{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Random Effects Neural Networks with Edward and Keras\n", "Bayesian probabilistic models provide a nimble and expressive framework for modeling \"small-world\" data. In contrast, deep learning offers a more rigid yet much more powerful framework for modeling data of massive size. [Edward](http://edwardlib.org/) is a probabilistic programming library that bridges this gap: \"black-box\" variational inference enables us to fit extremely flexible Bayesian models to large-scale data. Furthermore, these models themselves may take advantage of classic deep-learning architectures of arbitrary complexity.\n", "\n", "Edward uses [TensorFlow](https://www.tensorflow.org/) for symbolic gradients and data flow graphs. As such, it interfaces cleanly with other libraries that do the same, namely [TF-Slim](https://research.googleblog.com/2016/08/tf-slim-high-level-library-to-define.html), [PrettyTensor](https://github.com/google/prettytensor) and [Keras](https://keras.io/). Personally, I've been working often with the latter, and am consistently delighted by the ease with which it allows me to specify complex neural architectures.\n", "\n", "The aim of this work is to lay a practical foundation for Bayesian modeling in Edward, then explore how, and how easily, we can extend these models in the direction of classical deep learning via Keras. It will give both a conceptual overview of the models below, as well as notes on the practical considerations of their implementation — what worked and what didn't. Finally, this work will conclude with concrete ways in which to extend these models further, of which there are many.\n", "\n", "If you're just getting started with Edward or Keras, I recommend first perusing the [Edward tutorials](http://edwardlib.org/tutorials) and [Keras documentation](https://keras.io/) respectively.\n", "\n", "To \"pull us down the path,\" we build three models in additive fashion: a Bayesian linear regression model, a Bayesian linear regression model with random effects, and a neural network with random effects. We fit them on the [Zillow Prize](https://www.kaggle.com/c/zillow-prize-1) dataset, which asks us to predict `logerror` (in house-price estimate, i.e. the \"Zestimate\") given metadata for a list of homes. These models are intended to be demonstrative, not performant: they will not win you the prize in their current form. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import edward as ed\n", "from edward.models import Normal\n", "from keras.layers import Input, Dense\n", "from keras.regularizers import l2\n", "from keras import backend as K\n", "import numpy as np\n", "import pandas as pd\n", "import tensorflow as tf\n", "from sklearn.preprocessing import scale\n", "\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "%matplotlib inline\n", "plt.style.use('seaborn-whitegrid')" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# ensure you are using TensorFlow as your Keras backend\n", "sess = ed.get_session()\n", "K.set_session(sess)\n", "\n", "INIT_OP = tf.global_variables_initializer()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "## Data preparation\n", "After importing the data we rename its columns as per Philipp Spachtholz's [Exploratory Analysis - Zillow](https://www.kaggle.com/philippsp/exploratory-analysis-zillow) kernel on [kaggle.com](https://www.kaggle.com)." