{ "cells": [ { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "P20Z1RhWhPzX" }, "source": [ "##### Copyright 2018 The TensorFlow Authors.\n", "\n", "Licensed under the Apache License, Version 2.0 (the \"License\");" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "colab": { }, "colab_type": "code", "collapsed": false, "id": "qS8MroChhSxR" }, "outputs": [ ], "source": [ "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n", "# you may not use this file except in compliance with the License.\n", "# You may obtain a copy of the License at\n", "#\n", "# https://www.apache.org/licenses/LICENSE-2.0\n", "#\n", "# Unless required by applicable law or agreed to in writing, software\n", "# distributed under the License is distributed on an \"AS IS\" BASIS,\n", "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n", "# See the License for the specific language governing permissions and\n", "# limitations under the License." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "0ufLLTrrPIhi" }, "source": [ "# Probabilistic PCA\n", "\n", "\n", " \n", " \n", "
\n", " You can run this in CoCalc!\n", " \n", " View source on GitHub\n", "
\n" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "Py-bl6M32ZXY" }, "source": [ "Probabilistic principal components analysis (PCA) is a\n", "dimensionality reduction technique that\n", "analyzes data via a lower dimensional latent space\n", "([Tipping and Bishop 1999](#1)). It is often\n", "used when there are missing values in the data or for multidimensional\n", "scaling." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "WHNNrlLNPbpA" }, "source": [ "## Imports" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": { }, "colab_type": "code", "collapsed": false, "id": "mbM5dCFdUior" }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/local/lib/python3.6/dist-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " from ._conv import register_converters as _register_converters\n" ] } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import seaborn as sns\n", "\n", "import tensorflow as tf\n", "import tensorflow_probability as tfp\n", "from tensorflow_probability import edward2 as ed\n", "import warnings\n", "\n", "plt.style.use(\"ggplot\")\n", "warnings.filterwarnings('ignore')" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "QjIXsU55eq-d" }, "source": [ "## The Model\n", "\n", "Consider a data set $\\mathbf{X} = \\{\\mathbf{x}_n\\}$ of $N$ data\n", "points, where each data point is $D$-dimensional, $\\mathbf{x}_n \\in\n", "\\mathbb{R}^D$. We aim to represent each $\\mathbf{x}_n$ under a latent\n", "variable $\\mathbf{z}_n \\in \\mathbb{R}^K$ with lower dimension, $K <\n", "D$. The set of principal axes $\\mathbf{W}$ relates the latent variables to\n", "the data.\n", "\n", "Specifically, we assume that each latent variable is normally distributed,\n", "\n", "\\begin{equation*}\n", "\\mathbf{z}_n \\sim N(\\mathbf{0}, \\mathbf{I}).\n", "\\end{equation*}\n", "\n", "The corresponding data point is generated via a projection,\n", "\n", "\\begin{equation*}\n", "\\mathbf{x}_n \\mid \\mathbf{z}_n\n", "\\sim N(\\mathbf{W}\\mathbf{z}_n, \\sigma^2\\mathbf{I}),\n", "\\end{equation*}\n", "\n", "where the matrix $\\mathbf{W}\\in\\mathbb{R}^{D\\times K}$ are known as\n", "the principal axes. In probabilistic PCA, we are typically interested in\n", "estimating the principal axes $\\mathbf{W}$ and the noise term\n", "$\\sigma^2$.\n", "\n", "Probabilistic PCA generalizes classical PCA. Marginalizing out the the\n", "latent variable, the distribution of each data point is\n", "\n", "\\begin{equation*}\n", "\\mathbf{x}_n \\sim N(\\mathbf{0}, \\mathbf{W}\\mathbf{W}^\\top + \\sigma^2\\mathbf{I}).\n", "\\end{equation*}\n", "\n", "Classical PCA is the specific case of probabilistic PCA when the\n", "covariance of the noise becomes infinitesimally small, $\\sigma^2 \\to 0$.\n", "\n", "We set up our model below. In our analysis, we assume $\\sigma$ is known, and\n", "instead of point estimating $\\mathbf{W}$ as a model parameter, we\n", "place a prior over it in order to infer a distribution over principal\n", "axes." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "colab": { }, "colab_type": "code", "collapsed": false, "id": "Gwc6maZifKnb" }, "outputs": [ ], "source": [ "def probabilistic_pca(data_dim, latent_dim, num_datapoints, stddv_datapoints): # (unmodeled) data\n", " w = ed.Normal(loc=tf.zeros([data_dim, latent_dim]),\n", " scale=2.0 * tf.ones([data_dim, latent_dim]),\n", " name=\"w\") # parameter\n", " z = ed.Normal(loc=tf.zeros([latent_dim, num_datapoints]),\n", " scale=tf.ones([latent_dim, num_datapoints]), \n", " name=\"z\") # parameter\n", " x = ed.Normal(loc=tf.matmul(w, z),\n", " scale=stddv_datapoints * tf.ones([data_dim, num_datapoints]),\n", " name=\"x\") # (modeled) data\n", " return x, (w, z)\n", "\n", "log_joint = ed.make_log_joint_fn(probabilistic_pca)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "x2zF-wrTVSK4" }, "source": [ "## The Data" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "n4HYhXlTVZ1_" }, "source": [ "We can use the Edward2 model to generate data." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 68 }, "colab_type": "code", "collapsed": false, "id": "b23iIkX8VVyn", "outputId": "86fc2c3d-61f8-4625-e272-5d3c9b836aeb" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Principal axes:\n", "[[-0.19042172]\n", " [ 3.2923143 ]]\n" ] } ], "source": [ "num_datapoints = 5000\n", "data_dim = 2\n", "latent_dim = 1\n", "stddv_datapoints = 0.5\n", "\n", "model = probabilistic_pca(data_dim=data_dim,\n", " latent_dim=latent_dim,\n", " num_datapoints=num_datapoints,\n", " stddv_datapoints=stddv_datapoints)\n", "\n", "with tf.Session() as sess:\n", " x_train, (actual_w, actual_z) = sess.run(model)\n", "\n", "print(\"Principal axes:\")\n", "print(actual_w)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "O2ZdIFz7VuSO" }, "source": [ "We visualize the dataset." