azs7OygUCsjlchw8eBB//fUXvvvuO6xYsQI7duyotb9p06Zh5MiRcHJywvjx\n4yGX869Gqh+OTIlsVGZmJqZOnQp7e3t06NABHh4euHjxYpOvcs3Pz8cTTzyBWbNmQZIkDB06FJ9+\n+imqqqqq4y4pKdH5+eLiYty4cQPDhw9HXFyc1mnr5s2bo6ioqPrXPj4+8PHxweLFizF16lSDfyey\nfvznF5ENKisrwwMPPABHR0d4eXnBy8sLrVq1giRJuHjxIlxdXeHm5mbSeKKiolBVVQW5XI6HH34Y\nzz33HADg0UcfRU5ODqKjoyGEgJeXF3755RedbRUVFWH06NEoLy+HEALvv/++Rp2pU6fiiSeegLOz\nM/bt2wdnZ2dMmjQJ+fn5CAsLM9r3JOslqd9L6CM2NlbwPlMiy/fWW2/htddew9atW+Hn54fQ0FAA\ngEqlwvHjx+Hs7IygoKAmjtK0Zs2aha5du+KRRx5p6lCoiaSlpVX/WVCTJOmwECK2rs9ympfIxiiV\nSnz22We4++67MXz48BplMpkM3t7eKCwsNLsFScYUExOD5ORkTJ48ualDIQvFaV4iG7N161acO3cO\nH3zwgdZyLy8v5Obm4tKlS/D39zdxdE3j8OHDTR0CWTiOTIlszCeffIJ27dph5MiRWsvlcjm8vb1x\n9epVVFRUmDg6IsvEZEpkQ06dOoXff/8dM2bMqHX7h5eXFwBoHHhARNoxmRLZkDVr1kAmk+HRRx+t\ntZ6joyOcnZ2ZTIn0xGRKZEO2bt2KXr16oV27dnXWdXd3R1FRERQKhQkiI7JsTKZENiI3NxeHDx/W\nWMGri7u7OwDgxo0bxgwLwL9H+qkpFAp4eXnh3nvvBQBs2rQJS5curbUNXqtWP3FxcfVesR0XF1d9\njV1D6fN7uWvXrurfe20x1DfuW9vbsmUL5s+fX6/P64PJlMhG/PbbbwCgdzJ1cXGBvb29SaZ6mzVr\nhhMnTqCsrAzAzZtbbh09jxo1Ci+//HKtbTQkmdryqLu+SUmhUODLL7/EQw891Kh+9fm9rE1Dkumt\nRowYgU2bNhl86xeTKZGN+PXXX9GuXTtERkbqVV+SJLi7u+PGjRsGv6hbm2HDhmHr1q0AgHXr1mHi\nxInVZfHx8Zg1axYAYPTo0dWjo5UrV2LSpEka16qVlZWhY8eOKCgoAAAkJiaif//+AG5exfbYY49h\nyJAh+M9//qPzirfbrVmzBpGRkejSpUv1KPrMmTMYNGgQIiMjMWjQIJw9exbAzROWZs6ciQEDBsDf\n3x9///03pk+fjtDQ0BrHFbq6uuL5559HdHQ0Bg0ahPz8fABAUlISevTogcjISIwZMwbXrl0DAPTv\n3x8vvfQSunfvjqCgIOzZswcA6n1N3YcffoiLFy9iwIABGDBgAJRKJaZOnYqIiAh07txZ66lRO3bs\nQHR0NORyOfLy8hATEwMAOHbsGCRJqv7uAQEBKC0tRX5+PsaOHYtu3bqhW7duSEhI0Pi9PHXqFHr0\n6IFu3bph3rx5cHV1re6vuLi4zriBmxch9OzZE9HR0Rg/fjyKi4sB3PzHY0hICPr06YOffvqpul1J\nktC/f39s2bJF6+9zgwkh9P4vJiZGEJHlqaysFG5ubmLGjBkaZampqTV+fdddd1X/17t3bxEdHS0W\nLVqktVz937vvvquzXB/NmjUTx44dE2PHjhVlZWWiS5cuYufOnWLEiBFCCCFWr14tnnrqKSGEEJcu\nXRIBAQFi9+7dIjAwUFy5cqW630OHDlW32aFDB5Gfny+EEOLQoUPVscyfP19ER0eL0tJSIYQQK1eu\nrP5+5eXlIiYmRmRnZ9eI78SJEyIoKKi6PXWf9957r4iPjxdCCPHFF1+I0aNHCyGEmDJlinjwwQeF\nSqUSv/zyi2jevLlITk4WSqVSREdHi6NHjwohhAAgvvnmGyGEEAsWLKj+jp07dxa7du0SQggxd+5c\nMXv27Orv+NxzzwkhhNi6dasYNGhQrd9h586dws3NTZw7d04olUrRo0cPsWfPHo2fT2Jiorj77rur\nv++1a9c0fo/mzZsnPvzww+pfh4WFiRs3boiPPvpIxMbGim+++Ubk5OSIHj16CCGEmDhxYnVfZ86c\nESEhIRq/lyNGjBBr164VQgjx6aefimbNmgkhhN5x5+fni759+4ri4mIhhBBLly4VCxYsEGVlZcLX\n11dkZmYKlUolxo8fX/3/JSGE+Oabb8SsWbM0vuPtfxb+//coUeiRHzkyJbIBCQkJKCws1HuKV83O\nzg4ATLLfNDIyEjk5OVi3bl2tcbZu3RoLFy7EgAEDsGzZMnh4eNS7r1GjRsHZ2RlA7Ve8qe3YsQPj\nxo1Dq1atAKC6z3379lVPez788MPYu3dv9WdGjhwJSZLQuXNntG7dGp07d4ZMJkN4eDhycnIA3Dxx\n6sEHHwQATJ48GXv37sWNGzdw/fp13HXXXQCAKVOmYPfu3dXtqi8uj4mJqW6nvtfU3c7f3x/Z2dl4\n+umn8dtvv2k9lzk3N7d6yxQA9OrVCwkJCdi9ezdeffVV7N69G3v27EHfvn0BAH/++SdmzZqFqKgo\njBo1CoWFhTUuF1D//MaPHw8AGtPH+sS9f/9+pKamonfv3oiKisJXX32FM2fOID09HX5+fggMDIQk\nSRonW3l7exv8/TpPQCKyAb///jvkcjkGDRpUZ91du3bV+HVqamp1UtVWXtfn62PUqFF44YUXsGvX\nLly5ckVnvePHj8PT07PWvxDlcnn19HR5eXmNsmbNmlX/b6HjirdbCSEgSVKd8d9aR309nEwmq3FV\nnEwm0/muVp8+1G2pr5yr7Tvouqbudi1btsSxY8fw+++/4+OPP8b333+PL7/8skYdZ2fnGj/Hvn37\nYs+ePThz5gxGjx6Nt99+G5IkVS/0UalU1ZcINIQ+cQshMHjwYKxbt67G86SkpFp/luXl5Q2OSxeO\nTIlswN69exETE4PmzZvX+7Ourq4oKSkxyXvT6dOnY968eejcubPOOgcPHsS2bdtw9OhRvPfeezh9\n+jQAzWvVOnbsWH1M4IYNG3S2p88Vb4MGDcL3339fneCvXr0K4Obo7LvvvgMAfPvtt+jTp0+9vq9K\npcKPP/4IAFi7di369OmDFi1aoGXLltXvQ7/++uvqUWpjvsPtbv15FRQUQKVSYezYsVi0aBGOHDmi\nUT80NBQnT56s/nW/fv3wzTffIDAwEDKZDB4eHvj111/Ru3dvAMCQIUOwYsWK6vrarsLr0aNH9e+N\n+udYl1vj7tGjBxISEqrjKi0tRWZmJkJCQnD69GmcOnUKADSSbWZmJiIiIvTqT19MpkRWrqKiAocO\nHar+S66+XF1doVKpqlfaGpOvry9mz56ts7yiogIzZszAl19+CR8fHyxbtgzTp0+HEKL6WjX1AqT5\n8+dj9uzZ6Nu3b42R9e0effRRhIWFITo6GhEREXj88cc1RkHh4eF47bXXcNddd6FLly7V18N9+OGH\nWL16NSIjI/H111/rPO9Yl2bNmiElJQUxMTHYsWMH5s2bBwD46quvMGfOHERGRiIpKan6eWO+w+0e\ne+wxDBs2DAMGDMCFCxfQv39/REVFYerUqViyZIlG/WHDhtWYbu7YsSOAm0kVAPr06QN3d3e0bNkS\nwM2fTWJiIiIjIxEWFobPPvtMo824uDgsX74c3bt3R25uLlq0aFFrzLfH7eXlhfj4eEycOBGRkZHo\n0aMH0tPT4eTkhFWrVmHEiBHo06cPOnToUKONnTt3YsSIEXX2VS/6vFgVXIBEZLH++ecfAUBs2LBB\na7m2RRe3qqioEIcOHRKXLl0yRng2Tb3gxlLcd999IjMz02DtlZSUCJVKJYQQYt26dWLUqFEGa1uX\nS5cuiYEDB2ota8wCJL4zJbJy6i0JDR2ZOjg4wNHREcXFxWjdurUhQyMLs3TpUuTm5iIwMNAg7R0+\nfBizZs2CEALu7u4a72mN4ezZs1i2bJnB22UyJbJyCQkJCAgIaFQibNasGYqKivReiEP6Ue+JtBTB\nwcEIDg42WHt9+/bFsWPHDNaePrp162aUdvnOlMiKCSGQkJDQ4FGpWvPmzVFVVcUr2Yh0YDIlsmIn\nT55Efn5+ncn05qsh3dRbSepaIUpkqer6M1AXJlMiK6bP+1InJydcuXKl1r9MnJ2dIUmSwc8zJTIH\nQghcuXIFTk5ODW6D70yJrNj+/fvRokULhIaG6qzj6+uL8+fPV58Lq8uNGzdQVFRkce/5iPTh5OQE\nX1/fBn+eyZTIih0+fBgxMTGQyXRPQtnb28PPz6/OtuLi4vD999/j6tWrXIREdBtO8xJZqaqqKiQn\nJyM6Otog7UVHR+P69es4c+aMQdojsiZMpkRWKjU1FZWVlQZLpl27dgUAHD161CDtEVkTJlMiK6U+\nX9VQybRz586ws7PTem4rka1jMiWyUocPH4arq6vBTqtxdnZGSEgIR6ZEWjCZElmpI0eOoGvXrrUu\nPqqvrl27MpkSacFkSmSFlEolkpKSDDbFqxYdHY2LFy/i8uXLBm2XyNIxmRJZoYyMDJSVlRk8mXIR\nEpF2TKZEVkh9KXZMTIxB242MjAQAnDhxwqDtElk6JlMiK3TkyBE4Ozsb9IYPAPDw8ECbNm2QkpJi\n0HaJLB2TKZEVSk5ORkREBORywx9yFhYWhtTUVIO3S2TJmEyJrNDx48fRuXPnOuupVCpkZWXVq+3w\n8HCkpqY2+pYNImvCZEpkZS5fvoz8/Pw6k+nVq1fRsWNHBAUFoVWrVli6dKle7YeHh6O4uBhnz541\nRLhEVoHJlMjKHD9+HADqTKbdu3fHuXPn4O/vj2vXruGVV17BkiVL6mw/PDwcAPjelOgWTKZEVkbf\nZPrll1/ilVdewalTp5Cfn4/w8PA6LxEHmEyJtOEVbERW5vjx4/D29oa3t7fW8qtXr8Ld3R39+vVD\nv379ANxcpavvdpeWLVuibdu2TKZEt+DIlMjK1LX4aMiQIXB1ddV6yffu3bvh6+uLjIyMWvvgil6i\nmphMiayIUqlESkqKzmSalZWFw4cPo02bNnB1ddUoz83NxYULF/DGG2/U2o96Ra9KpTJE2EQWj8mU\nyIpkZ2ejrKxMZzL973//CwBYtmyZ1vLx48fDwcEB27Ztq7Wf8PBwlJSUcEUv0f9jMiWyInUtPtqz\nZw9cXFwwZswYreUymQy9e/fGjRs3kJiYqLMfLkIiqonJlMiKHD9+HJIkVSe7WyUnJ6OkpAQ9evSo\ntY05c+YAAN58802ddUJDQwEA6enpjYiWyHpwNS+RFTlx4gT8/f3h4uKiUdaqVStMnToVkydPrrWN\nYcOGwcPDA1VVVTrreHh4oFWrVnUuVCKyFUymRFYkPT0dYWFhWst8fHywevVqvdq5cuVKnXWCg4OZ\nTIn+H6d5iayEUqlEZmYmQkJCNMquXr2KCRMm1Osdp0qlQl5ens7yoKAgZGZmNihWImvDZEpkJU6f\nPo3KykqtyTQuLg7r16/Hpk2b9G7P1dW11verwcHBuHTpEgoLCxsUL5E1qTOZSpL0mCRJiZIkJebn\n55siJiJqAPViIPXioFv98ssvAICnnnpK7/Y8PT1x9uxZnXtJ1XelcqqXSI9kKoRYJYSIFULEenl5\nmSImImoAdTLVdiH4yZMn4e7uDjc3N73b69mzJ5RKJfbu3au1PCgoCACTKRHAaV4iq5GWlgZvb294\neHjUeH7p0iWUlZUhIiKiXu1NnDgRALBmzRqt5QEBAZDJZHxvSgQmUyKrkZ6ernWKd/369QCAwYMH\n16u9kSNHQpIk/P3331rLHR0d0bFjR45MicCtMURWQQiBtLQ0PPDAAxplTz/9NLp3747AwMB6tSmX\nyzF27Fj4+fnprMPtMUQ3MZkSWYH8/Hxcu3ZN68hUJpOhZ8+eDWr3hx9+qLU8ODgYf//9N1QqFWQy\nTnSR7eL/+4msgHrx0e3bYhQKBYKCgrB8+fIGtatQKPDrr78iISFBa3lQUBBKS0tx4cKFBrVPZC2Y\nTImsQFpaGgDNZLp161ZkZWVVl9dXeXk5RowYgWeffVZrObfHEN3EZEpkBdLT0+Hi4oI77rijxvMN\nGzYAgNZ3qfpwdXWFi4sLTp48qbWcyZToJiZTIiuQnp6O4OBgjfeWBw8ehCRJGDRoUIPbbt++Pa5f\nv6718Ia2bdvCyckJp06danD7RNaAyZTICqSlpWk9RvDcuXNwd3dv1OKg6OhoCCG0Ht4gk8ng7+/P\nZEo2j8mUyMKVlpbizJkzGit5VSoVFAoF/P39G9X+0KFDAQAbN27UWt6pUycmU7J53BpDZOHUJxDd\nPjKVyWSoqKiAQqFoVPv33XcfZs6ciYcfflhreUBAALZv3w4hBCRJalRfRJaKyZTIwulayasmlzfu\nj7mbmxs++eQTneUBAQEoKytDbm4ufHx8GtUXkaXiNC+RhUtPT4dMJtM44Wj48OFo3769zltf6mPX\nrl2YNm2a1rYCAgIAgFO9ZNOYTIksXHp6Ovz8/ODk5FTj+YEDB1BQUGCQk4k+++wzxMfH48CBAxpl\n6mSqa/sMkS1gMiWycNpW8qpUKly7dg2+vr4G6ePuu+8GAGzevFmjrEOHDrCzs+PIlGwakymRBVMq\nlcjMzNRYyZucnAwhBCIjIw3Sz/DhwwEAhw4d0ihzcHBA+/btmUzJpjGZElmwM2fOoKKiQmNkumnT\nJgBA//79DdKPj48P7OzskJWVpbU8ICCAyZRsGpMpkQXTtZK3oqICjo6OGDVqlMH68vDwwOXLl7WW\nMZmSrWMyJbJgum6LefPNN1FeXo727dsbrK/4+Hj8+eefWssCAgJw9epVXLt2zWD9EVkS7jMlsmDp\n6enw8vKCp6en0ftSvzfVplOnTgBubo+JjY01eixE5oYjUyILlpaWprH4qLKyEnK5vME3xehy8eJF\njB49Gt98841GGfeakq1jMiWyYOnp6RpTvHv37oVSqYSLi4tB+3JwcMCmTZuwevVqjTL1+b9MpmSr\nmEyJLFRBQQGuXLmikUx37doFAOjVq5dB+2vVqhXkcrnWFb2urq5o3bo1kynZLCZTIgulXsl7+zRv\nYmIigH9vezEkT09P5OXlaS3jil6yZUymRBZK10rerKwsyGQydOjQweB9+vn5oaKiAqWlpRplnTp1\n4pGCZLOYTIksVHp6OpydnTW2v3Tq1MlgJx/dLioqCsC/U8m3CggIwIULF1BWVmaUvonMGZMpkYVK\nS0tDcHCwxkH227Ztw9GjR43S5/z585Gdna11m4x6Re/p06eN0jeROWMyJbJQ2lbyVlZWorKy0mh9\ntmnTBn5+flrLuD2GbBmTKZEFKisrQ05OjkYyXb58ORwdHbVuXzGUMWPGaN3DymRKtownIBFZoMzM\nTAghNFbyqm916datm9H6/vvvv7WOflu1agU3NzcmU7JJHJkSWSBdK3nT09MhSRLCwsKM1rePjw9K\nS0uhUqlqPJckCQEBAVzRSzaJyZTIAqWlpUGSJAQGBtZ4fvHiRTRr1kxjUZIhBQUFQQhRvc/1Vtxr\nSraKyZTIAqWnp8PPzw/Ozs41nhcVFcHb29uofUdHRwO4Od17u4CAAOTk5ECpVBo1BiJzw2RKZIG0\nreRVqVTo2rUrRo8ebdS++/TpAwDIyMjQKAsICEBVVRXOnTtn1BiIzA0XIBFZGKVSiYyMDAwaNKjG\nc5lMVr0AyZj69OmDoqIiuLq6apTduqK3Y8eORo+FyFxwZEpkYc6ePYvy8nKNlbznz59HQUGB0fuX\ny+VaEynw772mXIREtobJlMjC6FrJ+8gjj8DLy0vnQfSGNHXqVAQHB2s8b9euHRwcHLgIiWwOkymR\nhdF1W0x2djZkMpnRFyABNxN6ZmYmysvLazy3s7NDx44deaQg2RwmUyILk56ejlatWsHT07PG88uX\nL6N58+YmiUG9jzUhIUGjzN/fH9nZ2SaJg8hcMJkSWRhtK3kBoLi4GG3atDFJDOoTlvbs2aNR5u/v\nz5Ep2RwmUyILk5aWpjHFe/bsWQgh4O/vb5IY+vfvDwA4duyYRpmfnx+uXbuGa9eumSQWInPAZEpk\nQQoKClBQUKAxMhVC4O6778aECRNMEkdwcDDs7Ow03pkCqE7oHJ2SLeE+UyILoj4o4fZk2qFDB2zf\nvt1kcchkMigUCq1l6mSanZ1dfVoSkbXjyJTIguhayXvgwAGcOHGiKULSoL7vlIuQyJYwmRJZkPT0\ndDg5OaF9+/Y1nk+YMAFRUVEmjeXpp59GixYtNEaoLVq0gKenJ5Mp2RQmUyILkp6ejqCgINjZ2dV4\nnp+fDzc3N5PGcuXKFRQWFuLw4cMaZVzRS7aGyZTIgqSmpmpM8QJAaWkpWrdubdJYIiMjAQD79u3T\nKONeU7I1TKZEFqKkpAQ5OTkaF3+fP38eQojqd5Wm0qNHDwBAUlKSRpmfnx+vYiObwmRKZCEyMjIg\nhEB4eHiN5+qDE25/bmzqZJqZmalR5u/vD4VCgfPnz5s0JqKmwmRKZCFSU1MBQGNkGhoainHjxmHc\nuHEmjcfJyQktWrSAk5OTRtmt22OIbAH3mRJZiNTUVMjl8uprztSioqLwww8/NElM169f1/r81mQ6\nYMAAU4ZE1CQ4MiWyECkpKQgKCoK9vX2N5xs2bDDpgQ36uOOOO2BnZ8cVvWQzmEyJLERqaqrGFC8A\nzJgxA/fff38TRAS8+OKLcHR01EiacrkcHTp04DQv2QwmUyILUFZWhuzsbK3JtLCwEK1atWqCqABJ\nklBZWan19hg/Pz8mU7IZTKZEFiAzMxMqlUpjxW5xcTGUSqXGiUimor6KTdfBDUymZCuYTIksgK6V\nvOrLuYODg00eEwD06dMHwM2TmW7n7++P/Px8FBUVmTosIpNjMiWyAKmpqbCzs0NgYGCN5wcOHAAA\ndO3atSnCQps2bSCTyZCTk6NRxqvYyJZwawyRBUhJSUGnTp3g6OhY4/moUaOQm5uLESNGNFFkN9+N\ntmnTRuP5rdtj1EcPElkrJlMiC6BrJW9UVBQ+/fTTJojoXydPntT6nCNTsiWc5iUycxUVFTh58qTW\nZBoXF4fvv/++CaKqW8uWLdGiRQsuQiKbUGcylSTpMUmSEiVJSszPzzdFTER0i6ysLCiVSq1n7778\n8suYPXt2E0T1r8WLF8POzg7btm2r8VySJG6PIZtRZzIVQqwSQsQKIWK9vLxMERMR3ULXSl6VSoWK\nigq0bdu2KcKq5unpCZVKhYMHD2qUcXsM2QpO8xKZuZSUFMhkMgQFBdV4rk6y6neTTaV3794AgOPH\nj2uUqS8JV6lUpg6LyKSYTInMXGpqKvz9/eHs7Fzj+f79+wFojlhNLSIiAgBw6tQpjTJ/f39UVFQg\nNzfX1GERmRSTKZGZ07WS99ixYwCAmJgYU4dUg0wmg5OTEy5evKhRxhW9ZCu4NYbIjFVVVSEzMxOj\nRo3SKHv88cfRsmVL3HXXXU0QWU2xsbGQJEnj+a17TdWnJRFZIyZTIjN28uRJKBQKrSt5IyIiqqdY\nm5q2g+4BoEOHDpAkiYuQyOpxmpfIjKWkpADQ/l70lVdewapVq0wdkk4qlQoKhaLGMwcHB/j6+jKZ\nktVjMiUyY6mpqZAkCSEhIRpl7733Ht56660miErTJ598Ajs7O62nMXF7DNkCJlMiM5aamoqOHTvC\nxcWlxvPy8nIoFAr4+vo2UWQ1qW+tOXr0qEYZkynZAiZTIjOmayWv+oCETp06mTokrXr27Ang5mlN\nt/P390fq84xPAAAgAElEQVRubi7KyspMHRaRyTCZEpmpyspKpKena11kdOjQIQBA586dTR2WVi4u\nLrCzs8P58+c1ytQrerVd00ZkLZhMicxUeno6qqqq0KVLF42y5ORkAEC3bt1MHZZOzZs3x5UrVzSe\n37o9hshacWsMkZlSJ0xtd4G+8cYbuPPOO9G9e3dTh6XT3XffzWRKNovJlMhMJScnw8HBQeNMXuDm\nhdxPPvlkE0Sl2w8//KD1uZeXF1xcXJhMyapxmpfITCUnJyM8PBz29vYaZdOnT8eyZcuaIKraXb9+\nHcXFxTWeSZLEFb1k9ZhMiczUsWPHtE7xAkB8fLxZHdgAAKtXr0bLli21Jnn17TFE1orJlMgM5eXl\n4dKlS1qTaV5eHoQQ6NChQxNEppv6wP0TJ05olKlHpkIIU4dFZBJMpkRmSH03qLaVvPv27QPw70EJ\n5kK9hUfbCNTf3x8lJSXIz883dVhEJsFkSmSGalvJm5iYCEB7om1KMpkMDg4OtV7FxvemZK2YTInM\n0LFjx9CmTRt4eXlplKWmpgL499Qhc9KiRQtcu3ZN4zmTKVk7bo0hMkPJyck6R57/+9//MHnyZISG\nhpo4qrqNHTsW586d03jesWNHAEymZL2YTInMTGVlJVJSUnD33XdrLffw8MCYMWNMHJV+tN0aAwDO\nzs5o27YtV/SS1eI0L5GZSUlJQWVlZfXq2NuNHDkSCxcuNHFU+lGpVDhx4gTy8vI0yrjXlKwZkymR\nmTly5AgAIDo6WqNMpVJhy5Yt+Pnnn00dll5+/PFHdO7cGW+//bZGGZMpWTMmUyIzc+TIEbi5uSEg\nIECjTH3FmZ+fn6nD0kuvXr0AAGlpaRpl/v7+OHfuHCorK00dFpHRMZkSmZnDhw+ja9eukMk0/3ju\n378fAMxy8REA+Pr6QpIknDlzRqPM398fQgitZUSWjsmUyIwoFAocO3ZM5/tS9RRwbGysKcOqF2dn\nZ1y+fFnjObfHkDVjMiUyI2lpaSgvL9f6vhQAMjMzAZjnHlM1T09PFBYWajxXT00zmZI14tYYIjNS\n2+IjANi8eTOSk5PRpk0bU4ZVL1OmTMHJkyc1nrdt2xaOjo7cHkNWicmUyIwcOXIEzZo103qHKQDI\n5XKdidZcLFq0SOtzmUwGPz8/jkzJKnGal8iMHD58GFFRUbCzs9Na3rNnT7z66qsmjqp+ysvLsW3b\nNpw6dUqjjNtjyFoxmRKZCaVSiaSkJJ0jz8rKSuzfvx+7du0ybWD1lJCQgOHDh2PJkiUaZf7+/jh1\n6hSvYiOrw2RKZCZSUlJQUlKCO++8U2v5oUOHAACdOnUyZVj1po5fvSf2Vv7+/igsLNR6GD6RJWMy\nJTIT6j2kPXr00Fp+4MABAEDnzp1NFlNDuLq6ws7ODufPn9co44peslZMpkRm4sCBA2jVqlX1fszb\nqS8M79atmynDahBXV1etF4GrvxtX9JK1YTIlMhP79+/HnXfeCUmStJZfuHABANC9e3dThtUgXl5e\nKCkp0XjOkSlZK26NITIDN27cQFpaGiZMmKCzzh9//IG8vDy4uLiYMLKGmTVrltbzeZs3bw4vLy+t\nK32JLBmTKZEZOHToEIQQOt+Xqnl7e5soosaZPXu2zrKAgAAmU7I6nOYlMgPqxUW1vQ8NDg7G888/\nb6qQGqW4uBhffPFF9YlOtwoMDNS60pfIkjGZEpmB/fv3IzQ0FO7u7lrLCwoKkJmZiWPHjpk4sobJ\nzMzEo48+infeeUejLDAwEOfOnUNZWVkTREZkHEymRE1MCIEDBw7o3F8KAP/88w8A6Dxm0NxERkYC\ngNbp3MDAQJ1lRJaKyZSoiWVlZSE/P7/6Ym1t1NOlUVFRpgqrUeRyORwcHHDx4kWNMnUy5VQvWRMm\nU6Imtnv3bgBAv379dNZJSUkBoPtAB3PUokULrScdMZmSNWIyJWpiu3fvhre3d61TuDdu3IAkSYiI\niDBhZI3TunVrlJeXazx3c3ODt7d39d2sRNaAW2OImtju3bvRr18/nYc1ADf3mCoUCshklvPv35de\negmpqalQqVQacXNFL1kbJlOiJnTmzBmcOXNGry0vcrll/XGdPHmyzrLAwED8/vvvJoyGyLgs55+5\nRFZoz549AGp/X6pSqdC6detaD0IwR4WFhViyZInWK+MCAwORm5uL4uJi0wdGZARMpkRNaPfu3XB3\nd6/1XWhGRgby8vJw7tw5E0bWeNeuXcOrr76K9957T6NMvQjp5MmTpg6LyCiYTIma0O7du9GnTx/Y\n2dnprJOQkAAACA8PN1VYBtGhQwdIkoScnByNMq7oJWvDZErURC5evIiMjIxap3gB4OjRowAs4+q1\n2zk5OeHy5csaz9UXnDOZkrVgMiVqItu3bwcADB48uNZ66enpAIA+ffoYPSZD8/DwQGFhocZzV1dX\ntG3blsmUrAaTKVET2b59O7y9vauP3tNFCAEnJyd4eHiYKDLDadu2LSorK6FQKDTKuD2GrIllrbUn\nshIqlQrbt2/H4MGD69w7umPHDhNFZXgLFy7EyZMnoVKpNMoCAwOxefPmJoiKyPCYTImaQHJyMvLy\n8jBkyJCmDsWohg0bprMsMDAQeXl5KCwshJubmwmjIjI8TvMSNQF935devXoVzZo1w5w5c0wRlsEV\nFhbi2Wefxc8//6xRxhW9ZE2YTImawB9//IGIiAi0bdu21np79+5FaWkpSktLTRSZYalUKsTFxeHD\nDz/UKGMyJWvCZEpkYqWlpdizZ49eU7yHDh0CAERHRxs7LKNwd3eHTCbD2bNnNcoCAgIAMJmSdWAy\nJTKx7du3o6KiAsOHD6+z7okTJwCg1rtOzV3z5s2Rn5+v8dzFxQW+vr5MpmQVmEyJTGzjxo1wd3ev\n87AGAMjOzgYABAcHGzsso2ndujVKSkq0lnF7DFkLJlMiE1IqldiyZQuGDx8Oe3v7Ouu7ubmhTZs2\nFnX12u38/PygUqlw8eJFjTImU7IWdf4JlSTpMUmSEiVJStQ2VUNE+tu3bx/y8/MxevRoverv2bMH\nubm5Ro7KuBYvXowffvhB66ETgYGBuHLlCq5du9YEkREZTp3JVAixSggRK4SI9fLyMkVMRFZr48aN\nsLe3xz333NPUoZhMbGwsxo0bBycnJ40yrugla2G5c0dEFkYIgY0bN2LgwIF6HVJw6NAh2Nvb4403\n3jB+cEakUqkwefJkLF++XKOMyZSsBZMpkYmkpKQgKytL7ynehIQEKBQKuLi4GDky45LJZFi7di1W\nrVqlUebv7w9JkphMyeIxmRKZyLp162BnZ4exY8fqVf/YsWMAgO7duxszLJNwdXXVehWbk5MT2rdv\nz2RKFo/JlMgEhBD47rvvMGjQIHh7e+v1mczMTABAjx49jBmaSXh5eaGoqEhrWVBQEDIyMkwcEZFh\nMZkSmcDBgweRnZ2Nhx56SO/PnDt3DnK5XOvCHUvTsWNHKJVKXL16VaMsJCQEGRkZEEI0QWREhsFk\nSmQCa9euhaOjI8aMGaP3Z+644w6EhoYaMSrTCQsLA3DzrOHbhYaGori4GBcuXDB1WEQGwyvYiIxM\nqVRi/fr1GDFiRL2uGktISDBiVKb10ksv4aGHHkK3bt00ykJCQgAAaWlp8PX1NXVoRAbBkSmRkf3x\nxx+4fPlyvaZ4rY2vry969uwJuVzz3+/q0Xd6erqpwyIyGCZTIiP73//+By8vL4wcOVLvz3z77beQ\nyWRa92ZaqgkTJuCpp57SeN66dWu0aNECaWlpTRAVkWEwmRIZ0aVLl7B582ZMmTIFDg4Oen/u8OHD\nEEJY1bTn5s2bsX79eo3nkiQhNDSUI1OyaEymREb01VdfQaFQ4NFHH63X51JTUwEAffr0MUZYTaJV\nq1a4ceOG1rKQkBCOTMmiMZkSGYkQAp9//jn69u1b7yvUcnJyIEkSfHx8jBSd6bVv3x4KhQKlpaUa\nZaGhobh06RKuX7/eBJERNR6TKZGR/PXXXzh58iRmzJhR78/m5eWhWbNmRoiq6ahX7e7bt09nGad6\nyVIxmRIZyQcffAAvLy+MHz++3p8NCwtD7969jRBV0+natSuAmwf4344resnScZ8pkRFkZWVh69at\nmDt3boNOMNJ2uIGl+89//oNRo0ZpXVTl5+cHBwcHvjcli8VkSmQEH330EeRyOWbOnFnvz5aWlkIu\nl9dr9a8lcHV1haurq9YyuVyOwMBAJlOyWJzmJTKwGzduYPXq1ZgwYQLatGlT788vWrQIjo6O+PHH\nH40QXdN64IEHMGzYMK1loaGhTKZksZhMiQzs008/RXFxMZ555pkGfT45ORkAtB69Z+kSEhKwY8cO\nrWURERE4deqU1tW+ROaOyZTIgEpLS7F8+XIMHToU0dHRDWojOzsbkiShQ4cOBo6u6fn6+qKyshKV\nlZUaZeHh4RBCcBESWSQmUyID+vLLL5Gfn49XX321wW3k5ubqfLdo6dT7bbWt6I2IiAAAnDhxwqQx\nERkCkymRgVRWVuKdd95B79690bdv3wa3U1RUpPcF4pamS5cuAIB//vlHo6xTp05wcHBgMiWLxNW8\nRAby1Vdf4dy5c/jss88gSVKD2lCpVOjWrVujkrE569WrFwDg9OnTGmVyuRwhISFISUkxdVhEjSbV\n53b72NhYkZiYaMRwiCxTWVkZOnXqhA4dOiAhIaHBydTaqVQqVFZW6tx7O2nSJOzduxdnzpwxcWRE\n2kmSdFgIEVtXPU7zEhnAihUrcPHiRSxdurRRifTs2bO4dOmSASMzLzKZrNZDLMLDw3H27FkUFhaa\nMCqixmMyJWqk69evY8mSJRg2bBj69evXqLYeeeQRtG3bFgUFBQaKzvxMmTIFQUFBWsvUi5DUt+YQ\nWQomU6JGevfdd3Ht2jW89dZbjW7r9OnTkMlkaNWqlQEiM08ZGRnIyspCeXm5Rll4eDgA8L0pWRwm\nU6JGyM3NRVxcHCZOnIioqKhGt3f58mW4ubkZIDLzFRYWBgDYs2ePRpmfnx+cnZ25opcsDpMpUSMs\nXrwYlZWVWLhwoUHaKykpadARhJakR48eALQnU5lMhrCwMCZTsjhMpkQNdOrUKaxatQozZsxAp06d\nGt1eRkYGhBA63ydai0GDBgEAjh49qrW8c+fOOH78uClDImo0JlOiBpo3bx7s7e0xd+5cg7Qnl8sx\ndOhQPPTQQwZpz1wFBATA3t5e6ztTAIiKisLly5etelUzWR8e2kDUAElJSVi7di1eeeUVtG3b1iBt\nBgQE4LfffjNIW+ZO29m8aupTko4dO2b1U95kPTgyJWqA1157DS1btsSLL75osDZ37NiBpKQkg7Vn\nqW5NpkSWgsmUqJ52796NX3/9FS+//DLc3d0N1u7EiRPRs2dPg7VnzhYsWABXV1etxwq2bNkS7du3\n5z8syKIwmRLVgxACr7zyCnx8fDBr1iyDtn316lV4eXkZtE1zpVAoUFJSgr/++ktreZcuXTgyJYvC\nZEpUD1u2bME///yD+fPnw8XFxWDtXr9+HQqFAv7+/gZr05z16dMHAHDgwAGt5V26dEF6ejrKyspM\nGRZRgzGZEulJqVTi1VdfRWBgIKZNm2bQttUjtMjISIO2a67Ut+LoOukoKioKKpWKJyGRxWAyJdLT\n2rVrceLECSxevBj29vYGbTshIQEA0Lt3b4O2a65cXFzg4OCAnJwcreVchESWhltjiPRQUVGBefPm\nITo6GuPGjTN4+6NGjUJubi4GDx5s8LbNVadOnaBSqbSW+fv7w9XVlYuQyGIwmRLpYdWqVcjJycHK\nlSshkxl+Qqd///7o37+/wds1Z7VN4cpkMkRGRjKZksXgNC9RHYqKirBo0SIMGDDAaCPHd999t3qq\nl27q2rUrkpKSdI5eicwJkylRHeLi4pCfn48lS5Y06uJvXRQKBV588UWDb7UxdwkJCXBwcMBzzz2n\ntTw2NhbFxcXIzMw0cWRE9cdkSlSLgoICvPvuuxgzZgzuvPNOo/Txzz//ALCdlbxq4eHhqKqqwqFD\nh7SWx8bGAgASExNNGRZRgzCZEtViyZIlKCkpweLFi43Wx/bt2wH8u13EVri7u8Pe3h7Z2dlay0NC\nQuDi4sJkShaByZRIh7Nnz+Ljjz/GlClTqi+0NoaDBw8CAO655x6j9WGuWrVqhYKCAq1lcrkcUVFR\nOHz4sImjIqo/JlMiHRYuXAghBN544w2j9pORkQE7Ozv4+voatR9z5O/vj8rKShQWFmotj42NxZEj\nR6BUKk0cGVH9MJkSaZGVlYX4+Hg88cQTaN++vVH7+uSTT/D2228btQ9zNWTIEPj6+iI3N1dreWxs\nLEpLS5Genm7iyIjqRxJC6F05NjZW8P0F2YLJkyfjp59+QnZ2Nu/UbEJpaWkICwtDfHw8pkyZ0tTh\nkA2SJOmwECK2rnocmRLdJiUlBWvXrsXTTz9t9ESalJSE6dOnIy0tzaj9mLvi4mKtz4OCguDq6spF\nSGT2mEyJbjN//ny4uroa9OJvXdasWYPVq1fb9Ek/bm5uCA4O1lpmZ2eH6OhondtniMwFkynRLY4c\nOYINGzbg2Wefhaenp9H7U69UHTp0qNH7Mldubm7Iz8/XWd6tWzckJSWhsrLShFER1Q+TKdEt5s2b\nh5YtW+LZZ581SX8nT56Evb09PDw8TNKfOQoODkZVVRUuXbqktbxnz56oqKjA0aNHTRwZkf6YTIn+\n3/79+7F161bMmTMH7u7uJukzPz8fXl5eJunLXKlPltq0aZPW8p49ewL496QoInPEZEr0/+bOnQsv\nLy88/fTTJunv6tWrqKqqQkBAgEn6M1fDhw8HAOzatUtruY+PD9q3b499+/aZMCqi+uEVbES4+Rf5\nn3/+ieXLl8PV1dUkfbq7u2Pnzp0m689c9erVC+Hh4dVn8eqqs3fvXhNGRVQ/3GdKNk8IgX79+iE7\nOxsnT56Es7NzU4dEt/nwww8xe/ZsnD17FnfccUdTh0M2hPtMifT0xx9/YO/evXj99dfrnUgvXbqE\nHTt24Ouvv8bevXtRVVWl92efeOIJTJ06tZ7RWieFQoFdu3ZBoVBoLe/VqxcAcKqXzBZHpmTThBDo\n3r078vPzkZmZCQcHB70+d/DgQcydOxd//PFH9TNJklBcXAwXFxeUl5fDycmp1jaaN28OOzs7XL9+\nvVHfwRpMmzYN8fHx+OuvvzBw4ECN8qqqKrRo0QKPP/443n///SaIkGwVR6ZEeti4cSMSExMxf/58\nvRMpAGRmZiIpKQkLFy7E9u3bkZaWhj///BMuLi4QQmDQoEGYO3euzgPaKysrUVxcDH9/f0N9FYvW\nv39/AMBvv/2mtdze3h6xsbFc0UtmiwuQyGapVCrMnTsXQUFBePjhh+usf/78eRw+fBijR4/GhAkT\nMHbs2BrTwiEhIQBuTlkGBwdj8eLFSExMxHfffYcWLVrUaOvPP/8EAMTExBjwG1mukSNHAgAOHDig\ns07v3r3x3nvvoaSkBM2aNTNVaER64ciUbNb69etx4sQJLFiwAHJ57f+uvHz5MgYNGoTHHnsMpaWl\nkMvlOt+v2tvb44svvsDKlSvx559/YuTIkSgtLa1RZ9u2bQBs++SjW3l4eMDBwQGZmZk66/Tv3x8K\nhYKjUzJLdSZTSZIekyQpUZKkxNqO/CKyJAqFAvPnz0fnzp3xwAMP1Fr3+vXrGDp0KM6dO4effvoJ\nLi4udbYvSRIee+wxfPPNN9i7dy9mzJhRo/zEiRMA/t1jSUDbtm1rPVawV69esLOzw99//23CqIj0\nU+c0rxBiFYBVwM0FSEaPiMgE1qxZg6ysLPzyyy+QyXT/m1KlUmHSpElITU3F5s2b0bt373r18+CD\nD6KiogJRUVE1nu/cuROnT5/WKzHbiv/+979IS0uDQqHQOlPQvHlzxMbG6jzcgagpcTUv2ZyKigoE\nBQWhdevWOHDgACRJ0ll33bp1eOihh/Dxxx/jySefbHTfZ8+eNfpl49bs5ZdfxvLly3Ht2jW+NyWT\n4GpeIh0+//xznD17FosXL641kQI3R5Y//vgjZs6c2eh+3377bUREROCXX36Br68v1q1b1+g2rc2G\nDRtq/bn0798fVVVV3G9KZofJlGxKaWkpFi9ejL59+2Lw4ME665WUlODy5cuQyWQYO3ZsnUlXHxMn\nToSdnR1mzZqFCxcuoLy8vNFtWptJkybhmWee0Vneu3dv2NnZcaqXzA6TKdmUTz75BJcuXapzVDp3\n7lyEh4fjypUrBuu7ffv2WLZsGS5cuAAAGDt2rMHatha+vr7Iz8+HSqXSWq5+b8pFSGRumEzJZhQV\nFWHp0qUYMmQI+vXrp7Pe/v37ERcXh/Hjxxv8gvBp06ZVL67hyUeaoqOjIYTAoUOHdNbp378/Dhw4\ngOLiYhNGRlQ7JlOyGXFxcbhy5QoWL16ss45SqcTMmTPh4+ODt99+2+AxVFRUVK9WTUpKMnj7lk69\n73bDhg066wwZMgRVVVXYuXOnqcIiqhOTKdmEvLw8vPvuu7jvvvvQrVs3nfU+//xzJCUlYdmyZXBz\nczN4HMePH4e9vT2mT5+OUaNGGbx9S6ee+q7turXevXujWbNm+P33300VFlGdeJwg2YSFCxeitLQU\nS5curbXe33//jbvuuqvOgxwaqlu3bqisrIRKpYIQAr/88gvuvfde2NvbG6U/S+Pu7o7FixdjyJAh\nOus4OjpiwIABOs/xJWoKHJmS1cvMzMTKlSvx2GOPITg4uNa63377LTZt2mSQ1bu1kclk+Pvvv3H/\n/ffjs88+M2pflua1116rdfYAuDkdfOrUKZw8edJEURHVjsmUrN7LL78MJycnzJ8/X2ed3NxcnDt3\nDpIkGWV6V83T07P6hpS77roLAwcOxKJFi1BUVGS0Pi1NVlYWxo0bV+v2l3vuuQcAONVLZoPJlKza\n3r178fPPP+Oll15C69atddabO3cuIiIijLpCNC8vD1evXoX61DFJkrBkyRLk5+dj+fLlRuvX0ly+\nfBkbNmzAJ598orNOp06d4O/vz2RKZoPJlKyWEAJz5syBj48PnnvuOZ31MjIyEB8fj+nTp8PV1dVo\n8Xz11VcAUOOwiO7du+P+++/He++9V+sh77akV69ekMlkOHjwYK31hg4dih07dqCiosJEkRHpxmRK\nVuvHH3/E/v37sWjRoloPlJ8/fz6cnJzwyiuvGDWeLVu2AACmTp1a4/mbb76JFi1aICMjw6j9WwqZ\nTIZ27drh/PnztdYbOXIkSkpK8Ndff5koMiLdmEzJKpWVleGll15CREQEpkyZorNeUlIS1q9fj2ee\neQbe3t5GjSk5ORkuLi7w9fWt8TwkJAQ5OTno06ePUfu3JN26dYNSqaz1svCBAweiefPm+Pnnn00Y\nGZF2TKZkld555x2cPn0aH3zwAezs7HTW++OPP9CyZUu88MILRo/Jz88PAwcO1Foml8t5EMEt7r//\nfgDAL7/8orOOo6Mjhg8fjk2bNkGpVJoqNCKteAUbWZ3s7GyEh4dj9OjR+O677+qsX1BQgFatWpkg\nstq99dZbeP3115GcnIyIiIimDqdJVVZWIjU1VeMe2Nt99913mDhxIvbs2cORPRkFr2Ajm/XMM8/A\nzs4Oy5Yt01lHCIGcnBwAMEkizcrKgkKhqLXOE088ATc3N7z++utGj8fcOTg41JlIAWD48OGwt7ev\ndQRLZApMpmRVtmzZgs2bN2P+/Plo166dznp//fUXAgICsH37dpPE1atXL7Rs2bLWOh4eHnj++eex\nceNGcAYIWLNmDXx8fJCWlqazjpubGwYNGoSff/4Z9ZllIzI0JlOyGuXl5Zg9ezZCQ0Mxe/ZsnfWE\nEHj11Vfh6+tb6+0xhoyroKAAHTp0qLPu7Nmz4enpiblz5xo9LmO4evUqsrKyqn+dlpbW4AMpKisr\nkZubi1WrVtVa7/7770d2djaOHDnSoH6IDIHJlKzGO++8g+zsbKxYsQIODg46623cuBGHDh3CG2+8\nAUdHR6PH9e233wKAzsVHt3Jzc8NLL72ErKwsXLt2zdihGcTVq1fx/vvvo3PnzvD09MQTTzxRXTZ4\n8GC4ubmhd+/e+N///levQzEmT54MAHWewTt27FjY29tX/5yJmoQQQu//YmJiBJE5SklJEY6OjuLB\nBx+stZ5CoRDh4eEiODhYVFVVmSS2AQMGCAAiPT1dr/rl5eWisrLSyFEZxkcffSRcXFwEANGrVy+x\nZMkSsWfPHiGEECqVSmzevFm88cYbIjQ0VAAQrVu3Fj///LPe7bdt21bI5fI6640ePVq0bdtWKBSK\nBn8XIm0AJAo98iNHpmTxFAoFpk6dCldXV3zwwQe11j106BDS09OxcOHC6ku6jS0xMRHNmjWr85B9\nNUdHR9jb26O0tBSnT582cnSNI5PJcM899+DYsWNISEjAyy+/XL2qVpIk3HvvvZg/fz5SUlKwZ88e\nBAQE1OuUqT59+kChUGDHjh211ps0aRJyc3O5tYiaDK9gI4v37rvv4tChQ1i/fn2t5+8CQI8ePZCR\nkQE/Pz8TRQfMnDmz1r2uugwcOBAymQwJCQlGv8VGX0IIrFixAh4eHpg0aRJmzpyJJ598ss7PSZKE\nPn36YO/evdXf5c0330RISEj1HabaTJs2DRs3bkR6enqt0+T33nsvmjdvjm+//RZ33313/b8YUWPp\nM3wVnOYlM3X8+HHh4OAgxo8fX2fdq1evmiAiw1m5cqUAILZu3drUoQghbk6Rz5w5UwAQEyZMaFRb\nlZWVolevXgKAePfdd4VKpWp0fFOnThXNmzcXJSUljW6LSA16TvMymZLFqqysFDExMcLLy0vk5eXV\nWre0tFS0a9dOvP766yaK7qZFixaJn376qUGfraysFP7+/qJr164GSTaNUVZWJsaMGSMAiBdffFEo\nlUqDtPnAAw8IAGL27Nm1fseSkhJRUVFRa3s7d+4UAER8fHyjYyNSYzIlq7do0SIBQPz444911l22\nbBBtBIgAAB97SURBVJkAIHbt2mWCyG5SKpXCzs5O+Pj4NLiNr776SgAQGzZsMGBk9VNRUSFGjBgh\nAIi4uDiDtq1UKsUzzzwjAIinnnpKa0L96quvhCRJYtmyZbW2pVKpRHBwsOjRo4dBYyTbpm8y5QIk\nskj79+/HggUL8OCDD9b6zg0ACgsL8dZbb2Hw4MG46667TBThzS04SqUSAwYMaHAbkyZNQkhICL7/\n/nsDRlY/crkcHTp0wMqVK2vdv9sQMpkMy5cvx5w5c9CpUyet74aHDBkCIQS+/vrrWtuSJAmPP/44\n9u/fj+TkZIPGSVQnfTKu4MiUzEhBQYG44447hJ+fn17vQRcsWCAAiIMHD5ogun+pt8QcPXq0Ue2c\nO3fOINOq9aVUKuucPjeG/Px8jWfe3t5CLpfX+XO4cuWKcHR0FE8++aSxwiMbA45MyRqpVCo8/PDD\nuHz5Mn744Yc6j+irqKjAxx9/jDFjxqBbt24mivKmffv2wc3NTa8zZmvj6+sLmUyGK1eumOwibCEE\nXnjhBcTExJj00vKkpCQEBARojELvueceKBQK/PTTT7V+3sPDAw888AC+/vrrBp+8RNQQTKZkUZYu\nXYpt27YhLi4OMTExddZ3dHTE4cOHERcXZ4Lo/pWYmIjy8nK9Tj3Sx/nz5xEQEICPP/7YIO3V5aOP\nPsL777+PMWPGmPRGndDQUMTGxmL69Ok1zk2eM2cOAODTTz+ts42nnnoKRUVF+OKLL4wWJ5EGfYav\ngtO8ZAZ27twpZDKZmDBhgl6rW4uKipp0FeyJEydETk6Owdq75557hLu7uygoKDBYm9ps27ZNyGQy\ncd999zXJ9PL169dFZGSkcHV1FUeOHKl+PnjwYPHRRx/p1Ua/fv3EHXfcYTEnSZH5AlfzkjU5e/as\naN26tQgODhaFhYV6fWbEiBHivvvuM3JkpnP8+HEhk8nE7NmzjdZHSkqKcHNzE126dBFFRUVG66cu\n58+fF3fccYdo27atOH/+fL0/v2XLFgFAfP3110aIjmyJvsmU07xk9m7cuIHhw4ejrKwMGzZsQPPm\nzev8zF9//YWtW7eiV69eJoiwpoSEBHh6emL9+vUGbTciIgKPPPIIPv744xo3sxiSh4cHBgwYgM2b\nN9fr2D9Da9euHX799VcMHjwY7u7u1c83bNiAJUuW1Pn5YcOGITw8HO+8887NUQORsemTcQVHptRE\nKisrxeDBg4VcLhfbt2/X6zMKhUJ06dJFdOjQQZSVlRk5Qk0DBw4UAKoPfDek3Nxc4erqKhYsWGDQ\ndisqKkx28H9DFBcXC6VSKTw8PPRa1SuEEPHx8QJAvQ7WJ7odOM1Llk6lUolHH31UABBffPGF3p9b\nvXq1ACDWrVtnxOi0q6qqEnK5XLRs2dJofZw6dcqg74JVKpWYNm2aGDp0qFkm1OvXr4vOnTuL119/\nXTz++OMCgPj444/r/FxVVZUICgoSYWFhvE2GGkzfZMppXjJbS5cuxeeff47XXnsN06dP1+szQgi8\n//776N69Ox588EEjR6jpgw8+gEKhwMSJE43Wh7+/PyRJwtmzZ6FUKhvd3rJly7B69WrceeedJrtJ\npz7c3NzQvXt3LF68GJGRkQBurjaui1wux+LFi5Gamsq7Tsn49Mm4giNTMjH1Ie8TJ06s9yisoKBA\nZGRkGCmy2nXs2FEAEFeuXDFqP2lpacLZ2VmsWLGiUe1s3LhRSJIkxo8f3yQrd/VVUVEh+vXrJxwd\nHUXbtm0FAHH58uU6P6dUKkV0dLTo2LGjKC8vN0GkZG3AkSlZqi+++AKPP/44hg8fjtWrV+t9/djl\ny5ehVCrh6emJoKAgI0epXVhYGAYNGgQPDw+j9hMcHIzevXvj1VdfxaVLlxrURlJSEh566CHExMQg\nPj4eMpn5/nXg4OCADRs2oF27digpKQEAxMfH1/k5mUyGpUuXIicnB++//76RoySbpk/GFRyZkoms\nXr1aSJIkhg4dWq/FQwqFQnTv3l0MHz7ciNGZl4yMDOHg4NDg69D27NkjunTpIi5evGjgyIwnJSVF\nxMTEiC1bttTrc2PGjBEuLi4G3fdLtgFcgESW5uuvvxaSJInBgweL0tLSen32nXfeEQDE2rVrjRRd\n7YqKisQzzzxj8tXDCxcurPeK1Vunc815alcX9bS/SqXSezr9zJkzwsXFxar2HZNpMJmSRVm5cqWQ\nyWRi4MCB9b7cOTU1VTg6OooxY8Y02YlHM2bMEADE4sWLTdpvZWWl6Nq1q3j++ef1qq9UKsX9998v\n3nzzTSNHZlwKhUI0a9ZMuLi46P2ZJUuWCAANvl+WbBOTKVkElUol5s2bJwCIYcOGieLi4np9vrKy\nUtx5553C09NTXLp0yUhR1k6pVApHR0fh6OjYJCM9fU8qUqlU/9fevUdFVa5/AP++M9zvKAoMoAIC\nooKKSQtvBzUNOyl5LC1d5VHMxTlmVsu81PKSmifNLOUcl2ag/vJ24liZirfUTt4VQYEUw0Mw4gVE\nEEFguMz39wcyRjKActmo72etvZbjM3v2s98Z5pl3v3u/m++++y4BcMWKFc2cVfPS6/XUaDQEwL/+\n9a8NWqf6ZvJOTk68fv16M2coPSlkMZVavfLyckZERBAAJ02a9EjzqF6+fJkeHh785ptvmiHDhvng\ngw8IgG+++aZiOZDkuXPnGBsbazS+ePFiAuC0adMUnbO4qVy+fJkACICbNm1q0DoXLlyghYUFhw8f\n/kS0gdT8ZDGVWrXCwkL++c9/JgDOnTu3UV9sD3tYuCmVlJTQzMyMpqamiuZBVs1FbGlpyZSUlAdi\n//rXvwiAr7/++mM5TmpM9WxTKpWKu3fvbtA6UVFRBMBly5Y1c3bSk6ChxbT1ngsvPbEuXbqE4OBg\n7NmzB2vWrMHChQsbfPlLNa1Wi7lz56KsrAxWVlbNlGn9jhw5gsrKSsyYMUPRPABg3bp1sLGxwSuv\nvII7d+7UiJWUlCA8PBzR0dGt+hKYh1U9GYNKpUJpaWmD1pk6dSpefvllzJ49G/v27WvO9KSnSUMq\nLmXPVGoi27dvp62tLZ2cnHjw4MFHeo2ioiL26NGDdnZ2TEtLa+IMH15BQUGr6e0dPHiQarWaL774\nIisqKlhQUGCItZYcm1pUVBQvXLhgeHz79u161yksLGRAQAAdHByYmpranOlJjznInqnUmlRUVGD2\n7NkYPXo0/P39kZCQ0KAbZ5eVlSEtLQ0JCQkAgMrKSrzwwgtISkrCzJkzcffuXdy6datqzKKFzZo1\nC7dv34adnV2r6e0NHjwYK1euxK5du/Dmm2/C09MTiYmJANBqcmxqb731Fvz9/VFWVoavv/4aXl5e\nOHHiRJ3r2NjYYMeOHTA1NcXQoUOh1WpbKFvpidWQikvZM5Ua4eLFiwwODiYARkZG1jut29atWzl2\n7Fh6eXlRpVIRANu1a0e9Xs/IyEjDSSe/Xzp16mQYdz19+jQzMzObdZ+WLFlCAAwLC2vW7TwKvV7P\niIgIqlQq9u/fv0bv9ElVUlJCGxsbenl50cfHhzY2Nty3b1+96yUkJNDe3p6+vr6KnQ0utW5oYM9U\n8CF+0T/zzDOMj49v+oouPZH0ej1WrlyJDz74AFZWVli9evUDk89rtVrs3LkTP/30E7Zt2wa1Wo2p\nU6di165dCA4Ohr+/P7y9vaHRaODi4oLevXtj8uTJmDJlCgoLC5GdnY2srCyUlJRgzpw5AIDg4GCc\nOXMGXbt2RVhYGMLCwjBw4ECYm5s3yX5lZmbC29sbarUa2dnZNe63qTSSWLRoEebPn4/nnnsO69ev\nR3x8PF566SWlU2swkrhx4wZSU1Nx5coVFBQUoKCgAKNGjUK3bt2g1WqxefNm2NjYwNHREZ07d4av\nry/CwsJw5swZ/P3vf8fRo0dx4cIFxMTE4PXXX69ze8eOHcOwYcOg0Wiwf/9+eHp6ttCeSo8DIcRZ\nks/U+8SGVFzKnqn0kC5dusSBAwcSAEeMGFHjur5r167xk08+YY8ePQw9S19fX8NUb3VdIpOcnFzv\nmb9JSUn87LPPOHToUJqZmRmuYa3WmLHDkpIStmvXjgC4YcOGR36d5vLVV18RACdMmECdTsfp06dT\nCNHoCfGbk1ar5ebNm3nx4kWS5I8//ljr0Yevv/6aJLl///5a4zExMbS2tiYAzpgxg/379ycAHj58\nuN4cjh8/TkdHR7q4uPDs2bPNubvSYwby0hhJCfn5+XzvvfdoYmJCOzs7btiwgXq9nnfu3GF+fj7J\nqpOQADAkJISffvppnSeAlJWVMSIi4pGnCSwqKuLOnTsNJzvl5uZSo9Fw6tSpPHHixENfktOnTx8C\n4Lhx4x4pn+ZS/QOhuLiYa9asMexXSUkJR44cSQBcsGBBq7i2srS0lN9//z0nTpzIjh07GorhokWL\nSFa9R1FRUTxw4AB//fVX5uTkUKfTGdbX6/UsLS1lbm4uL168yB9++IHLly9neno6T548WaPAOjs7\nc9q0adyzZ0+9U1SmpKTQw8ODFhYWrfKHkqQMWUylFlVRUcG1a9fSycmJQghOnjyZWVlZ3Lt3L8eN\nG0dLS0t+9NFHJKu+TC9fvlzva964cYMDBgwgAC5cuLBJ8kxPT+eYMWNoYWFBAPT29ub8+fN59erV\nBq2/ZcsWDhkypElyaQp6vZ4bN25kUFCQ0ZmQysvLOWHCBALgmDFjGjxjUlPKyclhcnIyyaqzbU1N\nTWlvb8+XX36ZK1euZEJCQpPdwHvp0qVUq9WcPHkyX3jhBVpaWhIAvby8eODAAaalpRmdASknJ8dw\n7eobb7zBvLy8JslJenzJYiq1CJ1Ox+joaPr4+BAABwwYwLNnz3LGjBmG+046OjoyMjKS8fHxDX7d\nAwcO0M3NjZaWls0yeX1BQQHXr1/PIUOGUAjBc+fOkayaED0nJ6fGcysrK7l06dImz6GxtFotX3rp\nJUO713X3F71ez2XLllGj0TArK6tF8ktLS+Py5cs5YMAAqlQq9uvXzxA7e/bsI8141VDVPxh0Oh0v\nXLjAmJgY+vv7G4qqEIIhISFcunTpA/e+LS8v57x586hWq6nRaBgbG9sqevSSMmQxlZpVUVERV65c\nSXd3dwJgt27d+M477xi+dMLCwhgeHs7t27c/9E2ZT58+TQD08/NjYmJic6Rfw++L0BtvvEETExO+\n+OKL/Pe//82MjAx6e3sTAOfPn9/suTREWVkZP/74Y1pZWdHS0pLLli1rcK+uushUH0loyrvc/L7g\njBs3znCoNTAwkPPmzWNCQkKTbauh+vbtSxMTE8bGxvLu3bucMWMGVSoVra2t2aFDB0OOzz333APr\nxsfHMzAwkAA4cOBAnjhxosXzl5Qni6nU5PR6PY8dO8aIiAja2NgYfuVX/+I3NTU1jIs+7Ek+Op2O\nJ0+eNGxn/fr1D30btqaQnJzMmTNn0s3NrcbY25/+9KeH2qfi4mImJSUxLi6O69at4/z58xkREcHz\n58+TJPft20c3Nzfa2trS0tKS5ubmNDMzM0yJ9+OPP9Lb25uBgYEMDQ3l2LFjOW3aNP7yyy+srKxk\nYGAgn3/+eaanp9e6/YKCAv7888/8z3/+w3Xr1nHVqlVcunSpYXKDL7/8kgDo4ODA8ePHc/Xq1dyy\nZYvhkqKysrIGFdr8/HzGxsZy0qRJ9PLyMhTrLVu28PPPPzeaX0v56quvDJdXjRo1ijqdjomJiezX\nrx/HjBnDzMxMRkVFcdWqVSSrPrdBQUGMjIzknj17WFRUxDVr1hhOOhs8eDB3797dZIekpdZPFlOp\nSVRWVjI+Pp4fffSR4VCutbU1n3322Ro9j08++eSRru3My8vjihUr6ObmRgsLi1Zzo+qQkBDD/g0Y\nMIBkVZGfMmUKY2JieP36dd69e5fnz59nbGwsP/74Y06YMIHHjx8nSe7Zs6dGMRZC0NXVlXFxcSSr\nJqWfNGkSp0+fzvfff58zZ87k7NmzDcUuPj6e48eP58iRI9m7d286ODhQCMEdO3aQJP/5z38SANVq\nNe3s7Ghvb08rKytDUdi3b1+tZ7xWTwh/8ODBWuObN28mSR4+fJgA2LZtWwYEBPD555/npEmTDGe6\nxsXFsU+fPoZCVT3+2dzX9z6KxMREOjk5GT67mzZtol6vN9yhKCkpiR4eHly4cCGTkpI4evRow1nB\ntra2DA8P565du/jZZ58Zhi46duzIuXPn1joPsvRkaWgxNan32hnpqUISWq0WJ0+exO7du7F7927k\n5eUBqJpBZ9q0aViyZAmuXr2KvXv3YsSIEfDy8nro7Vy4cAGLFy/Gt99+C51Oh9DQUERHR8PFxcVo\nXsXFxRBCwMrKCuXl5UhMTERxcTFKSkpQXl4OkvDx8UHXrl2h0+mwc+dOmJiYwMLCAgCg0+ng6emJ\nwMBAFBQUYO3atSgoKEBubi4KCgpw+fJlREZGYvLkyfD09MT58+fh7e2NwsJCdO/eHcXFxbh58ya+\n/PLLWnN0cHBAQEAAQkJC0LNnT6xbtw5dunRBhw4d4OrqClNTU8Nze/TogejoaKPtY2lpifLyciQk\nJCArKwtA1aw9v/76KwCgY8eOAKqu5a2srIRKpUJ5eTns7OwM7atWq+Hm5obOnTvDx8cHfn5+GDZs\nGABg0KBBqKioQFlZGbZt24bly5fjzp07CAsLA1A1l++CBQug1WqRmpqK5ORkHD58GH5+fggKCkJi\nYiLOnDkDlUoFNzc3+Pn5wd7eHnfv3gUAFBQUoKioCK6urorPvNSzZ09kZ2dj+vTpWL16NUpKSiCE\nQEZGBpydnVFRUQFfX1/MmzcPCxYsQEhICGbNmgUfHx8cOnQIBw8eRGFhId577z0MGTIEkZGRyM3N\nxeLFi7Fo0SJ4enpi8ODBGDRoEAYNGgSNRqPo/krKkJM2PMV0Oh3S0tJw/vx5nDhxAqdPn0Z6ejpu\n3br1wHO7du2KoUOHYtKkSQgMDGzwNkjiypUrSElJwdmzZxEaGooBAwbg1KlTGDZsGEJDQ9G3b1/Y\n29vj1q1b6NOnD4YNG4b8/HyMHDkSeXl5hqWsrAwffvghFi9ejOvXr9f6pfXqq69i69atSE1Nhb+/\n/wPxfv364ejRo0bjLi4uuH79Ok6dOoX+/fujoqKiRnz48OFYsmQJNm7ciKioKFRWVtaIe3h4YNSo\nUdBoNJg9ezaEEHBwcICjoyMcHR0RERGBv/3tb8jJycHbb7+N0tJS5OXl4caNG8jNzcWIESOwceNG\nfPfdd/jLX/4CADAzM4OrqytcXFwwfvx4TJs2DSUlJYiJiYGzszPMzc1hYmIClUqFTp06wc/PD6dP\nn0Z0dDSysrKg1WqRnp6O4uJiZGRkoGPHjli1ahXWrFkDHx8fdO7cGa6uriguLsbo0aPh5+cHJycn\n3LlzB9XfD0II+Pv7Y8mSJQgPD0dGRgb27duHjIwMZGRk4LfffkNGRgZ27tyJPn36YMOGDZg4cSLM\nzMzQoUMHdOrUCZ6enpgzZw48PT2Rn5+P0tJSODs7t2ixLSoqgo2NDQDA398fqampcHNzw+DBg/Hs\ns8/i2rVr2Lt3L5KSkpCTkwNHR0ds374dGRkZeOaZZ5Cbm4v3338fv/32m6FdrK2tDa8NVH2Gunfv\njl69eqFbt27w9fWFu7s7XFxcavygkh4PDZ20QRbTJ0BlZSV0Oh0KCwtRWloKnU6HW7duITk5GTdu\n3MDNmzdx8+ZNZGdngyTKy8tx5coVXLly5YHX8vf3x9SpUxEUFIT9+/cjKCgIAQEBsLGxQXFxMSwt\nLdGuXTuUl5cjNjYWOTk5yM3NRV5eHnJzc9G7d2/MmjUL165dQ9euXVFYWAi9Xm94/R49euDcuXPI\ny8tD27ZtH9h+aGgoDh8+jNzc3Bo9XpKoqKhASEgIDh06hOzs7Fp7sX379sWxY8dw48YNdO7cGcD9\n3ltlZSXc3NyQmZmJrVu3Yty4cQ+sr9FocPXqVZw7dw69evV6IO7l5YX//e9/SElJQUBAwANxU1NT\nmJmZGXpof1Tdu7927RpiY2NrXT87Oxupqano27fvA/Hu3bsjOTkZmZmZ6NSp0wPx4cOHIy4uDvn5\n+WjTps0D8REjRuCHH35AdHQ0pkyZUuO9AYChQ4ciLi4OY8eOxffffw8hhOEHg6enJ7Zv346uXbti\n9OjRUKlUcHZ2Rvv27eHq6oouXbqgX79+MDc3R1JSEo4fPw6tVluj2B49ehQ+Pj744osv8O6778Lc\n3BwdO3aEq6sr2rZti6ioKGg0GiQkJCAhIQEODg6wtraGlZUVrK2tERAQAHNzc5SWlkKv18PS0vKh\n7zhUbe3atfjiiy+QlpZm2Ee1Wo2KigrcunULc+bMwd27d5GUlISUlBTDehqNBj4+PpgxYwZOnTqF\ngwcP4rXXXoNarca2bdtw5MiRWrcnhEDbtm1haWkJW1tbODg4wN7eHg4ODvDw8IC9vT3UajXMzMxg\nZmYGU1NTmJiYwMTEBGq1Gmq1GiYmJjAzM4MQAjqdzrDv1T9ILCwsYGtrC5VKhdzcXAgharSPra0t\n2rdvDyEE0tPTIYQAScPrOzk5wdXVFUIIaLVaw7ZNTU2hVqthZ2eHNm3aQKVSIS8vD2q1GiqVyrBU\n507ScMTkjzk8blr9DEhhYWG1jtkAYHBwsGFsorald+/ebN++vdF4r169DGMktS2BgYF0dHQ0Gu/e\nvTvt7OyMxv39/Q0n4NS2+Pn5Ga5tq23p3Lkzzc3Njca9vLxoYmJiNO7i4mI01pAlNDTUMDtMbQt5\nf8zMWNzYmFtD4z///HOd8ePHj9cZ/+9//1tnPC4urs74kSNH6oz/8eL/P8Z37NhhNF5ZWcl//OMf\nRuO2traNev/c3d2pVquNxgMDA+v8fAYFBdHe3t5oPDg4mKampnWuX1d+jY337t27Vcfbtm3bqPdP\nLs27fP75501Wp8iGj5nWe3xFCDFFCBEvhIi/efNmfU9vMFtbW6OxNm3a1Pqrupqzs7PRsTUAcHd3\nh7u7u9G4p6dnneN8vr6+8PPzMxrv1q0bunfvbjTes2fPWns11YKDgxEcHGw03rdvX/Tr189ofMSI\nEQgPDzca37RpE+bOnWs0fvjwYXz66adG4wDqvTdn9dicMY6OjnXG63r/gaoxw7rUNx9ubb2233Ny\ncqozbm9vX2e8rs+HSqWq8/25c+cODh06ZDS+YsUKTJw40Wh82LBhdX4+PD0969z/6kPGxjg6OsLD\nw8No3MnJqc5xwfrem/o+O/V9Npo7Xn0Y2Ji6/vYBoEuXLnXG27VrV2e8eozfGBOTuk91qS+uVqvr\njNd32L2+eH290OaO1/fd0VzkYV5JkiRJMqKhh3mfzBscSpIkSVILksVUkiRJkhpJFlNJkiRJaiRZ\nTCVJkiSpkWQxlSRJkqRGksVUkiRJkhpJFlNJkiRJaiRZTCVJkiSpkWQxlSRJkqRGksVUkiRJkhpJ\nFlNJkiRJaiRZTCVJkiSpkWQxlSRJkqRGeqi7xgghbgLIbMLtOwHIbcLXe9zJ9rhPtkVNsj1qku1x\nn2yLmpq6PTqSrPu+eXjIYtrUhBDxDbm1zdNCtsd9si1qku1Rk2yP+2Rb1KRUe8jDvJIkSZLUSLKY\nSpIkSVIjKV1Mv1R4+62NbI/7ZFvUJNujJtke98m2qEmR9lB0zFSSJEmSngRK90wlSZIk6bGneDEV\nQiwSQiQJIc4JIfYLITRK56QUIcSnQojUe+3xnRDCQemclCSEeEUI8YsQQi+EeCrPVhRChAkhLgkh\nLgshZiudj5KEEDFCiBwhRIrSubQGQggPIcRhIcTFe38n05XOSSlCCAshxGkhxPl7bfFRi+eg9GFe\nIYQdyTv3/v02gK4kIxVNSiFCiGEADpGsEEIsBQCSsxROSzFCCH8AegBrAcwgGa9wSi1KCKEG8CuA\noQCyAJwB8BrJC4omphAhxEAARQD+j2R3pfNRmhDCFYAryQQhhC2AswBeeho/H0IIAcCaZJEQwhTA\nUQDTSZ5sqRwU75lWF9J7rAE8tYO4JPeTrLj38CQAdyXzURrJiyQvKZ2HgoIBXCaZTrIMwDYA4Qrn\npBiSPwPIUzqP1oLkdZIJ9/5dCOAiADdls1IGqxTde2h6b2nRWqJ4MQUAIcTHQogrAMYDmKd0Pq3E\nJAB7lE5CUpQbgCu/e5yFp/TLUqqbEKITgF4ATimbiXKEEGohxDkAOQAOkGzRtmiRYiqE+FEIkVLL\nEg4AJD8k6QFgM4C3WiInpdTXFvee8yGAClS1xxOtIe3xFBO1/N9Te+RGqp0QwgbAdgDv/OFI31OF\nZCXJnqg6ohcshGjRoQCTltgIyeca+NQtAHYDmN+M6SiqvrYQQkwA8CKAIVR6QLsFPMRn42mUBcDj\nd4/dAVxTKBepFbo3PrgdwGaS3yqdT2tA8rYQ4icAYQBa7GQ1xQ/zCiF8fvdwJIBUpXJRmhAiDMAs\nACNJFiudj6S4MwB8hBCeQggzAK8C+EHhnKRW4t5JN9EALpJcoXQ+ShJCtKu++kEIYQngObRwLWkN\nZ/NuB+CHqrM2MwFEkryqaFIKEUJcBmAO4Na9/zr5tJ7ZDABCiFEAogC0A3AbwDmSzyubVcsSQrwA\n4AsAagAxJD9WOCXFCCG2AghF1V1BsgHMJxmtaFIKEkL0B3AEQDKqvj8B4AOSccplpQwhRCCAjaj6\nO1EB+IbkwhbNQeliKkmSJEmPO8UP80qSJEnS404WU0mSJElqJFlMJUmSJKmRZDGVJEmSpEaSxVSS\nJEmSGkkWU0mSJElqJFlMJUmSJKmRZDGVJEmSpEb6f0t27EfTnkHuAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ix = 1\n", "\n", "ax.plot(x_plot, dpm_pdfs[ix], c='k', label='Density');\n", "ax.plot(x_plot, (w[..., np.newaxis] * dpm_pdf_components)[ix, 0],\n", " '--', c='k', label='Mixture components (weighted)');\n", "ax.plot(x_plot, (w[..., np.newaxis] * dpm_pdf_components)[ix].T,\n", " '--', c='k');\n", "\n", "ax.set_yticklabels([]);\n", "ax.legend(loc=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Sampling from these stochastic processes is fun, but these ideas become truly useful when we fit them to data. The discreteness of samples and the stick-breaking representation of the Dirichlet process lend themselves nicely to Markov chain Monte Carlo simulation of posterior distributions. We will perform this sampling using `PyMC3`.\n", "\n", "Our first example uses a Dirichlet process mixture to estimate the density of waiting times between eruptions of the [Old Faithful](https://en.wikipedia.org/wiki/Old_Faithful) geyser in [Yellowstone National Park](https://en.wikipedia.org/wiki/Yellowstone_National_Park)." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "old_faithful_df = get_rdataset('faithful', cache=True).data[['waiting']]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For convenience in specifying the prior, we standardize the waiting time between eruptions." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "old_faithful_df['std_waiting'] = (old_faithful_df.waiting - old_faithful_df.waiting.mean()) / old_faithful_df.waiting.std()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
waitingstd_waiting
0790.596025
154-1.242890
2740.228242
362-0.654437
4851.037364
\n", "
" ], "text/plain": [ " waiting std_waiting\n", "0 79 0.596025\n", "1 54 -1.242890\n", "2 74 0.228242\n", "3 62 -0.654437\n", "4 85 1.037364" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "old_faithful_df.head()" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfIAAAF3CAYAAABe7Mm7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCy33AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "n_bins = 20\n", "ax.hist(old_faithful_df.std_waiting, bins=n_bins, color=blue, lw=0, alpha=0.5);\n", "\n", "ax.set_xlabel('Standardized waiting time between eruptions');\n", "ax.set_ylabel('Number of eruptions');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Observant readers will have noted that we have not been continuing the stick-breaking process indefinitely as indicated by its definition, but rather have been truncating this process after a finite number of breaks. Obviously, when computing with Dirichlet processes, it is necessary to only store a finite number of its point masses and weights in memory. This restriction is not terribly onerous, since with a finite number of observations, it seems quite likely that the number of mixture components that contribute non-neglible mass to the mixture will grow slower than the number of samples. This intuition can be formalized to show that the (expected) number of components that contribute non-negligible mass to the mixture approaches $\\alpha \\log N$, where $N$ is the sample size.\n", "\n", "There are various clever [Gibbs sampling](https://en.wikipedia.org/wiki/Gibbs_sampling) techniques for Dirichlet processes that allow the number of components stored to grow as needed. [Stochastic memoization](http://danroy.org/papers/RoyManGooTen-ICMLNPB-2008.pdf) is another powerful technique for simulating Dirichlet processes while only storing finitely many components in memory. In this introductory example, we take the much less sophistocated approach of simply truncating the Dirichlet process components that are stored after a fixed number, $K$, of components. [Ohlssen, et al.](http://fisher.osu.edu/~schroeder.9/AMIS900/Ohlssen2006.pdf) provide justification for truncation, showing that $K > 5 \\alpha + 2$ is most likely sufficient to capture almost all of the mixture weight ($\\sum_{i = 1}^{K} w_i > 0.99$). In practice, we can verify the suitability of our truncated approximation to the Dirichlet process by checking the number of components that contribute non-negligible mass to the mixture. If, in our simulations, all components contribute non-negligible mass to the mixture, we have truncated the Dirichlet process too early.