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "properties_df = pd.read_csv('data/properties.csv', low_memory=False)\n", "transactions_df = pd.read_csv('data/transactions.csv')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "properties_df = properties_df.rename(columns={\n", " 'parcelid': 'id_parcel',\n", " 'yearbuilt': 'build_year',\n", " 'basementsqft': 'area_basement',\n", " 'yardbuildingsqft17': 'area_patio',\n", " 'yardbuildingsqft26': 'area_shed',\n", " 'poolsizesum': 'area_pool',\n", " 'lotsizesquarefeet': 'area_lot',\n", " 'garagetotalsqft': 'area_garage',\n", " 'finishedfloor1squarefeet': 'area_firstfloor_finished',\n", " 'calculatedfinishedsquarefeet': 'area_total_calc',\n", " 'finishedsquarefeet6': 'area_base',\n", " 'finishedsquarefeet12': 'area_live_finished',\n", " 'finishedsquarefeet13': 'area_liveperi_finished',\n", " 'finishedsquarefeet15': 'area_total_finished',\n", " 'finishedsquarefeet50': 'area_unknown',\n", " 'unitcnt': 'num_unit',\n", " 'numberofstories': 'num_story',\n", " 'roomcnt': 'num_room',\n", " 'bathroomcnt': 'num_bathroom',\n", " 'bedroomcnt': 'num_bedroom',\n", " 'calculatedbathnbr': 'num_bathroom_calc',\n", " 'fullbathcnt': 'num_bath',\n", " 'threequarterbathnbr': 'num_75_bath',\n", " 'fireplacecnt': 'num_fireplace',\n", " 'poolcnt': 'num_pool',\n", " 'garagecarcnt': 'num_garage',\n", " 'regionidcounty': 'region_county',\n", " 'regionidcity': 'region_city',\n", " 'regionidzip': 'region_zip',\n", " 'regionidneighborhood': 'region_neighbor',\n", " 'taxvaluedollarcnt': 'tax_total',\n", " 'structuretaxvaluedollarcnt': 'tax_building',\n", " 'landtaxvaluedollarcnt': 'tax_land',\n", " 'taxamount': 'tax_property',\n", " 'assessmentyear': 'tax_year',\n", " 'taxdelinquencyflag': 'tax_delinquency',\n", " 'taxdelinquencyyear': 'tax_delinquency_year',\n", " 'propertyzoningdesc': 'zoning_property',\n", " 'propertylandusetypeid': 'zoning_landuse',\n", " 'propertycountylandusecode': 'zoning_landuse_county',\n", " 'fireplaceflag': 'flag_fireplace',\n", " 'hashottuborspa': 'flag_tub',\n", " 'buildingqualitytypeid': 'quality',\n", " 'buildingclasstypeid': 'framing',\n", " 'typeconstructiontypeid': 'material',\n", " 'decktypeid': 'deck',\n", " 'storytypeid': 'story',\n", " 'heatingorsystemtypeid': 'heating',\n", " 'airconditioningtypeid': 'aircon',\n", " 'architecturalstyletypeid': 'architectural_style'\n", "})\n", "\n", "transactions_df = transactions_df.rename(columns={\n", " 'parcelid': 'id_parcel',\n", " 'transactiondate': 'date'\n", "})" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Build training DataFrame" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "data = transactions_df.merge(properties_df, how='left', left_on='id_parcel', right_on='id_parcel')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Drop columns containing too many nulls\n", "Bayesian probabilistic models allow us to flexibly model *missing* data itself. To this end, we conceive of a given predictor as a vector of both:\n", "1. Observed values.\n", "2. Parameters in place of missing values, which will form a posterior distribution for what this value might have been.