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 364 }, "colab_type": "code", "collapsed": false, "id": "ubJJvk0KVyVW", "outputId": "5f6effe3-f36d-474d-eb08-49f061c8b012" }, "outputs": [ { "data": { "image/png": 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" }, "execution_count": 5, "metadata": { "image/png": { "height": 265, "width": 383 } }, "output_type": "execute_result" } ], "source": [ "plt.scatter(x_train[0, :], x_train[1, :], color='blue', alpha=0.1)\n", "plt.axis([-20, 20, -20, 20])\n", "plt.title(\"Data set\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "qIZepLMgItfq" }, "source": [ "## Maximum a Posteriori Inference\n", "\n", "We first search for the point estimate of latent variables that maximizes the posterior probability density. This is known as maximum a posteriori (MAP) inference, and is done by calculating the values of $\\mathbf{W}$ and $\\mathbf{Z}$ that maximise the posterior density $p(\\mathbf{W}, \\mathbf{Z} \\mid \\mathbf{X}) \\propto p(\\mathbf{W}, \\mathbf{Z}, \\mathbf{X})$.\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "colab": { }, "colab_type": "code", "collapsed": false, "id": "s2AvQAYqIh6K" }, "outputs": [ ], "source": [ "tf.reset_default_graph()\n", "\n", "w = tf.Variable(np.ones([data_dim, latent_dim]), dtype=tf.float32)\n", "z = tf.Variable(np.ones([latent_dim, num_datapoints]), dtype=tf.float32)\n", "\n", "\n", "def target(w, z):\n", " \"\"\"Unnormalized target density as a function of the parameters.\"\"\"\n", " return log_joint(data_dim=data_dim,\n", " latent_dim=latent_dim,\n", " num_datapoints=num_datapoints,\n", " stddv_datapoints=stddv_datapoints,\n", " w=w, z=z, x=x_train)\n", "\n", "\n", "energy = -target(w, z)\n", "\n", "optimizer = tf.train.AdamOptimizer(learning_rate=0.05)\n", "train = optimizer.minimize(energy)\n", "\n", "init = tf.global_variables_initializer()\n", "\n", "t = []\n", "\n", "num_epochs = 200\n", "\n", "with tf.Session() as sess:\n", " sess.run(init)\n", "\n", " for i in range(num_epochs):\n", " sess.run(train)\n", " if i % 5 == 0:\n", " cE, cw, cz = sess.run([energy, w, z])\n", " t.append(cE)\n", "\n", " w_inferred_map = sess.run(w)\n", " z_inferred_map = sess.run(z)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 364 }, "colab_type": "code", "collapsed": false, "id": "UL1PmOM34brs", "outputId": "3929bdbb-0666-444d-a9c5-414bbc2acefc" }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 7, "metadata": { }, "output_type": "execute_result" }, { "data": { "image/png": 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CwwNUXfC66r4NUvTNGvpmDX2zhr5ZQ9+soW/WBKpvMTExgShHUoDuZNx///2KjY1VYmKiKioq9Nvf/vaix06bNk3/8A//oPHjx/vtr6io0JNPPqlXX31Vs2fP1rBhw3w/q6ysVF5enhISErR69WrfX9qXLl2qRx55RGvXrtWMGTMUHx/vm1NYWCiXy6W0tDStXLlS4ef/ortgwQI9/vjjWrNmjTIyMhQZGembk5eXp8rKSmVnZ+uXv/ylHA7P02Q5OTl6+umn9eKLL+qZZ57x7Zek119/XdXV1frud7+r+++/37f/vffe08svv6w//elPeuyxx6y0tV8yro+VxqdKRw9LbrfM/SUysufbXRYAAAD6UEDWZGRkZCgpKUmGYVz22Hnz5nULGJI0adIkTZ48WR0dHaqsrPT72QcffCBJys3N9bsrEB8fr4ULF6q9vV0FBQU9zlm+fLkvYEhSSkqKcnJydPbsWblcLt9+0zR9c+69916/IDFz5kylp6erqqpKFRUVvv0tLS3avn27nE6nli1b5nf9RYsWKS4uTmVlZTpxYnAtgDYyb/Zt85YpAACAwSeoFn6HhIT4/X+v8vJySZ67IN80ffp0v2Mkz2NPlZWVcjqdSk9P7zbHe56uc06cOKH6+nolJSX53RG51JzDhw+rra1NEydO9LsjIkkOh0OZmZ5F0AcOHLjYH3lAMqZlXxiUl8o812hfMQAAAOhzAXlcKhDq6upUXl7eLRi0tLTo1KlTioiI8HuEyisxMVGSZ0G5V01Njdxut+Lj47sFFklKSkrqNuerr77y+1kg5nhr8x53OStWrOhx/1NPPSVJGjFiRK/OczVCz7+C9mquZcbG6mTyOHVWHZNamxXx0SbF3PevAaowOAWib4MRfbOGvllD36yhb9bQN2vomzXB2LeguJPR3t6u5557Tu3t7fre977n90iUdwGLd0HLN3n3nzt3rk/mdF1QY2XOYGAYhqLvecA3bsp7S511NTZWBAAAgL5k+50Mt9ut//7v/1ZlZaVycnJ0553WXnnam/UgXqZpWp5zLXnvWFxMfX39Na/Bm4Cv9lpm6lRp3ATp2KdSe5tOvvS8HD/+ZSBKDEqB6ttgQ9+soW/W0Ddr6Js19M0a+mZNoPo2cuTIQJQjyeY7GW63W88995xcLpdmz56tn//8593+4n+5uwE93U243Jzm5uY+mXO5Ox0DmWEYctz9Q9/YdOXLrDpqX0EAAADoM7aFjM7OTj377LMqKirSLbfcooceeqjH9RMREREaPny4WlpadPr06W4/r6nxPIbTdV1EYmKiHA6Hamtr1dnZ2W2Od11F1zne5NZ1zcXVzvHWFshU2J8YaVOkqTM9A9OU+52/2FsQAAAA+oQtIaOjo0P/9V//JZfLpblz5+rf/u3f/F4Z+03er4Dv27ev289KS0v9jpGksLAwpaWlqbW1VQcPHuw2x3uernMSEhI0YsQIVVdXq7a2tldzUlNTFR4erkOHDvnudHi53W6VlZVJkiZPnnzRP9tA58i9XzLO/29bvlfmwTJ7CwIAAMA11+cho729XU8//bR2796t2267Tf/n//yfSwYMyfMBPUlav369GhsvvA61trZWW7duVVhYmObNm9fjnHXr1qmtrc23/8iRIyoqKtLQoUP9vkhuGIZvzquvviq32+37WUlJiQ4ePKjk5GRNmjTJtz8iIkJz585Va2ur3nrrLb/rb9myRXV1dcrMzFRCQkJvWjMgGaPGyJjzbd/Y/fbLMrv0FgAAAANPQBZ+FxcXq6SkRJJ05swZSdKnn36qF154QZLnE+X33XefJOl//ud/VFpaqpiYGA0fPlxvv/12t/NNnjzZ71//09LStGTJEuXl5enXv/61Zs2apY6ODn388cdqbGzUj3/8427ftpgzZ46Ki4vlcrm0YsUKZWVlqaGhQUVFRXK73XrwwQe7rZVYsmSJ9u7dK5fLpccee0wZGRmqr6+Xy+WS0+nUz372s26B6Pvf/74OHDigvLw8HTt2TCkpKaqqqtLu3bt13XXX6YEHHtBgZyz9Z5nFH0ltbdIXn8ks2SFj1rfsLgsAAADXSEBCxrFjx/TRRx/57Ttx4oTvS9dxcXG+kOF9FKmhoaHHgOH1zUeM7rvvPo0ZM0Zbt27Vtm3bZBiGxo8fr6VLlyorK6vbfMMw9NBDDyk1NVX5+fnavHmzwsPDNWnSJOXm5iotLa3bnLCwMK1cuVIbNmzQzp07tWnTJkVGRmrmzJlatmyZkpOTu82JiYnR7373O7311lu+Ox4xMTGaN2+eli9frtjY2Mt0b+AzhsXK+M4/yHzPc7fHfHetzBk5MsLCbK4MAAAA14Jh9sW7WREQvf2o39W4Vq+OM5vOyf3Yg1LjWUmSsewBORb8Q0CvYSdeuWcNfbOGvllD36yhb9bQN2vomzW8whaDlhE1RMaSe3xjM2+dzHONl5gBAACA/oqQgT5jfGuhFJfoGTQ1ytx88cflAAAA0H8RMtBnjNAwGXfd5xub2zbKPFlnY0UAAAC4FggZ6FPGTXOkcRM8g452mX99zd6CAAAAEHCEDPQpwzDkuPuHvrHpypf55VH7CgIAAEDAETLQ54y0KdLUmZ6Bacq9/i/2FgQAAICAImTAFo7c+yXj/K9f+V6ZFfvsLQgAAAABQ8iALYxRY2TM+bZv7H7nZZlut40VAQAAIFAIGbCNsfSfpfBwz+CLv8ss2WFvQQAAAAgIQgZsYwyLlfGdC1/9Nt9dK7O93caKAAAAEAiEDNjKWJgrRQ/1DE7WyszfZG9BAAAAuGqEDNjKiBoiY8k9vrG56U2Z5xptrAgAAABXi5AB2xnfWijFJXoGTY0yN79tb0EAAAC4KoQM2M4IDZNx132+sblto8yTdTZWBAAAgKtByEBQMG6aI42b4Bl0tMv862v2FgQAAADLCBkICoZhyHH3j3xj05Uv88ujNlYEAAAAqwgZCBpGWoY0daZnYJpyv/OyrfUAAADAGkIGgooj937JOP9reaBUZsU+ewsCAADAFSNkIKgYo8bImPNt39i98XUbqwEAAIAVhAwEHePO70shoZ7BkYMyP62wtyAAAABcEUIGgo4xfISM2fN9Y/eWd2ysBgAAAFeKkIGgZCy8SzIMz+CTEplVx2ytBwAAAL1HyEBQMhKTpenZvrG5db2N1QAAAOBKEDIQtByL/sm3bRZvl3my1sZqAAAA0FuEDAQtY3yqNHGqZ+B2y3x/g70FAQAAoFcIGQhqfnczdr4vs+FrG6sBAABAbxAyENwmTZPG3ODZbmuT+eEme+sBAADAZREyENQMw5DR9W7Gh3kyW5ptrAgAAACXQ8hA0DNm5EhxiZ5BU6PMHe/bWxAAAAAuiZCBoGeEhMhYmOsbmx/8VWZHu40VAQAA4FIIGegXjJzbpKHXewan62Xu2m5vQQAAALgoQgb6BSMsXMZ3lvrG5pZ3ZLrdNlYEAACAiyFkoN8wvrVYiozyDGqqpE+K7S0IAAAAPSJkoN8woobImLvIN3ZvfkemadpYEQAAAHpCyEC/YnxnqRQa6hn8vVL69IC9BQEAAKAbQgb6FeP64TJyvu0buze/Y2M1AAAA6AkhA/2OcftdkmF4BuV7ZH551N6CAAAA4IeQgX7HSBjp+UDfeeaW9TZWAwAAgG8iZKBfMhb/k2/bLNkhs67GxmoAAADQFSED/ZIxNkVKz/QMTLfM9zfYWxAAAAB8CBnotxyL7/Ztm4V/k3n2jI3VAAAAwIuQgf5r4lRpbIpnu71N5rY8e+sBAACAJEIG+jHDMOToujajYJPMliYbKwIAAIBEyEB/Nz1bih/p2W46J3P7VnvrAQAAACED/ZvhCJGxKNc3Nj/4q8z2dhsrAgAAACED/Z6RPV+6brhncOaUTFe+vQUBAAAMcoQM9HtGWJiMBUt9Y/P9d2W6O22sCAAAYHAjZGBAMOYukiKHeAY1x6V9u+wtCAAAYBALDcRJXC6XKioqdOzYMX3++edqbm7WLbfcol/84hcXnVNZWan169fr8OHDam9vV2JioubPn6/FixfL4eg5++zZs0cbN27U0aNH5Xa7NXr0aN1+++2aN2/eRa9TUFCgrVu3qqqqSg6HQ+PHj9edd96prKysHo93u93avHmz8vPzVV1drfDwcKWmpio3N1dpaWk9zmlra9OGDRtUWFio+vp6RUZGatKkSVq2bJmSk5Mv3jgEjBEZJWPeYpmb35Ykubesl2P6bBmGYXNlAAAAg0/IqlWrVl3tSf74xz9qz549amxsVGxsrBoaGjRmzBjNmjWrx+NLSkr0+9//XqdOnVJ2drYmTZqk48ePa+fOnaqqqtLs2bO7zdmyZYuef/55tbS0aM6cOUpJSdGRI0e0fft2NTc3KzMzs9ucV155Ra+99pocDoduvfVWjR49WuXl5crPz1dMTIxSUlL8jjdNU88++6w2bdqkIUOGaO7cuYqLi9PevXu1bds2jR07VqNGjfKb097erieffFI7duxQQkKCcnJyFBMTo+LiYuXn52vKlCmKjY29iu5e0NDQEJDzXEpUVJQkqampH74KdtQYmR9uktxu6cxJGakZMkYk9Mml+3XfbETfrKFv1tA3a+ibNfTNGvpmTaD6FhMTE4hyJAXoTsb999+v2NhYJSYmqqKiQr/97W8vemxTU5PWrFkjh8OhVatW6cYbb5QkLV++XE888YRcLpcKCws1Z84c35za2lqtXbtW0dHRWr16teLj4yVJd999tx599FHl5eUpOztbqampvjmVlZXKy8tTQkKCVq9erejoaEnS0qVL9cgjj2jt2rWaMWOG71ySVFhYKJfLpbS0NK1cuVLh4eGSpAULFujxxx/XmjVrlJGRocjISN+cvLw8VVZWKjs7W7/85S99d2FycnL09NNP68UXX9Qzzzxz0bszCBxj6DAZc74t86MtkiT35ncUMnGqzVUBAAAMPgH5m29GRoaSkpJ69WiKy+XS2bNnlZOT4wsYkhQeHq577rlHkvT+++/7zcnPz1d7e7sWLVrkFwqio6N111139Tjngw8+kCTl5ub6AoYkxcfHa+HChWpvb1dBQUGPc5YvX+4LGJKUkpKinJwcnT17Vi6Xy7ffNE3fnHvvvdcvSMycOVPp6emqqqpSRUXFZfuCwDBuv0syzv/vUFEqs+qovQUBAAAMQn3+z+vl5eWSpGnTpnX7WXp6upxOp2+dRm/mTJ8+XZJ04MCBXl/HO8d7jOR57KmyslJOp1Pp6end5njP03XOiRMnVF9fr6SkJL/wc6k5uLaM+CQZWTm+sflxgX3FAAAADFJ9HjKqq6slSSNHjuz2s5CQEMXHx6uzs1MnTpzw7f/qq68kSUlJSd3mDBs2TE6nUydPnlRra6skqaWlRadOnVJERISGDRvWbU5iYqJfLZJUU1Mjt9ut+Ph4hYSEdJvjvXbXOZeq62JzcO0ZOd/2bZvFH/E6WwAAgD4WkDUZV8K7IMW7QOWbelq40ps5ra2tampqktPp7PU1zp07d8V1WZnT20U4K1as6HH/U089JUkaMWJEr85zNUJDQ/vsWteKOffbqnv5jzLPnpHOnNJ1NV8qfOpN1/SaA6FvdqBv1tA3a+ibNfTNGvpmDX2zJhj7FnSrkU3TtDz3Sl9XeiXHe+uyMgd9ywgJVcQt3/GNm7e/f4mjAQAAEGh9fifjcv+639zc7Hecd7uhoUFNTU09vlrLey7vW58ud42e7kBYretK51yK947FxdTX1/fqPFfDm4D74lrXkpk5S3rP882MlqIP1fZPP5QRFn6ZWdYNlL71NfpmDX2zhr5ZQ9+soW/W0DdrAtW3npYzWNXndzK86xS86xm66uzsVG1trUJCQpSQcOH7Bt4/cE9rG06fPq3W1lbFxsbK6XRKkiIiIjR8+HC1tLTo9OnT3ebU1NT41SJ51mk4HA7V1taqs7P7M/zea3edc6m6LjYHfWR8qhTnWXuj5ibpkxJ76wEAABhE+jxkZGRkSJL27dvX7WcHDx5Ua2urUlNTFRYW1qs5paWlkqTJkyf3+jreOd5jJCksLExpaWlqbW3VwYMHu83xnqfrnISEBI0YMULV1dWqra3t1Rz0DcMwZMya5xu7XR/ZVwwAAMAg0+chIzvaX05AAAAgAElEQVQ7WzExMSoqKtJnn33m29/W1qY33nhDknT77bf7zZk/f77CwsK0ZcsWv7/MNzY26t133+1xzoIFCyRJ69evV2Njo29/bW2ttm7dqrCwMM2bN6/HOevWrVNbW5tv/5EjR1RUVKShQ4f6fcXcMAzfnFdffVVut9v3s5KSEh08eFDJycmaNGlSL7uDQDJmfevCYP9umeeu/RfTAQAAIIWsWrVq1dWepLi4WBs2bFBJSYn27dunEydOqLW1VUePHlVJSYkOHTqkzMxMSZ47BklJSSoqKtKOHTtUW1urQ4cO6S9/+YuOHTum7OxsLVu2zG+B9ZAhQxQVFaXi4mLt2LFDdXV1+uSTT/TSSy+prq5OS5Ys0W233eZX04gRI9Tc3KzS0lLt3LlT9fX12r17t15++WU1Njbqhz/8oa8mr9GjR6uqqkplZWXatWuX6uvrVVhYqFdffVWdnZ36+c9/rnHjxvnNSUlJ0YEDB1RWVqbS0lKdOHFC+fn5euuttxQeHq6HH344YCv9Gxqu/V+SA/VZ+mBgRA+VuX+3dOaUZLqluEQZY1OuybUGUt/6En2zhr5ZQ9+soW/W0Ddr6Js1gepbT2ufrTLMALwC6c0339Tbb7990Z/HxcXphRde8Nt36NAhvfvuuzp8+LDa2tqUmJio+fPn64477vD7cnZXu3fv1saNG3X06FGZpqnk5GQtXLiw2x2JrgoKCrR161ZVVVXJMAyNHz9eS5cuVVZWVo/Hd3Z2avPmzcrPz1dNTY3Cw8OVmpqq3NxcpaWl9Tinra1NGzZs8IWZyMhITZ48WcuWLVNycvJFa7tSPa1jCbSBtuDK/bf/lbnuT55B6mSF/Hr1NbnOQOtbX6Fv1tA3a+ibNfTNGvpmDX2zJhgXfgckZKBvEDKunHn2tNy//pF0/lE2x//zJxmx3b/OfrUGWt/6Cn2zhr5ZQ9+soW/W0Ddr6Js1wRgygu47GUAgGUOHSekXHoszi7fbWA0AAMDgQMjAgNf1LVOmq4CPJAIAAFxjhAwMeMb0WVL4+Q/xffWFVHXM1noAAAAGOkIGBjwjIkrGtGzf2NxVYF8xAAAAgwAhA4NC129mmLu2y+zyTRMAAAAEFiEDg8Ok6VL0UM/2mZPS4XJ76wEAABjACBkYFIzQUBkzb/GNzV0f2VgNAADAwEbIwKDh95apPUUy29vsKwYAAGAAI2Rg8LghTYpL9Gw3n5P277a3HgAAgAGKkIFBwzAMvwXgbleBfcUAAAAMYIQMDCpdQ4b275Z5rtG+YgAAAAYoQgYGFSMxWRqb4hl0dMjcW2RvQQAAAAMQIQODjt83M3hkCgAAIOAIGRh0jJm3Ssb5X/3D5TJP1dlbEAAAwABDyMCgY1w/XEqf6hubxdttrAYAAGDgIWRgUOKRKQAAgGuHkIFByZg+WwoP9wyOfy6z6pit9QAAAAwkhAwMSkZklIzMWb6xuesjG6sBAAAYWAgZGLT8Hpkq/kim221jNQAAAAMHIQOD1+TpUnSMZ/tUvfRphb31AAAADBCEDAxaRmiYjJtu8Y3NXQX2FQMAADCAEDIwqPk9MrWnUGZ7u43VAAAADAyEDAxuN6ZLsfGe7aZz0v7d9tYDAAAwABAyMKgZhiFj1jzf2M1bpgAAAK4aIQODnpF94ZEpfVIss6nRvmIAAAAGAEIGBj0jabQ05gbPoKND5p4iewsCAADo5wgZgOT3yBQf5gMAALg6hAxAknHzrZJheAaHy2Weqre3IAAAgH6MkAFIMq6PlSZO9QxMU2bJdnsLAgAA6McIGcB5fo9MuXhkCgAAwCpCBnCeMWO2FBbuGVQdlXn8c3sLAgAA6KcIGcB5RmSUjKkzfWNzV4F9xQAAAPRjhAygCyN7nm/bLN4h0zTtKwYAAKCfImQAXWXMkCKHeLZP1kpffGZvPQAAAP0QIQPowggNk5HZ5ZGpvR/bWA0AAED/RMgAvsGYkePbJmQAAABcOUIG8E2TpkvhTs92TZXMr76wtx4AAIB+hpABfIPhdEoZWb4xdzMAAACuDCED6IExY7Zv2ywlZAAAAFwJQgbQA2PqTCk01DP44u8y62rsLQgAAKAfIWQAPTAio6T0ab4xdzMAAAB6j5ABXIQxPdu3zboMAACA3iNkABdhTMuWjPP/iXx2SOaZU/YWBAAA0E8QMoCLMGKGSqmTfWOz1GVjNQAAAP0HIQO4BN4yBQAAcOUIGcAlGNMvhAxV7pfZeNa+YgAAAPoJQgZwCcawWOmGNM/A7ZZZVmJvQQAAAP0AIQO4DL9HpvYW2VgJAABA/0DIAC7D75GpilKZLU32FQMAANAPhNp58b179+q9995TVVWVGhoaNGzYMN1www1asmSJUlNTux1fWVmp9evX6/Dhw2pvb1diYqLmz5+vxYsXy+HoOS/t2bNHGzdu1NGjR+V2uzV69Gjdfvvtmjdv3kXrKigo0NatW1VVVSWHw6Hx48frzjvvVFZWVo/Hu91ubd68Wfn5+aqurlZ4eLhSU1OVm5urtLQ0S71B8DDik6Tk8VLVUamjQ+b+PTJm3mp3WQAAAEErZNWqVavsuPCrr76qP//5z2pqalJWVpYyMjIUFham3bt368MPP1RCQoLGjh3rO76kpES///3vderUKWVnZ2vSpEk6fvy4du7cqaqqKs2ePbvbNbZs2aLnn39eLS0tmjNnjlJSUnTkyBFt375dzc3NyszM7DbnlVde0WuvvSaHw6Fbb71Vo0ePVnl5ufLz8xUTE6OUlBS/403T1LPPPqtNmzZpyJAhmjt3ruLi4rR3715t27ZNY8eO1ahRowLSs4aGhoCc51KioqIkSU1N/Gu9n4avpcr9kiRDhoybbvH7MX2zhr5ZQ9+soW/W0Ddr6Js19M2aQPUtJiYmEOVIsulOxpkzZ7Rx40Zdd911euaZZ3Tdddf5flZeXq4nnnhCb775pubOnSvJ07A1a9bI4XBo1apVuvHGGyVJy5cv1xNPPCGXy6XCwkLNmTPHd57a2lqtXbtW0dHRWr16teLj4yVJd999tx599FHl5eUpOzvb745JZWWl8vLylJCQoNWrVys6OlqStHTpUj3yyCNau3atZsyY4TuXJBUWFsrlciktLU0rV65UeHi4JGnBggV6/PHHtWbNGmVkZCgyMvIadRN9wZgxW+b//l9Jklm+R2Zbq4xwp81VAQAABCdb1mTU1dXJNE1NmDDBL2BI8v2F/OzZC68KdblcOnv2rHJycnwBQ5LCw8N1zz33SJLef/99v/Pk5+ervb1dixYt8gsF0dHRuuuuu3qc88EHH0iScnNzfQFDkuLj47Vw4UK1t7eroKCgxznLly/3BQxJSklJUU5Ojs6ePSuXi4+49Xsjx0gJ5+9ItbZIFfvsrQcAACCI2RIykpKSFBoaqiNHjviFCUmqqKhQc3OzpkyZ4ttXXl4uSZo2bVq3c6Wnp8vpdPrWafRmzvTp0yVJBw4c8NvfmzneYySpvb1dlZWVcjqdSk9P7zbHe56uc9A/GYYhY0a2b2zu5cN8AAAAF2PL41LR0dH6wQ9+oFdeeUW/+tWvNHPmTMXExKimpkZ79uzR1KlT9ZOf/MR3fHV1tSRp5MiR3c4VEhKi+Ph4ffnllzpx4oSSk5MlSV999ZUkT6D5pmHDhsnpdOrkyZNqbW2V0+lUS0uLTp06pYiICA0bNqzbnMTERL9aJKmmpkZut1vx8fEKCQnpNsd77a5zLmXFihU97n/qqackSSNGjOjVea5GaGhon12rv2mfv1inNr/jGewvUez118s43y/6Zg19s4a+WUPfrKFv1tA3a+ibNcHYN9veLvXd735XcXFxevHFF7Vt2zbf/sTERM2bN8/vMSrvIhbvopZv6mmxS2/mtLa2qqmpSU6ns9fXOHfu3BXX1XUO+q/QlHQ5RiTIXX9CZmOD2sr3yjntZrvLAgAACDq2hYy//vWvev3117V48WItWrRI119/vY4fP67XX39dzz33nI4dO6Z77723V+cyTdNyHYZhXLPjvXX1do73jsXF1NfX9/raVnkTcF9cqz8yM2+Wtm2UJH1dsEWO5Bsk0Ter6Js19M0a+mYNfbOGvllD36wJVN96emrIKlvWZBw4cECvvfaabrrpJt1///1KSEiQ0+nUDTfcoIcffljDhw/Xxo0bdeLECUmXfy1Xc3Oz33G9mePd733rU2+Pv5Jr9FQX+je/r3+XumS6O22sBgAAIDjZEjL27NkjSZo8eXK3nzmdTqWkpMg0TR09elTShbUN3nUWXXV2dqq2tlYhISFKSEjw7fcmsZ7WQ5w+fVqtra2KjY2V0+l5DWlERISGDx+ulpYWnT59utucmpoav1okz6NdDodDtbW16uzs/pdN77V7WheCfiolXYo5/yjf2TPSZ5X21gMAABCEbAkZHR0dktTtzVJe3v3eRSwZGRmSpH37ur829ODBg2ptbVVqaqrCwsJ8+y81p7S0VFL3kNObOd5jJCksLExpaWlqbW3VwYMHu83xnqfrHPRvhiNExnTeMgUAAHAptoSMiRMnSpL+9re/6dSpU34/Ky0tVWVlpe8v8JKUnZ2tmJgYFRUV6bPPPvMd29bWpjfeeEOSdPvtt/udZ/78+QoLC9OWLVtUW1vr29/Y2Kh33323xzkLFiyQJK1fv16NjY2+/bW1tdq6davCwsI0b968HuesW7dObW1tvv1HjhxRUVGRhg4dqlmzZvWyM+gPjOldH5n6+KrWBAEAAAxEtiz8zs7O1pQpU7R//379+7//u2bOnOlb+L13716Zpqkf/OAHvk+bR0VF6cEHH9Qf/vAHrVq1SnPmzFF0dLR2796tr776StnZ2crJyfG7Rnx8vO6991699NJLevTRRzV79myFhoZq165dOnnypJYsWeL3tW9JSktL05IlS5SXl6df//rXmjVrljo6OvTxxx+rsbFRP/7xj/0+7CdJc+bMUXFxsVwul1asWKGsrCw1NDSoqKhIbrdbDz74IGsyBpqJU6TIIVLzOelkrfTFZ1JcnN1VAQAABA3DtOmfYTs6OrR161YVFRWpqqpKra2tio6OVkpKihYvXqzMzMxucw4dOqR3331Xhw8fVltbmxITEzV//nzdcccdcjh6vimze/dubdy4UUePHpVpmkpOTtbChQu73ZHoqqCgQFu3blVVVZUMw9D48eO1dOlSZWVl9Xh8Z2enNm/erPz8fNXU1Cg8PFypqanKzc313Y0JhJ7WpAQab3XoHfef/1+ZrnxJknHH9xT/L/8uib5dKX7frKFv1tA3a+ibNfTNGvpmTTC+Xcq2kIErR8gIHmapS+7/7/eeQWKyEl58UxJ9u1L8vllD36yhb9bQN2vomzX0zZpgDBm2rMkA+r1J06Vwz5vJVFOlji+P2lsPAABAECFkABYYTqc05cLjcy2uAvuKAQAACDKEDMCirm+ZanV9ZGMlAAAAwYWQAVhkTJ0pnf+WS8ffD6vzxLVfMwMAANAfEDIAi4zIKCl9mm/MI1MAAAAehAzgKhgzeGQKAADgmwgZwFUwMmdJhuc/o/ZD+2WeOXWZGQAAAAMfIQO4CkbMUCl1sm9slrpsrAYAACA4EDKAq2Rk5fi2zdKPbawEAAAgOBAygKtkTMu+MKjcL7PxrH3FAAAABAFCBnCVjGGxCvM+MuV2yywrsbcgAAAAmxEygABwzp7v2zb3FtlYCQAAgP0IGUAAOGfNvTCoKJXZ0mRfMQAAADYjZAABEJqUrNBxEzyDjg6Z+/fYWxAAAICNCBlAgDizv3VhsIdHpgAAwOBFyAACJGL2PN+2Wb5HZlurfcUAAADYiJABBEjI6PFSwijPoLVFqii1tyAAAACbEDKAADEMQ8aMC9/MMHlkCgAADFKEDCCAjKxbfNtmWbHM9jYbqwEAALAHIQMIpDE3SHGJnu3mJukAj0wBAIDBh5ABBJBhGDJumuMbm7t32lgNAACAPQgZQIAZN/HIFAAAGNwIGUCgjb5Bik/ybLc0Swf22lsPAABAHyNkAAFmGIaMrK6PTBXaWA0AAEDfI2QA14DfI1P7ivkwHwAAGFQIGcC1MHq8FD/Ss93azFumAADAoELIAK6B7m+Z4pEpAAAweBAygGuk21umeGQKAAAMEoQM4FpJHicljPJstzZL5bxlCgAADA6EDOAa6faWqT08MgUAAAYHQgZwDRkzu4QMHpkCAACDBCEDuJZGjZMSvY9MtUjle2wtBwAAoC8QMoBriA/zAQCAwYiQAVxjfm+Z+qREZiuPTAEAgIGNkAFca6PGSonJnm0emQIAAIMAIQO4xrp9mI+3TAEAgAGOkAH0gW4f5uORKQAAMIARMoC+MHKMlDTas93WKpXvtrceAACAa4iQAfQB3jIFAAAGE0IG0Ee6v2WqxcZqAAAArh1CBtBHjFHfeGRqP49MAQCAgYmQAfQhv7dM8cgUAAAYoAgZQB8ysro8MrWfR6YAAMDARMgA+pAxaoznTVOS1NYm8xMemQIAAAMPIQPoY35vmdqz08ZKAAAArg1CBtDHuq7L0P7dMlua7SsGAADgGiBkAH3MGDlGGjXWM2hrk8lbpgAAwABDyABswIf5AADAQBZqdwEHDx7Upk2bdPjwYTU2Nio6OlpjxozRHXfcoRkzZvgdW1lZqfXr1+vw4cNqb29XYmKi5s+fr8WLF8vh6Dkv7dmzRxs3btTRo0fldrs1evRo3X777Zo3b95FayooKNDWrVtVVVUlh8Oh8ePH684771RWVlaPx7vdbm3evFn5+fmqrq5WeHi4UlNTlZubq7S0NMu9wcBl3DRH5v/+X8/g/CNTRkSkvUUBAAAESMiqVatW2XXxd955R88//7zOnj2rGTNmaOrUqYqNjVVdXZ0Mw9DUqVN9x5aUlOj3v/+9Tp06pezsbE2aNEnHjx/Xzp07VVVVpdmzZ3c7/5YtW/T888+rpaVFc+bMUUpKio4cOaLt27erublZmZmZ3ea88soreu211+RwOHTrrbdq9OjRKi8vV35+vmJiYpSSkuJ3vGmaevbZZ7Vp0yYNGTJEc+fOVVxcnPbu3att27Zp7NixGjVqVED61dDQEJDzXEpUVJQkqamp6ZpfayC50r4ZMdfJ3FskNXwtuTul5HEyvI9QDSL8vllD36yhb9bQN2vomzX0zZpA9S0mJiYQ5Uiy8U7Gxx9/rHXr1mnKlCl6+OGHFRnp/6+4HR0dvu2mpiatWbNGDodDq1at0o033ihJWr58uZ544gm5XC4VFhZqzpwLj6DU1tZq7dq1io6O1urVqxUfHy9Juvvuu/Xoo48qLy9P2dnZSk1N9c2prKxUXl6eEhIStHr1akVHR0uSli5dqkceeURr167VjBkzfOeSpMLCQrlcLqWlpWnlypUKDw+XJC1YsECPP/641qxZo4yMjG5/PsC4aY7M459Lksw9hdLNc22uCAAAIDBsWZPhdrv12muvyel06qGHHurxL+ChoRfyj8vl0tmzZ5WTk+MLGJIUHh6ue+65R5L0/vvv+83Pz89Xe3u7Fi1a5BcKoqOjddddd/U454MPPpAk5ebm+gKGJMXHx2vhwoVqb29XQUFBj3OWL1/uCxiSlJKSopycHJ09e1Yul+vyTcGg0/XDfNq/h7dMAQCAAcOWkHH48GHV1tZq+vTpGjJkiPbu3asNGzbovffe0+HDh7sdX15eLkmaNm1at5+lp6fL6XT61mn0Zs706dMlSQcOHOj1dbxzvMdIUnt7uyorK+V0OpWent5tjvc8XecAXkZSspQ8zjNob5P5SYmt9QAAAASKLY9LHTlyRJJ03XXXacWKFfriiy/8fp6enq7/+I//0NChQyVJ1dXVkqSRI0d2O1dISIji4+P15Zdf6sSJE0pOTpYkffXVV5KkpKSkbnOGDRsmp9OpkydPqrW1VU6nUy0tLTp16pQiIiI0bNiwbnMSExP9apGkmpoaud1uxcfHKyQkpNsc77W7zgG6MrLmyKw6Jkkyd+/kkSkAADAg2BIyzp49K8nzqFF8fLxWrlypCRMmqK6uTq+88orKysr0hz/8Qd416d5FLN5FLd/U02KX3sxpbW1VU1OTnE5nr69x7ty5K7rGN+dcyooVK3rc/9RTT0mSRowY0avzXA3vY2p9ca2BxGrfOhYs0cm/vuYZlO/V8CGRckQOCXR5QYvfN2vomzX0zRr6Zg19s4a+WROMfbNtTYbkeTPTr371K02ZMkUREREaPXq0fv3rXys2NlYVFRU9PjrVE9M0LddiGMY1O95b15VeA4NH6KixCh03wTNob1Mr38wAAAADgC13MoYM8fxLbUJCgsaNG+f3s/DwcGVmZurDDz/UkSNHlJqaetnXcjU3exbMdr2jEBUVpYaGBjU1NfX4Oi7vubyLzi93jZ7uWlip61K8dywupr6+vlfnuRreBNwX1xpIrqZv7mmzpGOfSpLOfrhF59JnXGbGwMHvmzX0zRr6Zg19s4a+WUPfrAlU33pammCVLXcyvH8Ab9j4Ju/+trY2SRfWNnjXWXTV2dmp2tpahYSEKCEhods1eloPcfr0abW2tio2NlZOp1OSFBERoeHDh6ulpUWnT5/uNqempsavFsmzTsPhcKi2tladnZ3d5niv3dO6EMCr69e/Vb5HZjPvBgcAAP2bLSEjPT1dISEhqq6u9vsehteXX34pSYqLi5MkZWRkSJL27dvX7diDBw+qtbVVqampCgsL8+2/1JzS0lJJ0uTJk/3292aO9xhJCgsLU1pamlpbW3Xw4MFuc7zn6ToH+CYjcZQ0erxn0NHOW6YAAEC/Z0vIGDp0qGbPnq2mpia9/fbbfj/75JNPVFZWpqioKN8rYLOzsxUTE6OioiJ99tlnvmPb2tr0xhtvSJJuv/12v/PMnz9fYWFh2rJli2pra337Gxsb9e677/Y4Z8GCBZKk9evXq7Gx0be/trZWW7duVVhYmObNm9fjnHXr1vnuvEieN2gVFRVp6NChmjVrVu+bg0Gp690Mc/dOGysBAAC4eiGrvK9w6mMTJ05USUmJSkpKVF5eri+//FLbtm3TG2+8IYfDoX/913/VDTfcIMlzxyApKUlFRUXasWOHamtrdejQIf3lL3/RsWPHlJ2drWXLlvktsB4yZIiioqJUXFysHTt2qK6uTp988oleeukl1dXVacmSJbrtttv8ahoxYoSam5tVWlqqnTt3qr6+Xrt379bLL7+sxsZG/fCHP1RmZqbfnNGjR6uqqkplZWXatWuX6uvrVVhYqFdffVWdnZ36+c9/3m3diVUNDQ0BOc+lBOqz9IPNVfftumEyP8zzbNfXyvj2nTK63JkbqPh9s4a+WUPfrKFv1tA3a+ibNYHqW0/rmK0yzKt5NdNVamxs1DvvvKPi4mKdOnVKkZGRmjhxov7xH/9Rqamp3Y4/dOiQ3n33XR0+fFhtbW1KTEzU/Pnzdccdd8jh6PmmzO7du7Vx40YdPXpUpmkqOTlZCxcu7HZHoquCggJt3bpVVVVVMgxD48eP19KlS5WVldXj8Z2dndq8ebPy8/NVU1Oj8PBwpaamKjc3V2lpaZZ605Oe1qQEGguurAlE3zqf/KX0xd8lScYDv5Ije14gSgtq/L5ZQ9+soW/W0Ddr6Js19M2aYFz4bWvIwJUhZASvQPTN/d5bMt9d6xlk3qyQf/tNIEoLavy+WUPfrKFv1tA3a+ibNfTNmmAMGbasyQDQnXFTl7dMHdgrs6nx4gcDAAAEMUIGECSM+JHS2BTPoKNDZvEOewsCAACwiJABBBEj58LLCMyibTZWAgAAYB0hAwgixqxvSaGhnsHRwzKPf2FvQQAAABYQMoAgYgyJkZF54bsqZtHfbKwGAADAGkIGEGSMOd/xbZsf58vs6LCxGgAAgCtHyACCzeRp0vXDPdsNX0vle+ytBwAA4AoRMoAgYzhCZMye7xu7C1kADgAA+hdCBhCEjJwLj0xpf4nMs2fsKwYAAOAKETKAIGQkjpJunOgZdHbK3PWRvQUBAABcAUIGEKT8FoAX/k2madpYDQAAQO8RMoAgZdx0ixTu9AyOfy598Zm9BQEAAPQSIQMIUkZklIysHN/Y3Mk3MwAAQP9AyACCmN8jU8UfyWxvs7EaAACA3iFkAMFswmRpRIJnu+mczH277K0HAACgFwgZQBAzHA4ZOd/2jc1CHpkCAADBj5ABBDkj5zbJMDyDin0yT9XbWxAAAMBlEDKAIGfExksTp3oGpinz4w/tLQgAAOAyCBlAP+D3yFTRNr6ZAQAAghohA+gHjOmzpcgoz6C2Wjpy0N6CAAAALoGQAfQDhtMpY+atvjELwAEAQDAjZAD9hN83M3bvlNnSbGM1AAAAF0fIAPqL8alS0mjPdmuLzD1F9tYDAABwEYQMoJ8wDEPGnK4LwHlkCgAABCdCBtCPGNnzJcf5/2wPH5BZW21vQQAAAD0gZAD9iHHdMCkjyzc2i7bZWA0AAEDPCBlAP+Po+sjUxx/KdHfaWA0AAEB3hAygv5k6U4oe6tk+VS8d+sTeegAAAL6BkAH0M0ZomIxZ3/KNzUIemQIAAMGFkAH0Q37fzNj7scxzjTZWAwAA4I+QAfRDxujx0pgbPYOOdpkl2+0tCAAAoAtCBtBP+X0zg0emAABAECFkAP2UMetbUmioZ3DsU5nHv7C3IAAAgPMIGUA/ZQyJkZE5yzfmC+AAACBYEDKAfsxvAfjH+TI7OmysBgAAwIOQAfRnk6dJ1w/3bDd8LZXvsbceAAAAETKAfs1whMiYPd83drMAHAAABAFCBtDPGTkXHpnS/hKZZ8/YVwwAAIAIGUC/ZySOkm6c6Bl0dsp0FdhaDwAAACEDGAD8FoAXbZNpmjZWAwAABjtCBjAAGDfdIoU7PYPjn0v/f3v3HtbUle4P/LsDIVzlKoKiFbWgQGup2iKtDuio6Kjn1Ir2dno6nflNr/bi6RzHM+NlWk97PD2d6bTWaZ/2WLW1T9LfgK8AACAASURBVLVWO0dU0FqoF8RLVVpQQFpUqFwVlGsSkvX7IyQQE5DEwA7J9/M8echee62936yupHlde+1cLJU3ICIiInJrTDKIXIDk4wtpQrJpWxzaL2M0RERE5O6YZBC5COm+Gabn4ug3XABOREREsmGSQeQqYuKBEaMNz7UaiG8y5I2HiIiI3BaTDCIXIUkSpLQHTdsiew9EW4uMEREREZG7YpJB5EKkCZOBwRGGjZYmiIP75A2IiIiI3BKTDCIXIik8IM1aYNoW+/8B0a6VMSIiIiJyR0wyiFyMlDwNGBRk2Gi4AnHsW3kDIiIiIrfDJIPIxUhKL0i/nG/aFplfQuj1MkZERERE7sZT7gCMDh48iHXr1gEAnnrqKUyfPt2iznfffYddu3ahrKwMer0ew4cPx8yZM5GSktLtcXNycpCVlYWKigooFApER0dj3rx5mDBhgtX6er0ee/fuRXZ2NiorK+Hl5YWYmBgsWLAAsbGxVttoNBp89dVXOHLkCOrq6uDj44O4uDgsWrQIUVFRtncG0S2SfjEbYu92oLUFqPoZyD8OJCbJHRYRERG5CaeYyairq8OGDRvg7e3dbZ3MzEysXbsW5eXlmDJlCqZPn476+nqsX78emzdvttpm8+bNWL9+PRoaGjB9+nRMmTIFly5dwtq1a5GZmWlRXwiBt99+G5s2bUJ7ezvS0tJwzz334OzZs1i1ahVOnDhh0Uar1eK1117D9u3b4evri9mzZ+OOO+7AiRMnsHz5cpw/f97+jiGyk+TrB+kXs03b+r3bIYSQMSIiIiJyJ7LPZAgh8Pe//x0BAQG45557sGvXLos6NTU1+OSTT+Dv74833ngD4eHhAICFCxdi+fLlyMjIQFJSEmJiYkxtiouLkZGRgSFDhuCNN96Av78/AGD+/Pn4wx/+gE8++QR333236VgAcOTIEeTl5SE2NhYrVqyAl5cXAGDGjBlYuXIlPvjgAyQkJMDHx8fUJiMjA8XFxUhKSsJLL70EhcKQtyUnJ+PNN9/E3//+d/zP//yPqZyov0jT50F8/Q+gvR0oKwFKCoHYBLnDIiIiIjcg+zffvXv3oqCgAM888wxUKpXVOtnZ2dBqtUhLSzNLCvz9/fHAAw8AAPbtM79V5/79+wEACxYsMCUYABAeHo5Zs2ZBq9UiJyfHapvFixebEgwAGDNmDJKTk3H9+nXk5eWZyoUQpjaPPfaYWSIxadIkjBs3DhUVFTh79myv+4PIUaSgEEjJnZcd6jO3yxgNERERuRNZk4yKigps2bIFs2fPRlxcXLf1CgoKAAB33XWXxb7ExEQAQGFhoc1tjHUAw2VPxcXFUKlUGDdunEUb43G6tqmurkZdXR0iIyPNkp+e2hD1J2nmA4AkGTYKTkGUl8kbEBEREbkF2S6X0ul0WLduHcLCwvDII4/0WPfy5csAgMjISIt9wcHBUKlUuHLlCtRqNVQqFdra2nD16lV4e3sjODjYok1EhOHHyiorK01lVVVV0Ov1CA8Ph4eHh0Ub47m7tukpru7a9GTZsmVWy9euXQsACAsL69VxboWnp2e/ncuVOG2/hYWhYXIq1LnfAAC8sjMQuPTPMgfVyWn7zcmx3+zDfrMP+80+7Df7sN/s44z9JttMxvbt21FWVobnnnvO7NIka1paWgAAvr6+Vvcby431elu/ubnZ5nPY08ZYj0gOfgseMz1vO3IA7VU/yxgNERERuQNZZjJKS0uxc+dOzJs3z2yx9q2SjJeF9EF945157GnTW8YZi+7U1dXZdDx7GDPg/jiXK3HqfgsMA8aNB87lA3o9rm79GIpHn5Y7KgBO3m9OjP1mH/abfdhv9mG/2Yf9Zh9H9dvQoUMdEQ4AGWYydDod3n33XURGRmLx4sW9anOzGQFjufGuT72t33UG4mZtWltbHdKGSA6K2QtNz8WRryGuN8gYDREREbm6fp/JaGtrM61RePTRR63W+eCDD/DBBx9gzpw5eOKJJzB06FAUFxejsrISAQEBZnXr6+uhVqsRGhpqujuVt7c3QkJCcPXqVdTX11usy6iqqgJgvpYiIiICCoUCNTU10Ol0FusyjDF3bWPM9rpbc2GtDZEsxt4J3DYGuFgKaDUQBzIgPfDYzdsRERER2aHfZzKUSiWmTZtm9REdHQ0AGDt2LKZNm2a6lCohwXBv/zNnzlgc7/Tp0wCA+Ph4s/LetDHWMcYVGxsLtVqNc+fOWbQxHqdrmyFDhiAsLAyVlZWoqanpVRsiOUiSBMXsB03bImc3RBvXChEREVHf6Pckw8vLC08//bTVx4QJEwAAv/jFL/D0008jOTkZAJCamgqlUonMzEyzL/NNTU3YuXMnAGDmzJlm55kxYwYAYMeOHWhqajKV19TUICsrC0qlEikpKVbbbN26FRqNxlReWlqK3NxcDBo0CPfee6+pXJIkU5tPP/0Uer3etO/EiRM4d+4coqKierw9L1G/SUwCwjuutWxphjiYJW88RERE5LJk/8Xv3ggPD8djjz2Gjz/+GMuXL8fkyZPh6emJY8eO4cqVK5g7d67FAvLY2FjMnTsXGRkZ+P3vf497770X7e3tOHr0KJqamvDkk09a/LbFfffdh+PHjyMvLw/Lli3DhAkT0NjYiNzcXOj1ejz11FMW6yvmzp2LU6dOIS8vD3/84x+RkJCAuro65OXlQaVS4ZlnnuGvfZNTkBQekGY9APHJewAAsf8fEKlzISmVMkdGRERErmZAJBkAMHv2bAwePBi7du3CwYMHIYRAVFQUFi9ebDEjYfT4449jxIgRyMrKwoEDByBJEqKjozF//nzTrElXkiThxRdfRExMDLKzs7F37154eXkhLi4OCxYsQGxsrEUbpVKJFStW4KuvvsLhw4exe/du+Pj4YNKkSVi0aBGioqIc3RVEdpMmp0L832fAtXqg4SrEsRxI98+QOywiIiJyMZKw9T6rJBvjj//1Jd46zj4Dqd/0mV9CfLnJsBExDIo/vwdJptm2gdRvzoT9Zh/2m33Yb/Zhv9mH/WYf3sKWiGQnTU0DfDou+6v6GThzTN6AiIiIyOUwySByM5KvH6SU2aZtfeaXNv9wJBEREVFPmGQQuSFp+nzAs2PBd1kJUPyDvAERERGRS2GSQeSGpMBgSMnTTdv6zC9ljIaIiIhcDZMMIjclzfpnQOr4CCg8DXHpR3kDIiIiIpfBJIPITUnhQyFNSDZti8wdMkZDREREroRJBpEbk9IeND0XJ49A1FTKGA0RERG5CiYZRG5Mum00EHeXYUPoIfZ/JW9ARERE5BKYZBC5OUXX2YzDX0Ncr5cxGiIiInIFTDKI3N3YO4Hbxhiet2shDmTIGw8RERENeEwyiNycJElQzF5o2hbZeyBammWMiIiIiAY6JhlEBCTeCwwZZnje2gzx1afyxkNEREQDGpMMIoKk8IA0/2HTtsjZA1F6TsaIiIiIaCBjkkFEAABp0hTgjomGDSGg37wOQquVNygiIiIakJhkEBGAjrUZjz4DqHwMBZXlEHu+kDcoIiIiGpCYZBCRiRQ6GNKCfzFti73bIX6+KGNERERENBAxySAiM1LKHGD0WMOGrh36Te9C6HXyBkVEREQDCpMMIjIjKRRQ/OsSwNPTUFBWAvENfzuDiIiIeo9JBhFZkCKHQ/rVItO22PkpRF21jBERERHRQMIkg4isktIeBIbdZtjQqKH/ZD2EEPIGRURERAMCkwwiskryVELx+POAJBkKzp6GOJotb1BEREQ0IDDJIKJuSaNiIU2fZ9oW2/4X4nqDjBERERHRQMAkg4h6JP3zY0BouGGjuRHi8w/lDYiIiIicHpMMIuqRpPKG4l+eM22LE4cg8o/LGBERERE5OyYZRHRTUnwipMmppm39lvchWltkjIiIiIicGZMMIuoVadFvgIBAw0Z9HcSOTfIGRERERE6LSQYR9YrkPwjSw78zbYucvRAlhTJGRERERM6KSQYR9Zo08X7gzkmmbf3mdRBajYwRERERkTNikkFEvSZJEhSPPgN4+xgKqn+GyNgmb1BERETkdJhkEJFNpJAwSA/+q2lbZH0JUVEmY0RERETkbJhkEJHNpKlpwJg4w4ZOB/3GdyF0OnmDIiIiIqfBJIOIbCYpFFA8/jzg6WkouFgKceD/5A2KiIiInAaTDCKyixQZBWnuQ6Zt8Y8tELVVMkZEREREzoJJBhHZTZq1AIgaadjQaKD/5D0IIWSNiYiIiOTHJIOI7CZ5ekLx+BJA6vgoOZcPceRreYMiIiIi2THJIKJbIkXfDumX80zbYsv7EAWnZIyIiIiI5MYkg4humfRPjwLhQw0b7Vro178OcfaMvEERERGRbJhkENEtk1TeULz8ZyBksKFAq4F+3RqIc/nyBkZERESyYJJBRA4hhQ2B4pX/BELCDAVaDfTrXoMoLpA3MCIiIup3TDKIyGGkwRFQ/NsaICjUUKDRQP/OnyFKCuUNjIiIiPoVkwwicigpfKhhRiMwxFCgURsSjdKz8gZGRERE/YZJBhE5nDRkKBSvrAECgw0F6jbo3/4zxI9F8gZGRERE/YJJBhH1CSkiynDp1KAgQ4G6Ffq3V0H8VCxvYERERNTnmGQQUZ+RIodDsXQNEBBoKGhrhf7t1RAXzssbGBEREfUpJhlE1KekYSOgWPoa4D/IUNDaDP1fV0Jc/FHewIiIiKjPMMkgoj4nRY00JBp+AYaClmbo/7ICWl46RURE5JKYZBBRv5CGRxsSDV9/Q0FLE+pXvQhtGS+dIiIicjVMMoio30gjRnUkGn4AANF0HfWrXoCouCBvYERERORQnnKctLGxEcePH8epU6dw6dIlXL16FZ6enhgxYgRSU1ORkpIChcIy/ykuLsaOHTtQUlICrVaLiIgIpKamYvbs2VbrA8B3332HXbt2oaysDHq9HsOHD8fMmTORkpLSbXw5OTnIyspCRUUFFAoFoqOjMW/ePEyYMMFqfb1ej7179yI7OxuVlZXw8vJCTEwMFixYgNjYWLv6iMhVSbeNhuLlV6H/y0qgtRmi8RrEX1ZA8W//CWnYCLnDIyIiIgfwWL169er+Pum3336LDz/