\n", "\n", "Our (truncated) Dirichlet process mixture model for the standardized waiting times is\n", "\n", "$$\n", "\\begin{align*}\n", " \\alpha\n", " & \\sim \\textrm{Gamma}(1, 1) \\\\\n", " \\beta_1, \\ldots, \\beta_K\n", " & \\sim \\textrm{Beta}(1, \\alpha) \\\\\n", " w_i\n", " & = \\beta_i \\prod_{j = i - 1}^i (1 - \\beta_j) \\\\\n", " \\\\\n", " \\lambda_1, \\ldots, \\lambda_K\n", " & \\sim U(0, 5) \\\\\n", " \\tau_1, \\ldots, \\tau_K\n", " & \\sim \\textrm{Gamma}(1, 1) \\\\\n", " \\mu_i\\ |\\ \\lambda_i, \\tau_i\n", " & \\sim N\\left(0, (\\lambda_i \\tau_i)^{-1}\\right) \\\\\n", " \\\\\n", " x\\ |\\ w_i, \\lambda_i, \\tau_i, \\mu_i\n", " & \\sim \\sum_{i = 1}^K w_i\\ N(\\mu_i, (\\lambda_i \\tau_i)^{-1})\n", "\\end{align*}\n", "$$\n", "\n", "Note that instead of fixing a value of $\\alpha$, as in our previous simulations, we specify a prior on $\\alpha$, so that we may learn its posterior distribution from the observations.\n", "\n", "We now construct this model using `pymc3`." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "N = old_faithful_df.shape[0]\n", "\n", "K = 30" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "def stick_breaking(beta):\n", " portion_remaining = tt.concatenate([[1], tt.extra_ops.cumprod(1 - beta)[:-1]])\n", "\n", " return beta * portion_remaining" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "with pm.Model() as model:\n", " alpha = pm.Gamma('alpha', 1., 1.)\n", " beta = pm.Beta('beta', 1., alpha, shape=K)\n", " w = pm.Deterministic('w', stick_breaking(beta))\n", "\n", " tau = pm.Gamma('tau', 1., 1., shape=K)\n", " lambda_ = pm.Uniform('lambda', 0, 5, shape=K)\n", " mu = pm.Normal('mu', 0, tau=lambda_ * tau, shape=K)\n", " obs = pm.NormalMixture('obs', w, mu, tau=lambda_ * tau,\n", " observed=old_faithful_df.std_waiting.values)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We sample from the model 2,000 times using NUTS initialized with ADVI." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "INFO (theano.gof.compilelock): Refreshing lock /Users/fonnescj/.theano/compiledir_Darwin-17.0.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock\n", "100%|█████████▉| 2497/2500 [01:12<00:00, 37.49it/s]/Users/fonnescj/Repos/pymc3/pymc3/step_methods/hmc/nuts.py:467: UserWarning: Chain 0 contains 262 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n", " % (self._chain_id, n_diverging))\n", "100%|██████████| 2500/2500 [01:12<00:00, 34.27it/s]\n" ] } ], "source": [ "with model:\n", " trace = pm.sample(2000, random_seed=SEED)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The posterior distribution of $\\alpha$ is highly concentrated between 0.25 and 1." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAACICAYAAAD6SUoaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJEnSgDjBkiRJkqQB+QVy3DK5UXDLwwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace, varnames=['alpha']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To verify that truncation is not biasing our results, we plot the posterior expected mixture weight of each component." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfcAAAF3CAYAAAC4xQL/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n4S5JUs/8N7ah5fNFviNaAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "plot_w = np.arange(K) + 1\n", "\n", "ax.bar(plot_w - 0.5, trace['w'].mean(axis=0), width=1., lw=0);\n", "\n", "ax.set_xlim(0.5, K);\n", "ax.set_xlabel('Component');\n", "\n", "ax.set_ylabel('Posterior expected mixture weight');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that only three mixture components have appreciable posterior expected weights, so we conclude that truncating the Dirichlet process to forty components has not appreciably affected our estimates.\n", "\n", "We now compute and plot our posterior density estimate." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "post_pdf_contribs = sp.stats.norm.pdf(np.atleast_3d(x_plot),\n", " trace['mu'][:, np.newaxis, :],\n", " 1. / np.sqrt(trace['lambda'] * trace['tau'])[:, np.newaxis, :])\n", "post_pdfs = (trace['w'][:, np.newaxis, :] * post_pdf_contribs).sum(axis=-1)\n", "\n", "post_pdf_low, post_pdf_high = np.percentile(post_pdfs, [2.5, 97.5], axis=0)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeUAAAF3CAYAAACbnlMqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "n_bins = 20\n", "ax.hist(old_faithful_df.std_waiting.values, bins=n_bins, normed=True,\n", " color=blue, lw=0, alpha=0.5);\n", "\n", "ax.fill_between(x_plot, post_pdf_low, post_pdf_high,\n", " color='gray', alpha=0.45);\n", "ax.plot(x_plot, post_pdfs[0],\n", " c='gray', label='Posterior sample densities');\n", "ax.plot(x_plot, post_pdfs[::100].T, c='gray');\n", "ax.plot(x_plot, post_pdfs.mean(axis=0),\n", " c='k', label='Posterior expected density');\n", "\n", "ax.set_xlabel('Standardized waiting time between eruptions');\n", "\n", "ax.set_yticklabels([]);\n", "ax.set_ylabel('Density');\n", "\n", "ax.legend(loc=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As above, we can decompose this density estimate into its (weighted) mixture components." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAeUAAAF3CAYAAACbnlMqAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTdO0AuL/AaT1jPz286GEAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "n_bins = 20\n", "ax.hist(old_faithful_df.std_waiting.values, bins=n_bins, normed=True,\n", " color=blue, lw=0, alpha=0.5);\n", "\n", "ax.plot(x_plot, post_pdfs.mean(axis=0),\n", " c='k', label='Posterior expected density');\n", "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pdf_contribs).mean(axis=0)[:, 0],\n", " '--', c='k', label='Posterior expected mixture\\ncomponents\\n(weighted)');\n", "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pdf_contribs).mean(axis=0),\n", " '--', c='k');\n", "\n", "ax.set_xlabel('Standardized waiting time between eruptions');\n", "\n", "ax.set_yticklabels([]);\n", "ax.set_ylabel('Density');\n", "\n", "ax.legend(loc=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Dirichlet process mixture model is incredibly flexible in terms of the family of parametric component distributions $\\{f_{\\theta}\\ |\\ f_{\\theta} \\in \\Theta\\}$. We illustrate this flexibility below by using Poisson component distributions to estimate the density of sunspots per year." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "sunspot_df = get_rdataset('sunspot.year', cache=True).data" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