8EK2trRg7dizuuusuhIWF4dy5czh69CjKy8sxefJkSJJkanPixAm8/vrruHr1KpKSkhAXF4eff/4Zhw8fRkVFBSZPnmxxnszMTKxbtw5tbW247777MGbMGJSWluLgwYNobW3F+PHjLdps3rwZW7ZsgUKhwJQpUzB8+HAUFBQgOzsbAQEBGDNmjFl9IQTefvtt7N69G35+fpg6dSoGDx6MU6dO4cCBA7jtttswbNgwh/RbY2OjQ47TE19fXwBAS0tLn5/LlbDfbCMFhUKKvQM4lQtotYBGDfHdEUh3ToJkvBMVdYvjzT7sN/uw3+zDfrMP+80+juq3gIAAR4QDAJCEEMJhR+ulgoICtLW14e677zabgWhoaMDy5ctx5coVLF26FElJSQAMHfbCCy+gpaUFr732GkaPHg0A0Gg0ePXVV1FSUoIXX3wR9913n+lYNTU1ePnll6FSqfBf//VfCA8PBwA0NTVh+fLlqK6uxpo1axATE2NqU1xcjBUrVmDIkCF444034O/vbzrWH/7wB6jVavz1r381HQsADh8+jHfeeQexsbFYsWIFvLy8AAClpaVYuXIlfH198e6778LHx+eW++3y5cu3fIybCQsLAwDU1dX1+blcCfvNPoPqKtHw55ch2jo+FAODofjtv0Eae6e8gTk5jjf7sN/sw36zD/vNPuw3+ziq34YOHeqIcADItCYjISEBEydOtLjEKSgoCDNmzAAAnD171lSel5eH69evIzk52ZRgAICXlxceeughAMC+ffvMjpWdnQ2tVou0tDSzpMDf3x8PPPCA1Tb79+8HACxYsMCUYABAeHg4Zs2aBa1Wi5ycHKttFi9ebEowAGDMmDFITk7G9evXkZeX14teIXI/XmPvQNDKvwAqb0PBtXro3/oT9Bv+CnG9Qd7giIiIyG5Ot/Db09OwTKRrAlJQUAAAuOuuuyzqjxs3DiqVyrROozdtEhMTAQCFhYVm5b1pY6wDAFqtFsXFxVCpVBg3bpxFG+NxurYhInNe4+6E4oVVgI+fqUwczYZ+xbPQH8yC0OtljI6IiIjs4VRJhk6nw7fffgvA/It+ZWUlAOtTOB4eHggPD4dOp0N1dbWp3HhpUWRkpEWb4OBgqFQqXLlyBWq1GgDQ1taGq1evwtvbG8HBwRZtIiIizGIBgKqqKuj1eoSHh8PDw8OijfHcXdsQkSUpJh6KV9dBmtB5ySNamiA+eQ/6N5dD/HxRvuCIiIjIZrLcXao7W7ZsQXl5ORITE82SDOMiFuOilhtZW+zSmzZqtRotLS1QqVS9Pkdzc7PNcXVt05Nly5ZZLV+7di2Azuvt+pJxJqk/zuVK2G/2Meu3sDDgT29C/d1RNH74FnTVHWuQSs9B/9pL8J3/EPwXPQnJ+9bXNw10HG/2Yb/Zh/1mH/abfdhv9nHGfnOamYw9e/YgIyMDw4YNw5IlS2xqeytr17vewcrR9Y1x2XoOInemmjAZoX/7FL4PPg4YZwh1OrTs3IK6Fx6F+uQReQMkIiKim3KKmYzMzExs3LgRUVFRWLlypdmia+Dmt+VqbW01q2d83tjYiJaWFqu34zIey3jXp5udw9qshT1x9cQ4Y9Gd/rjTAu/qYB/2m3167Le0hVDccQ/0W9YD5w03gtDXVqHhP38P3D0ZisX/D1KI8/yLTX/ieLMP+80+7Df7sN/sw36zD+8uZcXu3buxYcMGDB8+HKtWrUJQUJBFHePaBmu3cNXpdKipqYGHhweGDBliKjd2krX1EPX19VCr1QgNDYVKpQIAeHt7IyQkBG1tbaivr7doU1VVZRYLYFinoVAoUFNTA51OZ9HGeG5r60KI6OakYSOgeOV1SP+6BPDr8o8Fp45Cv/I56L/+Pwgr7z0iIiKSl6xJxldffYVNmzZh5MiRWLVqFQIDrf8IV0JCAgDgzJkzFvvOnTsHtVqNmJgYKJXKXrU5ffo0ACA+Pr7X5zG2MdYBAKVSidjYWKjVapw7d86ijfE4XdsQkW0khQKK+2dA8drfISVP79yhboXY+hH0r78CUXZevgCJiIjIgmxJxvbt2/HZZ59h1KhRWLlyJQYNGtRt3aSkJAQEBCA3Nxc//vijqVyj0eDzzz8HAMycOdOsTWpqKpRKJTIzM1FTU2Mqb2pqws6dO622Mf5Gx44dO9DU1GQqr6mpQVZWFpRKJVJSUqy22bp1KzQajam8tLQUubm5GDRoEO69996b9gcR9UwKGATFr1+E4pXXgcjhnTsu/Qj9G69A/9kHEC29u8kCERER9S2P1atXr+7vk+bk5GDjxo1QKBRISkrChQsXUFhYaPaora3FyJEjARhmDCIjI5Gbm4tDhw6hpqYGRUVF2LRpEy5cuICkpCQsWrTIbIG1n58ffH19cfz4cRw6dAi1tbX4/vvv8fHHH6O2thZz587FtGnTzOIKCwtDa2srTp8+jcOHD6Ourg4nT57Exo0b0dTUhCeeeALjx483azN8+HBUVFQgPz8fx44dQ11dHY4cOYJPP/0UOp0OS5YsMb2OW9XY2OiQ4/TEUT9L727Yb/axp9+ksHBIU2YCSi/gxyJA33G51IXzENm7gaoKw29uhAx22ZsucLzZh/1mH/abfdhv9mG/2cdR/WZtHbO9JHErt2ay07Zt27B9+/Ye68TFxeHG/KeoqAg7d+5ESUkJNBoNIiIikJqaijlz5lj8erjRyZMnsWvXLpSVlUEIgaioKMyaNctiRqKrnJwcZGVloaKiApIkITo6GvPnz8eECROs1tfpdNi7dy+ys7NRVVUFLy8vxMTEYMGCBYiNje3xddrC2poUR+OCK/uw3+xzq/0maiqh/+x9oPC05c7QcEiTUw2PcMctZHMGHG/2Yb/Zh/1mH/abfdhv9nHGhd+yJBlkHyYZzov9Zh9H9JsQAuLkYYhdnwOV5dYrjRkHafI0SBPvh+TrZ73OAMLxZh/2m33Yb/Zhv9mH/WYfZ0wynOIWtkRE9pIkCdKkKRAT7wculEIcPQBx7CDQ0rmuCqXnIErPQXz+IaTEJMMC8nF3QlJ4yBc4ERGRC2OSQUQuQZIkIPp2SNG3Q6T/Bvj+BPRHvwF+OAno9YZKWg3E8YMQxw8CQaGQklIgJU+D1HUhOREREd0yJhlE5HIkpRKYkAyPCckQ1+shjh2EyP0GqCjrrNRwBSLzS4jML4HoGEPCMfZOICIKUjdrvIiIiKh3mGQQkUuTBgVDmvFPwIx/grj0E8TRbyCOfQs0XuusVFYCUVYCAQC+foakY1QspFFjgVExkHz95QqfiIhoQGKSQURuQxoxCtKIURAPPgEUnoI+9wCQfwLQtXdWamkGCk9DFJ6G6a4YkcMhjYoFRo81JB6RnO0gIiLqCZMMInI7kqcnMP4eeIy/B6LpOsSJQxCFp4Gfis1nOIwqyyEqy4EjXxsSDx/fjtmOsZBGxwLRsZD8ONtBRERkxCSDiNya5D8IUuqvgNRfQQgB1FVD/FgE/FQE8VMJUP5T58Jxo9YW4OwZiLNnOmc7QsOBwRGQBkeY/cXgCF5uRUREbodJBhFRB0mSOhOEpBQAgFCrgYvnIX4shvipGPipCLjeYNn4Sg1wpQai6HtDu677fP0tEw/j8+BQ3kqXiIhcDpMMIqIeSCoVEJMAKSYBADpnO34qBn4qNsx6VJQBOl33B2lpAi6WQlwsNRWZkhAPTyB0MBAYDAwKghQQBAQEAoMCIQ0KArpsw8fPkAgRERE5OSYZREQ2MJvtuPcXAACh1QB1NUBtJURtteFvXTVQUwnUVQNaTfcH1LUb6tVUGo7VZZe4sa6nJxAQhCvBoVAEBkPv7WtIPvwHAT5+gK8fJB8/w5oRX/+Ov36A0ovJCRER9SsmGUREt0hSegGRUYa7Tt2wT+j1wPV6oLYaorYSqK0G6qogaquA2irrl151p70dqK9De31dt1UsEhPAMFvi25F8dCQj8PGDZExCvH0Albfh4eUNydvw11Rm9lDx8i4iIropJhlERH1IUiiAoFDDL4zfHmexX7S1AldqgcYGiMZrhqTj+jXD9vUGw92uGq8ZytSt9gWha+88Ttdzd1O9u3ITpVeXpERleCi9AKUS8FIZki6lElCqAK8bnnt6dZR5ddbzVBpmaTytPFcqDUlSx1/eOpiIaGBgkkFEJCPJ2wcYNgLACItZkBsJtRpobECQQoL+Wj2uVVw0JCUtTUBrC0THX7Q0Gx6tHY/29psc2UZajeHRdN16nL08TG/rmfHwtExIPDwM5cZ9Hh6GfR7G556QPDxxzc8P8PCEvl13Q7ve/ZXMtm94rvC44bkn4KEw/O26z8MDkBS8fI2IXB6TDCKiAUJSqQDVECjDwgAAiujYXrUTWk1n0tHS3JGQdElC2toATZvprzBuq298qA3lwq70wDF07YaHus2mZgKAbS2sH8NhjEmIMSFRKKwnKxbJi0dHXc/O5wqF4RK2G+uYlSnMj2cqs1JuPGbHdltQECQPD4im5i7HVXSpe8M5e1mHiRaRa2OSQUTk4iSlFxDoZbiDlbHMzmMJIQCNxnDplroN0KgN28bZDa0aQqvtKFMDWq2hTvuNZRoIrdowy9KuNZS1azu3zR7tnX9dha4d6OGGZLbqi7TPeEwrP0/pGJLihkSnSzIiKawkLorOfYou+7upKymstO/V8y7bHgpA6vrcsp1krZ1CAU1wMKBQQDQ2de6XrLyObmO4oYwzYDTAMMkgIqJekyQJUKkMj+7q9NG5hRCGREOnBbQdiYeuvaOsvctzXcc+nalM6NoR4OMD6NrR2FDfUcfYTnfTv8K03XVfx3O93rxM3/VvO6Dr2G8sl3MmyJkIPdCuv3k9ew/fZ0fu3Xnq++JkFomJ4iZlHj3XsyjvkrgpJEhW21hJkCSpy3MryVJ3+7uWd5y3LTDQkJyZZs6sxG5sJyluqCN1Ht/snNbi6P5YTOYcg0kGERENCJIkdSwiVwLeNrYF4NNxmVlzXfd35+oPQq+3TEb0OqC9y3Od3jxJ0d+Q4IjOY4iu+29sr79hnynh6bJfZ6WeXg/RUd/L0wPQ6aBRt3UmUkLfpe2N7fVdHjqLeE37yHZC3/HfsJ9O1z+nMdNnM2e2sjU5saWOJPWijgKSQgFpweOGW6YPQEwyiIiI+pHp8hooHXM8hxyle8EdyVmdA5MzIUTnF2ZTwmMl6bnxr1n9np7ruiRzNxy/x3Y3Pu95n7ixrug8p9LDA9DrodWozROz7o5tsd/Ksan/6PUA+i+hs0YAkGY/KF8At4hJBhEREfUrSTJe1tJ3v7ki9wUvIQ5OzkyJWU+JitVkRQ+IGxOn3tUVQliey2ob0bv9wlhHdBuHl1IJCD3UrW2d5Tce02JbmJcLa7F13S+6r+dsyZykkDsCuzHJICIiInJy/ZGYWZyz387UKagPZs5sJXqTiFgkV6LnOta2b1JXCAGEDpatH24VkwwiIiIiog6mH/306L+Ezmocsp791g3cORgiIiIiInJKTDKIiIiIiMihmGQQEREREZFDMckgIiIiIiKHYpJBREREREQOxSSDiIiIiIgcikkGERERERE5FJMMIiIiIiJyKCYZRERERETkUEwyiIiIiIjIoZhkEBERERGRQzHJICIiIiIih2KSQUREREREDsUkg4iIiIiIHIpJBhERERERORSTDCIiIiIicihJCCHkDoKIiIiIiFwHZzKIiIiIiMihmGSQmWXLlmHZsmVyhzHgsN/sw36zD/vNPuw3+7Df7MN+sw/7zT7O2G9MMoiIiIiIyKGYZBARERERkUMxySAiIiIiIodikkFERERERA7FJIOIiIiIiByKv5NBREREREQOxZkMIiIiIiJyKCYZRERERETkUEwyiIiIiIjIoZhkEBERERGRf9b8oAAADyNJREFUQzHJICIiIiIih2KSQUREREREDsUkg4iIiIiIHMpT7gDIOVy5cgVbt25Ffn4+GhsbERwcjEmTJmHhwoXw9/eXOzzZNDY24vjx4zh16hQuXbqEq1evwtPTEyNGjEBqaipSUlKgUHTm6jU1NXj++ee7PV5ycjJeeuml/ghdds899xxqa2ut7gsMDMSHH35oUV5cXIwdO3agpKQEWq0WERERSE1NxezZs8362VXl5ORg/fr1PdaRJAlbt24F4H7jLS8vD2fPnsWFCxdw8eJFtLa24v7778cLL7zQbRt7xtR3332HXbt2oaysDHq9HsOHD8fMmTORkpLSR6+sb9nSb5WVlTh27Bjy8/NRVVWFhoYG+Pv74/bbb8ecOXOQkJBg0eZm4/a3v/0tZs6c6dDX1B9s6bdbeS/m5OQgKysLFRUVUCgUiI6Oxrx58zBhwgSHvZb+ZEu/vffee/j22297PF5CQgJWrlxp2nbF8Wbrdw0jZ/98Y5JBqKqqwooVK3Dt2jVMnDgRw4YNQ2lpKfbs2YMzZ87gtddeQ0BAgNxhyuLo0aP46KOPEBwcjPj4eISFhaGhoQHHjx/H+++/j9OnT2Pp0qWQJMms3W233YZJkyZZHG/EiBH9FbpT8PX1xZw5cyzKvb29LcpOnDiBt956C0qlEsnJyfD398d3332HTZs2obi4GEuXLu2PkGU1cuRILFy40Oq+oqIiFBQUIDEx0WKfu4y3L7/8EhcvXoS3tzdCQ0Px888/91jfnjGVmZmJDRs2ICAgAFOmTIGnpyeOHTuG9evX49KlS3j88cf76uX1GVv6bevWrcjNzUVUVBQSExPh7++Py5cv4+TJkzh58iSeeOIJq+9pAJg4cSJGjhxpUT569GhHvZR+Zet4A2x/L27evBkZGRkIDQ3F9OnT0d7ejtzcXKxduxZPPvkk0tLSbvl19Ddb+m3SpEkYPHiw1X2HDh1CdXU17rrrLqv7XWm82fNdY0B8vglye2vWrBHp6eliz549ZuUbN24U6enp4oMPPpApMvn98MMP4sSJE0Kn05mV19fXi6efflqkp6eLo0ePmsqrq6tFenq6WLduXX+H6nSeffZZ8eyzz/aqbnNzs/jNb34jHn74YVFaWmoqV6vV4o9//KNIT08Xhw8f7qtQB4T/+I//EOnp6eLEiROmMncbbz/88IO4fPmy0Ov1oqCgQKSnp4u//e1vVuvaM6aqq6vFI488In7961+L6upqU3ljY6N4/vnnRXp6uiguLu6bF9eHbOm37Oxs8dNPP1mUFxYWioceekg8/PDD4urVqxZt0tPTRXZ2dl+ELxtb+s2e92JRUZFIT08Xzz//vGhsbDQ71q9//WvxyCOPmI3DgcKWfutOU1OTePTRR8XDDz8srl27ZrbPFcebrd81Bsrnm+tff0A9qq6uRn5+PgYPHoxZs2aZ7Vu0aBFUKhUOHTqEtrY2mSKUV0JCAiZOnGgx7RgUFIQZM2YAAM6ePStHaC4lLy8P169fR3Jystm/Qnl5eeGhhx4CAOzbt0+u8GR36dIlnD9/HiEhIbj77rvlDkc2CQkJiIyMtJg5tMaeMZWdnQ2tVou0tDSEh4ebyv39/fHAAw9YbTMQ2NJvKSkpiI6OtiiPi4tDfHw82tvbUVxc3BdhOh1b+s0e+/fvBwAsWLDA7LLk8PBwzJo1C1qtFjk5OX1y7r7kiH47ePAgNBoN7rnnHgwaNMiB0TknW79rDJTPN14u5eYKCgoAAOPHj7cY3D4+Phg7dizy8/Nx/vx53HHHHXKE6LQ8PQ1vH2vXPdbX12P//v1obGxEQEAAYmJicNttt/V3iLLTarU4ePAg6urq4O3tjREjRiAuLs6iz4zj0Nq0+Lhx46BSqUzXnCqVyn6J3Zl8/fXXAIBp06ZxvPWSPWOqpzbGy9QKCwv7KmSn5+HhYfb3RhcuXMDu3buh1WoREhKC+Ph4hIaG9meIsrPlvXiz8fbll1+ioKAAixYt6tOYndGBAwcAAL/85S+7reMu483ad42B8vnGJMPNXb58GQAQGRlpdX9ERATy8/NRWVnJJKMLnU5nWqxm7Q37/fff4/vvvzcri4+Px3PPPYewsLB+idEZNDQ0YN26dWZl4eHhePbZZxEXF2cqq6ysBAAMHTrU4hgeHh4IDw9HeXk5qqurERUV1bdBOxmNRoNDhw5BkiRMmzbNah2ON0v2jKmePg+Dg4OhUqlw5coVqNVqqFSqPoze+dTW1qKgoAAqlQrjxo2zWmfPnj1m2wqFAtOmTcMTTzwBLy+v/ghTdr19L7a1teHq1avw9vZGcHCwxXEiIiIAdI5jd1JSUoJLly4hMjLS6o0GjNxhvHX3XWOgfL4xyXBzLS0tAAwLdK0xljc3N/dbTAPBli1bUF5ejsTERLM3vkqlwoMPPohJkyZhyJAhAICLFy/iiy++QGFhIV599VX893//t9WFz64mJSUF48aNQ1RUFHx8fFBdXY3MzEwcOHAAr7/+OtasWWNatNfbcWis505yc3PR3NyMu+++2yJh4Hjrnj1jqjdt1Go1Wlpa3CrJ0Gq1eOedd6DVavHYY49Z3HEwPDwcTz75JO68806EhoaipaUFRUVF+Oyzz/D111+jtbUVL774okzR9w9b34v8f2/3jDO306dPt7rfncZbd981BsrnG9dkUI+EEADQZ9ekDkR79uxBRkYGhg0bhiVLlpjtCwwMxOLFizFq1Cj4+fnBz88PcXFx+NOf/oTbb78dVVVV+Oabb2SKvH+lp6cjISEBQUFBUKlUGDFiBH73u9/hV7/6FTQaDb744oteH8s4Dt1RT5cNcLzZ71bGlDt9Hur1erz77rsoLi5GcnIy5s2bZ1EnLi4OaWlpGDp0KFQqFYKDgzF58mSsWrUKfn5+OHLkCC5cuND/wfejvnovutNYAwxfhI8ePQpPT89ub6nqLuOtp+8aN+Msn29MMtzczf6FuLW11ayeu8vMzMTGjRsRFRWFVatW9fo3RDw8PEyXurj7QnHj/cvPnTtnKuM4tK6iogLFxcUIDQ21acE3x5t9Y+pmbYzlPj4+DovTmen1erzzzjvIy8vD5MmTsWTJEpu+gISFhZmu9e76fncn3b0XezvW3O0z7+DBg1Cr1XYt+Hal8Xaz7xoD5fONSYabM17P1911n1VVVQC6X7PhTnbv3o0NGzZg+PDhWLVqFYKCgmxqb/zAVKvVfRHegGGtH4zjy3jNaFc6nQ41NTXw8PAwXYbgLox3n0lNTbX5xwjdfbzZM6Z6+jysr6+HWq1GaGioW1wqpdPp8PbbbyM3Nxf3338/XnzxxW4XfPfE3cchYL0PvL29ERISgra2NtTX11u0cdf/9xpnbo13VLKVK4y33nzXGCifb0wy3Fx8fDwAID8/H3q93mxfa2srioqK4OXlhdtvv12O8JzGV199hU2bNmHkyJFYtWoVAgMDbT7G+fPnAcDtvijfqKSkBADMbqFnXNx35swZi/rnzp2DWq1GTEyMW91ZSqPR4ODBgz0u+O6Ju483e8ZUT21Onz4NoPMz05W1t7fjrbfeQl5eHqZOnYrnn3/e5iTXqLS0FID5+93ddPde7M1462nhs6s5f/48Ll68iMjISLvfZwN9vPX2u8ZA+XxjkuHmIiIiMH78eNTW1iIrK8ts37Zt26BWqzF16lS3XDhqtH37dnz22WcYNWoUVq5c2eMU7vnz59He3m5RXlBQgN27dwMApkyZ0mexOovy8nI0NTVZlNfW1mLDhg0AzPshKSkJAQEByM3NxY8//mgq12g0+PzzzwF0XmblLvLy8tDc3IzExMRu7xDF8dY9e8ZUamoqlEolMjMzUVNTYypvamrCzp07rbZxNVqtFm+++SZOnjyJadOm4dlnn71pgmHt0hQhBHbu3ImSkhIEBAR0+6vNrsKe96LxX+t37Nhh9nlZU1ODrKwsKJXKbtcluCLjgu+eblsLuO54s+W7xkD5fJOEO6+oJACGadkVK1bg2rVrmDhxIqKionD+/HkUFhYiMjISa9asQUBAgNxhyiInJwfr16+HQqFAWlqa1etjw8PDTf8jWL16NcrLyxEfH4+QkBAAhh9SM96fevHixXjwwQf7LX65bNu2Df/4xz8QHx+P8PBweHt7o7q6GqdOnYJWq0ViYiJ+//vfm+7/DQDHjx/HX/7yFyiVStx3333w9/fHyZMncfnyZSQlJeHll192q0WQK1euRFFREf793/8dEydOtFrH3cbb8ePHceLECQCG2yPn5+djyJAhGDt2LAAgICAAjz/+uFl9W8fU3r178fHHHyMgIACTJ0+Gp6cnjh07hitXrmDu3Llmxx8obOm39evXIycnBwEBARY/0GoUHx9v9i+eixYtQmRkJEaPHo2QkBC0tLSguLgY5eXlUKlUeOWVVzB+/Pg+fpWOZ0u/2fte3Lx5MzIyMhAaGop7770X7e3tOHr0KBobG/Hkk08iLS2tP16qQ9n6PgUM6wGeeuop6HQ6vP/++z1+wXbF8Wbrdw1gYHy+MckgAEBdXR22bduGM2fOoLGxEcHBwZg0aRLS09N7vbjZFW3btg3bt2/vsU5cXBxWr14NAPjmm29w/PhxlJeX4/r169DpdAgMDERMTAzS0tK6vb+8qzl79iz27duHCxcuoKGhAWq1Gr6+vhg5ciSmTp2KqVOnWk0YioqKTP8apdFoEBERgdTUVMyZM8fuyzUGooqKCixduhShoaF47733un3t7jbebvZ+HDx4MN577z2zMnvG1MmTJ7Fr1y6UlZVBCIGoqCjMmjVrwP6rsi39tnr16pveLGDhwoVmPxD3ySefoLS0FFVVVWhqaoIkSQgLC8Mdd9yBuXPnDthL9mzpt1t5L+bk5CArKwsVFRWQJAnR0dGYP38+JkyY4PDX1B/seZ/u27cPH330EZKTk/HSSy/1eHxXHG+2ftcwcvbPNyYZRERERETkUO7zT4NERERERNQvmGQQEREREZFDMckgIiIiIiKHYpJBREREREQOxSSDiIiIiIgcikkGERERERE5FJMMIiIiIiJyKCYZRERERETkUEwyiIiIiIjIoZhkEBERERGRQzHJICIiIiIih2KSQUREREREDsUkg4iIiIiIHIpJBhERERERORSTDCIiIiIicigmGURERERE5FBMMoiIiIiIyKH+P9yXbgvEIVtGAAAAAElFTkSuQmCC" }, "execution_count": 7, "metadata": { "image/png": { "height": 250, "width": 396 } }, "output_type": "execute_result" } ], "source": [ "x = range(1, num_epochs, 5)\n", "plt.plot(x, t)" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "TqTuhkTsP90b" }, "source": [ "We can use the Edward2 model to sample data for the inferred values for $\\mathbf{W}$ and $\\mathbf{Z}$, and compare to the actual dataset we conditioned on. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 402 }, "colab_type": "code", "collapsed": false, "id": "T3O6PHe3XX8a", "outputId": "56daaadd-1752-482a-f108-fdb3e22f6520" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "MAP-estimated axes:\n", "[[-0.21629956]\n", " [ 3.4028006 ]]\n" ] }, { "data": { "image/png": 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" }, "execution_count": 8, "metadata": { "image/png": { "height": 252, "width": 383 } }, "output_type": "execute_result" } ], "source": [ "print(\"MAP-estimated axes:\")\n", "print(w_inferred_map)\n", "\n", "def replace_latents(w=actual_w, z=actual_z):\n", "\n", " def interceptor(rv_constructor, *rv_args, **rv_kwargs):\n", " \"\"\"Replaces the priors with actual values to generate samples from.