timesunspot.year
017005.0
1170111.0
2170216.0
3170323.0
4170436.0
\n", "
" ], "text/plain": [ " time sunspot.year\n", "0 1700 5.0\n", "1 1701 11.0\n", "2 1702 16.0\n", "3 1703 23.0\n", "4 1704 36.0" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sunspot_df.head()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For this example, the model is\n", "\n", "$$\n", "\\begin{align*}\n", " \\alpha\n", " & \\sim \\textrm{Gamma}(1, 1) \\\\\n", " \\beta_1, \\ldots, \\beta_K\n", " & \\sim \\textrm{Beta}(1, \\alpha) \\\\\n", " w_i\n", " & = \\beta_i \\prod_{j = i - 1}^i (1 - \\beta_j) \\\\\n", " \\\\\n", " \\lambda_i, \\ldots, \\lambda_K\n", " & \\sim U(0, 300)\n", " \\\\\n", " x\\ |\\ w_i, \\lambda_i\n", " & \\sim \\sum_{i = 1}^K w_i\\ \\textrm{Poisson}(\\lambda_i).\n", "\\end{align*}\n", "$$" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "K = 50\n", "N = sunspot_df.shape[0]" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "INFO (theano.gof.compilelock): Refreshing lock /Users/fonnescj/.theano/compiledir_Darwin-17.0.0-x86_64-i386-64bit-i386-3.6.1-64/lock_dir/lock\n" ] } ], "source": [ "with pm.Model() as model:\n", " alpha = pm.Gamma('alpha', 1., 1.)\n", " beta = pm.Beta('beta', 1, alpha, shape=K)\n", " w = pm.Deterministic('w', stick_breaking(beta))\n", " \n", " mu = pm.Uniform('mu', 0., 300., shape=K)\n", " obs = pm.Mixture('obs', w, pm.Poisson.dist(mu), observed=sunspot_df['sunspot.year'])" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "scrolled": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 100000/100000 [03:23<00:00, 490.60it/s]\n" ] } ], "source": [ "with model:\n", " step = pm.Metropolis()\n", " trace = pm.sample(10000, step=step, tune=90000, random_seed=SEED)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For the sunspot model, the posterior distribution of $\\alpha$ is concentrated between 0.6 and 1.2, indicating that we should expect more components to contribute non-negligible amounts to the mixture than for the Old Faithful waiting time model." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAA18AAACICAYAAAAYlVFjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace, varnames=['alpha']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed, we see that between ten and fifteen mixture components have appreciable posterior expected weight." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgQAAAF3CAYAAADaXFNkAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkgT8f3pIN5oN8Fa1AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "plot_w = np.arange(K) + 1\n", "\n", "ax.bar(plot_w - 0.5, trace['w'].mean(axis=0), width=1., lw=0);\n", "\n", "ax.set_xlim(0.5, K);\n", "ax.set_xlabel('Component');\n", "\n", "ax.set_ylabel('Posterior expected mixture weight');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now calculate and plot the fitted density estimate." ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "x_plot = np.arange(250)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [], "source": [ "post_pmf_contribs = sp.stats.poisson.pmf(np.atleast_3d(x_plot),\n", " trace['mu'][:, np.newaxis, :])\n", "post_pmfs = (trace['w'][:, np.newaxis, :] * post_pmf_contribs).sum(axis=-1)\n", "\n", "post_pmf_low, post_pmf_high = np.percentile(post_pmfs, [2.5, 97.5], axis=0)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdMAAAF3CAYAAAD+c6FVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.hist(sunspot_df['sunspot.year'].values, bins=40, normed=True, lw=0, alpha=0.75);\n", "\n", "ax.fill_between(x_plot, post_pmf_low, post_pmf_high,\n", " color='gray', alpha=0.45)\n", "ax.plot(x_plot, post_pmfs[0],\n", " c='gray', label='Posterior sample densities');\n", "ax.plot(x_plot, post_pmfs[::200].T, c='gray');\n", "ax.plot(x_plot, post_pmfs.mean(axis=0),\n", " c='k', label='Posterior expected density');\n", "\n", "ax.set_xlabel('Yearly sunspot count');\n", "ax.set_yticklabels([]);\n", "ax.legend(loc=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, we can decompose the posterior expected density into weighted mixture densities." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdMAAAF3CAYAAAD+c6FVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nM2uQk6mZmVmDnEzNzMwa9B/OmUyoWHpLAAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "ax.hist(sunspot_df['sunspot.year'].values, bins=40, normed=True, lw=0, alpha=0.75);\n", "ax.plot(x_plot, post_pmfs.mean(axis=0),\n", " c='k', label='Posterior expected density');\n", "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pmf_contribs).mean(axis=0)[:, 0],\n", " '--', c='k', label='Posterior expected\\nmixture components\\n(weighted)');\n", "ax.plot(x_plot, (trace['w'][:, np.newaxis, :] * post_pmf_contribs).mean(axis=0),\n", " '--', c='k');\n", "\n", "ax.set_xlabel('Yearly sunspot count');\n", "ax.set_yticklabels([]);\n", "ax.legend(loc=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An earlier version of this example first appeared [here](http://austinrochford.com/posts/2016-02-25-density-estimation-dpm.html)." ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" }, "widgets": { "state": {}, "version": "1.1.2" } }, "nbformat": 4, "nbformat_minor": 1 }