\"\"\"\n", " name = rv_kwargs.pop(\"name\")\n", " if name == \"w\":\n", " rv_kwargs[\"value\"] = w\n", " elif name == \"z\":\n", " rv_kwargs[\"value\"] = z\n", " return rv_constructor(*rv_args, **rv_kwargs)\n", "\n", " return interceptor\n", "\n", "with ed.interception(replace_latents(w_inferred_map, z_inferred_map)):\n", " generate = probabilistic_pca(\n", " data_dim=data_dim, latent_dim=latent_dim,\n", " num_datapoints=num_datapoints, stddv_datapoints=stddv_datapoints)\n", "\n", "with tf.Session() as sess:\n", " x_generated, _ = sess.run(generate)\n", "\n", "plt.scatter(x_train[0, :], x_train[1, :], color='blue', alpha=0.1, label='Actual data')\n", "plt.scatter(x_generated[0, :], x_generated[1, :], color='red', alpha=0.1, label='Simulated data (MAP)')\n", "plt.legend()\n", "plt.axis([-20, 20, -20, 20])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "YdtvGLvmg341" }, "source": [ "## Variational Inference\n", "\n", "MAP can be used to find the mode (or one of the modes) of the posterior distribution, but does not provide any other insights about it. We next use variational inference, where the posterior distribtion $p(\\mathbf{W}, \\mathbf{Z} \\mid \\mathbf{X})$ is approximated using a variational distribution $q(\\mathbf{W}, \\mathbf{Z})$ parametrised by $\\boldsymbol{\\lambda}$. The aim is to find the variational parameters $\\boldsymbol{\\lambda}$ that _minimize_ the KL divergence between q and the posterior, $\\mathrm{KL}(q(\\mathbf{W}, \\mathbf{Z}) \\mid\\mid p(\\mathbf{W}, \\mathbf{Z} \\mid \\mathbf{X}))$, or equivalently, that _maximize_ the evidence lower bound, $\\mathbb{E}_{q(\\mathbf{W},\\mathbf{Z};\\boldsymbol{\\lambda})}\\left[ \\log p(\\mathbf{W},\\mathbf{Z},\\mathbf{X}) - \\log q(\\mathbf{W},\\mathbf{Z}; \\boldsymbol{\\lambda}) \\right]$.\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "colab": { }, "colab_type": "code", "collapsed": false, "id": "BfXGOtI9g7bG" }, "outputs": [ ], "source": [ "tf.reset_default_graph()\n", "\n", "def variational_model(qw_mean, qw_stddv, qz_mean, qz_stddv):\n", " qw = ed.Normal(loc=qw_mean, scale=qw_stddv, name=\"qw\")\n", " qz = ed.Normal(loc=qz_mean, scale=qz_stddv, name=\"qz\")\n", " return qw, qz\n", "\n", "\n", "log_q = ed.make_log_joint_fn(variational_model)\n", "\n", "def target_q(qw, qz):\n", " return log_q(qw_mean=qw_mean, qw_stddv=qw_stddv,\n", " qz_mean=qz_mean, qz_stddv=qz_stddv,\n", " qw=qw, qz=qz)\n", "\n", "\n", "qw_mean = tf.Variable(np.ones([data_dim, latent_dim]), dtype=tf.float32)\n", "qz_mean = tf.Variable(np.ones([latent_dim, num_datapoints]), dtype=tf.float32)\n", "qw_stddv = tf.nn.softplus(tf.Variable(-4 * np.ones([data_dim, latent_dim]), dtype=tf.float32))\n", "qz_stddv = tf.nn.softplus(tf.Variable(-4 * np.ones([latent_dim, num_datapoints]), dtype=tf.float32))\n", "\n", "qw, qz = variational_model(qw_mean=qw_mean, qw_stddv=qw_stddv,\n", " qz_mean=qz_mean, qz_stddv=qz_stddv)\n", "\n", "energy = target(qw, qz)\n", "entropy = -target_q(qw, qz)\n", "\n", "elbo = energy + entropy\n", "\n", "\n", "optimizer = tf.train.AdamOptimizer(learning_rate = 0.05)\n", "train = optimizer.minimize(-elbo)\n", "\n", "init = tf.global_variables_initializer()\n", "\n", "t = []\n", "\n", "num_epochs = 100\n", "\n", "with tf.Session() as sess:\n", " sess.run(init)\n", "\n", " for i in range(num_epochs):\n", " sess.run(train)\n", " if i % 5 == 0:\n", " t.append(sess.run([elbo]))\n", "\n", " w_mean_inferred = sess.run(qw_mean)\n", " w_stddv_inferred = sess.run(qw_stddv)\n", " z_mean_inferred = sess.run(qz_mean)\n", " z_stddv_inferred = sess.run(qz_stddv)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 783 }, "colab_type": "code", "collapsed": false, "id": "CpSsruVIqAv5", "outputId": "a47e3bb0-25ac-4544-87b4-13ae65d6096c" }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Inferred axes:\n", "[[-0.1579684]\n", " [ 2.5440261]]\n", "Standard Deviation:\n", "[[0.00821651]\n", " [0.00942224]]\n" ] }, { "data": { "image/png": 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" }, "execution_count": 10, "metadata": { "image/png": { "height": 250, "width": 410 } }, "output_type": "execute_result" }, { "data": { "image/png": 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" }, "execution_count": 10, "metadata": { "image/png": { "height": 252, "width": 383 } }, "output_type": "execute_result" } ], "source": [ "print(\"Inferred axes:\")\n", "print(w_mean_inferred)\n", "print(\"Standard Deviation:\")\n", "print(w_stddv_inferred)\n", "\n", "plt.plot(range(1, num_epochs, 5), t)\n", "plt.show()\n", "\n", "with ed.interception(replace_latents(w_mean_inferred, z_mean_inferred)):\n", " generate = probabilistic_pca(\n", " data_dim=data_dim, latent_dim=latent_dim,\n", " num_datapoints=num_datapoints, stddv_datapoints=stddv_datapoints)\n", "\n", "with tf.Session() as sess:\n", " x_generated, _ = sess.run(generate)\n", "\n", "plt.scatter(x_train[0, :], x_train[1, :], color='blue', alpha=0.1, label='Actual data')\n", "plt.scatter(x_generated[0, :], x_generated[1, :], color='red', alpha=0.1, label='Simulated data (VI)')\n", "plt.legend()\n", "plt.axis([-20, 20, -20, 20])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "rWrL1mCNIcNy" }, "source": [ "## Acknowledgements\n", "\n", "This tutorial was originally written in Edward 1.0 ([source](https://github.com/blei-lab/edward/blob/master/notebooks/probabilistic_pca.ipynb)). We thank all contributors to writing and revising that version." ] }, { "cell_type": "markdown", "metadata": { "colab_type": "text", "collapsed": false, "id": "ZJd8RbQxvyp6" }, "source": [ "#### References\n", "\n", "[1]: Michael E. Tipping and Christopher M. Bishop. Probabilistic principal component analysis. _Journal of the Royal Statistical Society: Series B (Statistical Methodology)_, 61(3): 611-622, 1999." ] } ], "metadata": { "colab": { "collapsed_sections": [ ], "name": "Probabilistic_PCA.ipynb", "provenance": [ ], "toc_visible": true, "version": "0.3.2" }, "kernelspec": { "display_name": "Python 3 (Ubuntu Linux)", "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": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 0 }