\n", " \n", "In a (partially-specified, for brevity) linear model, this might look as follows:\n", "\n", "$$\n", "y_i \\sim \\mathcal{N}(\\mu_i, \\sigma)\\\\\n", "\\mu_i = \\alpha + \\beta_N N_i\\\\\n", "N_i \\sim \\mathcal{N}(\\nu, \\sigma_N)\\\\\n", "$$\n", "\n", "where $N_i$ is our sometimes-missing predictor. When $N_i$ is observed, $\\mathcal{N}(\\nu, \\sigma_N)$ serves as a likelihood: given this data-point, we tweak retrodictive distributions on the parameters $(\\nu, \\sigma_N)$ by which it was produced. Conversely, when $N_i$ is missing it serves as a prior: after learning distributions of $(\\nu, \\sigma_N)$ we can generate a likely value of $N_i$ itself. Finally, inference will give us (presumably-wide) distributions on the model's belief in what was the true value of each missing $N_i$ conditional on the data observed.\n", "\n", "I tried this in Edward, albeit briefly, to no avail. Dustin Tran gives an [example](https://discourse.edwardlib.org/t/how-to-handle-missing-values-in-gaussian-matrix-factorization/95/2) of how one might accomplish this task in the case of Gaussian Matrix Factorization. In my case, I wasn't able to apply a 2-D missing-data-mask placeholder to a 2-D data placeholder via [`tf.gather`](https://www.tensorflow.org/api_docs/python/tf/gather) nor [`tf.gather_nd`](https://www.tensorflow.org/api_docs/python/tf/gather_nd). With more effort, I'm sure I could make this work. Help appreciated.\n", "\n", "For now, we'll first drop columns containing too many null values, then, after choosing a few of the predictors most correlated with the target, drop the remaining rows containing nulls." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "keep_cols = data.columns[ data.isnull().mean() < .25 ]\n", "data = data[keep_cols]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Which columns are most correlated with the target?" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "logerror 1.000000\n", "area_live_finished 0.041922\n", "area_total_calc 0.038784\n", "num_bathroom_calc 0.029448\n", "num_bath 0.028845\n", "num_bathroom 0.027889\n", "num_bedroom 0.025467\n", "tax_building 0.022085\n", "build_year 0.017312\n", "censustractandblock 0.008892\n", "Name: logerror, dtype: float64" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "float_cols = [col for col in data.columns if data[col].dtype == np.float64]\n", "\n", "data[float_cols]\\\n", " .corr()['logerror']\\\n", " .abs()\\\n", " .sort_values(ascending=False)\\\n", " .head(10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Drop rows with null values" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "data.dropna(inplace=True)\n", "data.reset_index(inplace=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Select three fixed-effect predictors" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "fixed_effect_predictors = [\n", " 'area_live_finished', \n", " 'num_bathroom', \n", " 'build_year'\n", "]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Select one random-effect predictor" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "zip_codes = data['region_zip'].astype('category').cat.codes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Split data into train, validation sets" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Dataset sizes:\n", " X_train: (36986, 3)\n", " X_val: (36986, 3)\n", " y_train: (36986,)\n", " y_val: (36986,)\n" ] } ], "source": [ "train_index = data.sample(frac=0.5).index\n", "val_index = data.drop(train_index).index\n", "\n", "X = data.drop('logerror', axis=1)[fixed_effect_predictors]\n", "X = scale(X)\n", "y = data['logerror'].values\n", "\n", "X_train = X[train_index]\n", "y_train = y[train_index]\n", "X_val = X[val_index]\n", "y_val = y[val_index]\n", "\n", "print('Dataset sizes:')\n", "print(f' X_train: {X_train.shape}')\n", "print(f' X_val: {X_val.shape}')\n", "print(f' y_train: {y_train.shape}')\n", "print(f' y_val: {y_val.shape}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayesian linear regression\n", "Using three fixed-effect predictors we'll fit a model of the following form:\n", "\n", "$$\n", "y_i \\sim \\mathcal{N}(\\mu_i, 1)\\\\\n", "\\mu_i = \\alpha + \\beta x_i\\\\\n", "\\alpha \\sim \\mathcal{N}(0, 1)\\\\\n", "\\beta \\sim \\mathcal{N}(0, 1)\\\\\n", "$$\n", "\n", "Having normalized our data to have mean 0 and unit-variance, we place our priors on a similar scale.\n", "\n", "To infer posterior distributions of the model's parameters conditional on the data observed we employ variational inference — one of three inference classes supported in Edward. This approach posits posterior inference as posterior *approximation* via *optimization*, where optimization is done via stochastic, gradient-based methods. This is what enables us to scale complex probabilistic functional forms to large-scale data.\n", "\n", "For an introduction to variational inference and Edward's API thereof, please reference:\n", "- [Edward: Inference of Probabilistic Models](http://edwardlib.org/tutorials/inference)\n", "- [Edward: Variational Inference](http://edwardlib.org/tutorials/variational-inference)\n", "- [Edward: KL(q||p) Minimization](http://edwardlib.org/tutorials/klqp)\n", "- [Edward: API and Documentation - Inference](http://edwardlib.org/api/inference)\n", "\n", "Additionally, I provide an introduction to the basic math behind variational inference and the [ELBO](https://www.cs.princeton.edu/courses/archive/fall11/cos597C/lectures/variational-inference-i.pdf) in a blog post of mine: [Further Exploring Common Probabilistic Models](http://willwolf.io/2017/07/06/further-exploring-common-probabilistic-models/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fit model\n", "For the approximate q-distributions, we apply the [softplus function](https://www.tensorflow.org/api_docs/python/tf/nn/softplus) — `log(exp(z) + 1)` — to the scale parameter values at the suggestion of the Edward docs." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "N, D = X_train.shape\n", "\n", "# fixed-effects placeholders\n", "fixed_effects = tf.placeholder(tf.float32, [N, D])\n", "\n", "# fixed-effects parameters\n", "β_fixed_effects = Normal(loc=tf.zeros(D), scale=tf.ones(D))\n", "α = Normal(loc=tf.zeros(1), scale=tf.ones(1))\n", "\n", "# model\n", "μ_y = α + ed.dot(fixed_effects, β_fixed_effects)\n", "y = Normal(loc=μ_y, scale=tf.ones(N))\n", "\n", "# approximate fixed-effects distributions \n", "qβ_fixed_effects = Normal(\n", " loc=tf.Variable(tf.random_normal([D])),\n", " scale=tf.nn.softplus(tf.Variable(tf.random_normal([D])))\n", ")\n", "qα = Normal(\n", " loc=tf.Variable(tf.random_normal([1])),\n", " scale=tf.nn.softplus(tf.Variable(tf.random_normal([1])))\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Infer parameters" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 35405.105\n" ] } ], "source": [ "latent_vars = {\n", " β_fixed_effects: qβ_fixed_effects,\n", " α: qα\n", "}\n", "\n", "sess.run(INIT_OP)\n", "inference = ed.KLqp(latent_vars, data={fixed_effects: X_train, y: y_train})\n", "inference.run(n_samples=5, n_iter=250)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Criticize model" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def visualize_data_fit(X, y, β, α, title_prefix, n_samples=10):\n", " '''Plot lines generated via samples from parameter distributions of the first \n", " two fixed effects, vs. observed data points.\n", " Args:\n", " X (np.array) : A design matrix of observed fixed effects.\n", " y (np.array) : A vector of observed responses.\n", " β (ed.RandomVariable) : A multivariate distribution of fixed-effect parameters.\n", " α (ed.RandomVariable) : A univariate distribution of the model's intercept term.\n", " title_prefix (str) : A string to append to the beginning of the title.\n", " n_samples (int) : The number of lines to plot as drawn from the parameter distributions.\n", " '''\n", " \n", " # draw samples from parameter distributions\n", " β_samples = β.sample(n_samples).eval()\n", " α_samples = α.sample(n_samples).eval()\n", " \n", " # plot the first two dimensions of `X`, vs. `y`\n", " fig = plt.figure(figsize=(12, 9))\n", " ax = plt.axes(projection='3d')\n", " ax.scatter(X[:, 0], X[:, 1], y)\n", " plt.title(f'{title_prefix} Parameter Samples vs. Observed Data')\n", " \n", " # plot lines defined by parameter samples\n", " inputs = np.linspace(-10, 10, num=500)\n", " for i in range(n_samples):\n", " output = inputs * β_samples[i][0] + inputs * β_samples[i][1] + α_samples[i][0]\n", " ax.plot(inputs, inputs, output)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Visualize data fit given parameter priors" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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NjuMUybVUC5WOHPPiL32FQs3FXMlkEolEIuVvFIUlxJBYJeqKTDZUUh6AkUgE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uHafa3PVhjXbn2PuDqboeLQt2icH5EaHYIakK7+5qZQaDg+HDuB1wyiWwEsx895VeYdj8Os4iIk\nkITLSGOao5W3GatPIiGY8u3hh6H3M+EfxZVWH6SC0JmST3ZFR/uRiUkyfbIEiowps/iSqMqCrAyn\nZEFWESzIUJBdijKUZCjLYMggFHk5kWyTS2WF75aQS1rLbAVRcUXr5bTeJbf1nXDbfwuwRGc5uf0u\nIO5TKVUtLMtFWiScuwIefunhYbyqwkLZ4CeX8pycKmPbbmedf/Kx/fzei1PMFxoIR+BRWtIRAeyN\n+4kGPIS8KtmKyT8+PMyvv7ZAInjVoWKhZvJXjwXxexT+5bOXyNUsvKrM//ThMY7vvuql+3d+eBZv\n3qC/L4AQcOlSkfxYjPftiwFe4OoDiuM4NJtNms0m5XIZy7JQVbWj0dZ1HVXdWGGWXmFHBrA1EELs\nkNVNYIes9gi2bXP58uXOgL3WC6FX5vq3EhspkdoNWZaxV5ETSKqKFAwiB9dfcrBUKmGaJv39/asu\nIxxnGQm2a3UqpSqFfJlysUqlWKVertKo1DGrNZrlCsI0odlEt030iom3WEV3LHyXZ/E7Fl7XxGOb\naGsgw21Mt4+5k/DmRfIuvl8jj7iubtjrQ3g8uJUypmktTajzejdMhoUQTE21zGBHR0fX7Wqhyiqa\niPAfv5/l5KxOxHcff++jn+HBPSHKldfIZv8YX+F7PBow0bz7cQPv5bnZfr7+zjQmJSS1jKSWUf5/\n9t47SrL7vu78vPwqV3VXdZzYM5g8IAASBEGCCWCmSJGUaMm29ihxJduHWh1JtLxa71qWV5S0lmWt\nLO/RHz7Srqgj76G0EmEqkCYkMIEgAYqDNJhBmtAzPd3VXTm//Ns/KnRVp+lUgyHQ95w69erVq1fp\nhfu+v/u9NzSHpFaQ5PY2IwmJqBsl4SSI26PE7RRxN0o00HueqR5QQWUhCFP2xlDcKGNujAN+iIQs\n05DhOTPgUjxgQRcIRULIGoZwmHbnmXKyaCGPpbH9PB1+M9nQBJZmosoSIVnGUCQMWUaTQZFlZLk9\nZI0s4SnQkOBFReI5uV31c2RwlF0iLP4yCSQQSO1M2GXi6AV9z9Mmin2v6RLLgdf3zZP6nmsLLFfM\n6+vu3w6MqIaou+gdDu0FsEiTzy9a/Nibp/nZeyY5971F3joSwVBlAiHI1x1CAeyPGiiBIFdzqLZc\nvKC9jqtFi7myxXTS5HA6wr6kSVhXqFkeMVOl5fjIkkQ6ovNv//YlKi2PdFSn5fj87qNX+N0fOsVI\nJ7FssWoT0tr7jCRJCCDfWFs8oSgKkUiESF8sq+d5PQJbLpfxPA9N03rk1TTN1VIhEYDbRHLq4DSQ\nnPrytFtHchrQmdee357XvwyA9eE/ILiJy8itsHV6tREEwdBcePrfY4+sbh97ZHVIUFV1W8RsmDKA\nWw3XdVlcXMTzPKampratwx0Wgd+MG4CkKEiRCHLfyUWna9+zNi5fvsy+fftYXMqxUG4ihZNUbDHg\nTbvUCWLIVVq06k1Mz8HwHUzfwfQcIsJjXA/IqIJRNSDsNhkzFRKyT1S4hAMP3XeQHatDoi38YgnP\nWhiUVFjWht9vbq3vbJqrdMODJLhLkrvPm7SCAN+2CU1PE06N4C1k8UN9RLpLlk0TaYN94lf/5iWe\nuVElZCoUXJ9/+aWX+K1PnGAkejf25F2Q/gz58nfIl79DvfACqnGVN84c5bniXSxaY+hKgCl56MJH\nx0dTfGRZIjBlKrJMQVawlXaF0lXAU8CTJQJZRcJAwkBIKv4miaILvMgUL67xnCwEkt/mFX4g8ANQ\nOuQt6FQVAy/As9ter+0mnHZntwgEyobEEPBXksI+Ytklm+LV8hVoF2S7BVtTl6nZ29uHG51QEgl6\nbgEAIU3hC89kOT0RxenzyZWlto+uHwh+/t2H+c9fv4oqSUR1hZYXMBLWuFpoYXsBVcvjF959GF1V\n+Mx7Zvidv79Mvu6gKRI//65DyLJEseEy2qm4hnQFqxEwX7F7ZPXUZJRvvdwiEmr/j7IkcXh0hauH\nEODbfSSyQxzdOqrTINRHOhu1CrlCAc+tkVAtdL+B5DRQ/Ray10L2mkhuE2kTimuBBHoUoUcQehQ6\n90HoACI8ijBvnkf/eqmsfr/4rL5esUdWh4SuDdVWMUwZQBfD0iB1h5aFEBQKBSqVyqblDzdb7zDI\n6jDcAIQQeJ7H7OwsY2Nj7Jueuul3t12fpbozELrQnX6pc5+tWDS7EUgS7dZuBcJRZYXzgdnXJGaQ\niWikNTA9p1Mdbssj/GaTxdlZxhKJXuU4aLVwLBvbtrFdF8txsB0X2/OxXQ/b87C8AKfSxC41lm1x\nNA1H1XBVDedGsf1Y03FVFUftm+7O13QcvX1zNb2zjIqjqNgHNILDg1nn/3R2acUvdrJ963obdaUA\ntCukTUAOgt6tPdzcJo2BLyECgeQKsMHwBRkvIOnKhH0JOXCpy2UqWgFPKxLBIxFA0lcYtU0mWlHG\n7AhJESaKgR6A7oMRCLQAbOFQFQ6lwCMnYClQWULuaUVzCG5WS3+tHJRl2nw5Yqr82U/fzdxShZ97\n+GX8QOD2RbNqMr10r7WgqzJSx0qs+xpJgmRYo9ryyNYc3nl0hL97sUDcVLFcn5Amc2I8StRQ+fQ7\nDxLWFL50IcdfPp0laqicmYrRdNpJVePxdjLe0UyE//TJ01RaHnFTRZcFXqvKOHkSTZuEYqN6DbxW\njYNzF9AWHSSnzr/SqjwhzxIUWoRFiyNxwfjX3eXKptshosFmm011JClEkxAlJcxEehQtNU2ghrFl\nE1c2cCUDTwkhm3GUcAI1kkQNp5DMGELrkFIjBmpoxzKO10tldU+zenvjtXJcvC2xHV2goiirXAR2\nE12CNiyy2rVjSiQSW5I/bIRhWUztNgluNpssLCwAbCke1tAU9iVNxhJGmwD2LG2C3uPri4tIoShl\nF/JNh3zLpWR5lCyXiuMx6/icd1zqRQu/yCotoqrJqJqCqsrIqoKkxPEnTyOpCn6iLRd0xaAX5nah\nITAAQwg0EWCIAN330QMf3feJeC5J10VzHXSrge7YaI6DZlu0ynVMx8a0LcKOhea5+JqKp2s4hoFt\nGtghE6EoKCJACXwiVo3p8CXGpq4QmSii+R7qCwrSEyGcl6LYkoHVaZazFQ0rNI6aOkkkepCIHsGU\nQMVCxcNUZOKqQVyeQpYGu3bdwKbp1SiJCtf1HE9HmizpRXLmEgV9gXxoDkdtrPo9hG+2NbNuAsWL\nIa2hpRVeFG5BEtUwkTIVylb7QrurMoB2GtO//MIL/MQb06iyRMtthzGonWUmEyYPHh/lC09nadg+\nXQcyRYKPnB3joeNpPvfEHM/cqOH4Agk4PhZBlSUkCSbiBu8+NkpEVzh/LcdY3OFIzOeLX3mEC9ey\n4NQJY3Eo6vPOWoVI0SKpOKRUi1OSROgL/kC1M9kdVvfa7Wf/Za0v+83lSV1SeFANIYw46BEkI4rQ\nY4joWLuqqXWrmisqnFr7cXt+e/r//NYS37pSY7RTtc3XHR7cn+ZfvGM5trlznTrgAdt1yxCWwBAG\npmy0pSdKu9K7E9zqyup8xSJfd5hOmr3fYdjYs666/bH3y91mGHZltTukvts7ZvdgWa1Wt6VX3AjD\nkgF0SXCw0vOwQxJ7BtorTbc7PolWZ+i25XmUanUsP0ANh6m0mihXlnAlqc+MO1ie7ltH7/GmyPiK\n3m0JCAGh7ukLDEkiLEtogCzaNwKB8DtDzl6A0wpwHJ9gxTCyFAhiqkxMU4jrKklDJWWojIQ00mGN\ndFgnE9YwPQunXmciPcJILIYhyxiyxI0rlzlx9OimTo5da7fuRZPrurx8PcsfPXqe+UKRpNZCyM1e\ns5MMqELCdiBouDiOh28H0PJpOBIV/yCXvUmS0SKHT18nc3IO9XQVuekSfeUE47P3EfKOYxgxTEVZ\n9RmFryNaDYJGEdEqYVklilKLG4ZDSW5hO2Um8nn2F6rE3YAjis4+RcdSOwRY0bHUcWxFwdbA1gS2\nLrB1H0d3sQ0X28zhGNexDQtHD7A1CTsMtgaWKmHJUSzieCLRI7HLDWMJAi8GfphXb2B/Y9Sc9j7a\nvyWbqowkwWyxyW/8/TVanRJqIECRJY6OaMTkJj97NsONl7JMjHqERItQ0ETYNT4cinCoGPDgvhqF\nSBG3VaNQKqE3moTqLTK6Q/KvbSS3wU87dSSxxnGie6hr0rseaAYGth8mbidBdEhkdIJA7yeW7Rta\nhGsNhf/yD0UCNYJsRlm0NaKxJL/1yTciaSFmr13j4MGDq997i6g7uYFwAU2RaDjr6PX7PGATifbQ\nghCiZ/FWqVQGfIr7gza2Uqy4lZXVv3hqgT958gZKJ6nwf37fEe49mBz6++5VVm9/7JHV2wzD1qx2\nyfBuXeH12zGZprmuf+x68NYghNYKMle3HXJ1h1i+slx57L6m8/qVr+k34F7rcfs17Wlvtrrj30Gm\n459oN1BFgOlamIrcsbdp3ydUuW1703lsdC1wOo+7djhGxw+x30uxVioxGouSCIc6/onyCl9FGW0L\n/olBIDj3/EtE0lPL0bj9mtpCixtVm2caDit5tCxBOqozFiv1AhbGYjq06uQp9DxrU+HVtjxBEFAs\nFllaWiKbzVIsFsnn85RKZUAwCYwpEhVhkg1ilIMwpU7kaAOdMBLjssyYKTFmyowl5FUZ9GZRQjzu\n00g/S2X6G9TPPEPtzqdoFY/hXXs717N38YJQmZMFS8KnFLhYvo0p2UwqVY4oV5jU5lEIqAcxKkEa\nW5rkUsrDiLs9XbHhd6dtDN8l4lqMWA6m5/b0x4bnoGzazbUMlHHlNoF1NLD67m1Nat8UjZaqY8sm\nlhzCksNYcgRLjtEihiUlsJRwH4nWsZVOZVnV8OTt7/sSAWFsIlhEpdbgPS0iisWIYqMHDSJYJGSL\nMBaRoEU4aBHVLMKiRUSyiGJhNDqjSH/SqWCuzGToxAHrik5Ia1chD0Yj2EoYSR9HC8fxteWKZcXX\n+fz5Op4a5uWKTMU3aGBiy2GKnoGrhjgykcaXFMotj4d/6o033Wdars9TLxV42rhGMtw5tmlwo+7S\nwiC8i0TugSMjPDVXpdXRSTi+4G0zqU2/XpKkHintIgiCHoEtFos4jjOwXH/Qxlq4VdZV10st/uTJ\nG0QMBVWWsFyf337kMn/6k3dtKR1sOxg2WQ2CYI+s7hB7ZHWI2I4MYNhuAN31CyHwBNiij8z1EcB1\nK4B9VcVKo0m11UIxTYQWolxrQGsRX5YGKoZ2EKyO++sQxS3VkAvza87WJG5KAGOKjCHLA4RQFQK3\n1WQsmViHAErLr+kjhYYs4VstyrkcqWiU6bEMet9B6MaNG4yMjGzJR/VmWLDrxCMGkcjurFOWJZIh\nhaOTMU5Oru/96fkBS1WLF2YXyFZaeFqEYivokdrrpRbfu1am3OyQjm8XOq8UJBWXg2GPCd0mKTUx\nvQaSXWuLRwEkiUQiQSiW5OlciFoQQhERYiLEGAozW4z6vETAd4WH5EPYlQhfPkvrlTPcCJeQD3+L\nowcfJ3PXHzLqmmjZN3L9xv3MVvejSz7HrSucqT5P2i3iSBrPx07yfOwUeSO9sx9aCLTAaxNbr0Ng\nV5Hdwea67nzDtzCDJqGg2Z52bBK+g+F5mF4Tw6tjum17p63AlyRcVcVTFAJFJlBlhNIel5cUgawK\nZDVAU3xU1UdXPQzVbd8UF0ULkPuWW36NQJIFkgRCkahj0iREAxNLClMJDG4QpyZMakH7OU8LY8th\nFCPKXEtlydZpEMKSQqSSSf79j76ZaCwBytrDwSuPHwv5Jl965QWihsqz5Sp251hqyDIWASFJJpAU\nHC8gbt7cIuqrL+b53a9ewXYDCk0XTZGIGG1drKnJmNruEpx33jFCy/X54nOLyJLEj923j/sPb56s\nrgW54+3afzzyfb9HYOv1Oq7rIsvyAIHtesDeKhlAvu6gyBJqp6pqagqVlkfV8oYuBxj2d+wS/td6\no9owsUdWbzPstgyg5Qf8xMXrzNlumyD6Ac71OrYQuxbbZ9gWhmyjBgGGKwipy4B++ygAACAASURB\nVEkrYVkmpa5MXpFXEcKBpJW+x7osoYqAci7HoenpvmrjMhlVtnnV73kec3NzHNq/vnXVSriuSzab\nhSDgzMED6Prqg+gwPExfDY9cIQS1aoVmocA9h9IkEok1T+6NRoP57CJPnb+IZbuUinla1RLC99rt\n8i7YkkEpCOH642hBhJiIkBERxlsqY1mZtyGR2mbUpx7AMVfhhKuw35ORkLguB7ygO7yg+VQUE+Ye\ngrkHOZa6xNunv839U0/yrv3folSKU70QoZqNsSCN8+joO3kpegeuvEsyFknCVTRcRaOuh2++PCAT\ntKuUWESkFtH+e5arkhGpRVg0MWjiSw0C0cLDxhVu5yI0wAokLF/GCSQ0V8JwwXAFhuthOh4xVxBz\nBBFHEHJBtyW0BiiuhOKB7IEvJJroNNkcYfAlGbsjj3A1Ay0SRg2ZXGuIXnXXknW0SAglFCKQNJY8\nj4YAWZUxFZuJEY1Gs8I/PP4ybzs13XGi6HgOb2Ckvy/ZbjCcr9pMJnRmC203jEAIwppM3FQpWx6y\nJPELD248bD9fsfiPj15BV2TCYYWm43Mp3+LgSAhZgl9+75Ed60FXQpIkPnh6jA+eHrv5wjuAoiiE\nw2HC4eVtcj0PWCEEhmH0Hg+ryjqVMNsyBi/AUGXqtkc8pJIIDddSCoYvdbgVMoPXOvbI6m2G3ZYB\nKJLEqYjBlKH1KoJhTSNmGmuTxoG4vsFqpex5VPJ5dAn2T4wTMYyBg3U2myUSiRCLbS+lZz0EQcDV\nYo6Z8OYaljaLrRDAIAh6Dgfj4+MbfsdhuBfcarLaHwnbtWCzbZtcLkc+nyeXy/Vuzeby2K2pGYyG\nkxxJHSZFlJQTJtk00RqsiozyVIklAmY9jxc61dHFTUZ9GgEcdRUecBUOeTIyEgU54HHD4wXdp6is\n9VtJXCkcRJt1sCyVOw5cYeREhYNvW8B7yxLNpSjBDQWvuNWhOoGJQxSLqNTsDIkPEs3+4fIILaKS\nte68sGRv6l09IdPApE6IhjBpEKImYjRoT9eF2Z4WIWoYlGSF66qgpvrUFY+m5uAoFkrIZjTlUrAL\nWMFqSYziyhhWDK0VRbfCnZuJYRsYts6oZCA1Zc6OhhnTAiqlOnE8jicUDN9FWC28RotkqwBWCd1z\nCfkO8Vw70EMJNrg4/xIsrpwny207NMMYsFXr2qz9iqrzUtWnFCgYkRBmLIISCjGVSdKUNVqyxuRY\nkvHSVZxWtudH3LVmozMkfq3YQpLabgQA00mTQtPh0+88yKmJWM9F4LWSWL6eB2wul8PzvJ4NYdcD\ntj/EYDcwHjf4pffM8LuPXsFueURNlX/zwTt6ldZhY4+s3t7YI6tDxHY2/t0mOros8auHJ3qPc7kc\nuq73BPmbQRAE5HI56vU6R8fHia5jwP9q+qEOc73dRKbNOhwMw73gVpFV3/fJZrNks1lkWaZcLvPY\n179JLpej2qj1llMlhRElxv5ghKQ3TSqIMBJECVk6Uk0CTUZJ6MhxHWW6fS8n9M48Aymu4Uk+n/3L\nCzzyQm2DT7QMTcARV+GEo3DYk1GRKMsBTxoeL2o+S8r6pqJpO8+Z2vMcr7+MLlwK2gh/u/R+FpuT\n7Ess8Kbpp7hr8jz3TZ6j2QqzND9NbSGD4YjBCmcfqeyfp0ib+28awhgkkoTIihQNpmgEJjVCNERo\ngITWO4RzcF4IG431vrAqt83zJfquEXxY6Zs1Glb46OFJPnrnBF4g+Pk/fxqHCnW/hEMZSa2i6VUc\ntQqRCiTKyNoskrz6MuI7aoR0KE3azFBvhJkvGGiM8N47Znjo6BEidYXLOQNFC3PndJwDo2Gevl7h\np//4HJq7LIUIBS7RwGVfCD79lglGZJ+g1fETtpbT6ERnXmC1lqerVSSrxTHLblu0tVrIfYEi/U7P\nufX+JFlGMk2mDYNfc2U83cDtuEk4ms7Z+QnkUIhSN0TDMJEcm/rERB/x7YZ2LPsMS6aJbJpgGN83\nVlCqqqKqKuFwmEgk0rPmsyyLZrNJsVjE9310XR8gsNvVZr5tZoQ3HUhSbbkkw9rQtaq3Cr7v75HV\nHWKPrN5mGPZBbCsyAyFEz4oqlUoNRGeut+5hkcph4GYE0HGc9pA/bSuqtYb8t7Pe7WAY6xRBQH5+\niaXrWZYWFllcWiRfLVJzm3RFIpKQSIowGRHlWDBGSkRISVESsQRq0lgmoXGdnFUiPjOFPhJGCikb\n/m9CCHB8Hjqe5u9eKKwrSVEEzLgyJ1yFI66ChkRL8pgzipSNJYRSYERq8V6p0+DTI5AWIdHCqfkU\nKwo1S0eWAg7HytyVmudgqLRsP+kCV8GfhVxaZ37CIXykCTMvkSp5JBcEal7vEMYQFRHhBqM0gtUE\nsr6CVDYwe/OamARrSB2GAa+zG8qAokgoskTLbb+7LEscGjHJVh2QZL58IceXL+T4+XcfRgiVpUqU\ndgjsfiTa+QOSDIYqY7kBEwkTQ3eoeyVOTXt8+K4QuVauF5P7YmGebOMSwqyC5PP5Ofh8J31CQiJp\nJMnkMqRDaar1COakhGVHcb0EVTeG78Y5OprhJz5ykn0TW0+ma39/wS/9xQXOL9SQPI9Q4PKzbxrj\nA0fifWl0gwQ4sOwOEV5+fmmuQHaxguG3E+eOKxbeSy91SHI7eAPXRabdHrcpSNIyiTUNJLM/Yc7s\nkd3u83IndU7qfz4UQu6f1xfgIe0yGe7Xc0qShKZpaJrWG10SQuC6bk//WigUCIJgFYHdLFkzVJlM\nbHdH0V5t7DVX7Rx7ZHWIuB2vnjdLVlutFgsLC5imyaFDhzY11PP9FhW73v8TBAH5fJ5arcb4BpXk\njdY7DLK61d9WOD5+xcGv2FSWyuSyS+RLefK1IkW7Qsmv40uddQqIixApEeGIPsFoOEU6OcLI6Aha\nKrRcJU0YSGG1HRW6AsHVFupEGFlV24k9ngVOHezByMf2vBp6q8LHnDpjk9eZzxV6Q+Jh4eK6+ynZ\nd7Jk34knDEypwtHQ49wReoxJ7SLSOpXMQEhct5M8W57kSiWJG+iYus9kxkGLa9TkSb7MDHXPXGMI\nPURjzqQxF0I3m9w19Sz3Tz/JyOkKVSfKt+fv5Zs33sJCY3LL/9+wIQNIbasj1xcEnZ8nAHy/7XsL\n7SqrrkjYnqDl+qTCKoam4PoBv/mVV6i0PJSOq4TfWYmmySiSRCqscve+BP9wrULL0jg1PsOvv/fY\nKk3hp/70WWrFFroKQmpQ94vcfUjizQdtKl6FSlAh32oT27nm84hUhZXUJC+p/C9Pp0mbaTKhDGlz\ncLp7H9EirIXvXStzMVsnrMlIuoHn6/yn5+p86J2nULdwXH4jMF5uUWi47E+avdSqfni2TXZ2lsmR\nkVXRzKJlIezlNLmgtTwt+ivCrRbCtgjyhYHng5YFznpimPWxTIbNgeleAp1hot95J9FPfPym67qZ\nnlOSJHRdR9d14vE4MOgBW61W2x6wHe1rl7xuhcAOE7dixGpPBrBz7JHV2xTDsguRZXnD0IGuNslx\nnC1HpN5s3bc7hBDUajWWlpZIJpM3rSSvh2GQ9pUEWHgBQdXBrzjL9xWHZqlKrlyk0ChR9GqU5Dol\nqYEjLQ+FhiWDUTNJRh1lNDVCJBLh0LEZEpNJZMNG8jpRkHYdnGs9okm2jnStsQYBbZPPQ40SWtD2\nvMSp3zSxp0tx3q0aWOEoz1dPc816iEv2XfgijCRZaPolNOMqda3EYxj8d+6n7r57hS4zRNPXyDQX\nOVZ9mWl7AR+ZVyIznI+dZt6cbKf4BLDp1IMWXL50kC9c+jCn0y/w9ulv89CBr/P+Q1/llfIhvnnj\nfr6bvQfb370KUMyQkSWJt86MoLgNHr3SpLmJ0COJtp1YAIyYCosND0VuXy905QBeIDBUiSAQJEIa\nTdcnYrSJKoCmyHi+QIjlwCNFbm9zn/3IcR44MoKhyiiyhO0F2F5AzFi7eh41FPxAIKEgiRiSG+JI\nZIL3T8ZRVI3PPVXg3DOLSBK85/go37iUw6GCrFbxpApvPiJzcMzpVWovVy/z5OKTNLzVgQthNTxI\naENpMmaGbNHA1y0CKYkcxFFkBcsTeL5AV7e2T+9LhtiX3MCFoxPJrKR36ByxDoTvL5Nfy26T2H4y\nPFAdXl0xFh1JhLBa+MXC8vOt1qbI6nbORbfKA3Y3cCuIpO/7e5XVHWKPrN6GGGbK1HoNXF3/y3K5\nvO2I1O+3ymo/bNsmm82iKMqOQw12WlkVviCot8mnX3UIyg4iVyWoepSsefyKg9OwKEkNSnKDklSn\nKDUoyXVa0nIVxtBl0obGKVNhLOQxblYZU8qEgypBq4LbKKGXbZRCC15eTuy56eeTFDCWjdPp3Bwl\njhxPI5vxAWN19AgYg8sGWgRbaOQXZa48W2H2mSJW3cNB8Irmc1G3uaoKAmkGmFntUdRB0i1zunqB\nk/UXCQUWZTXBY6m3cDF2AkvZuc2XQOZ8/hTn86eI6TXun/wub5/+Nj95+v/lHx//S57M3s1jN+7n\nUuUQOzHrN1WZmKnhBYK67fGv7s/wm//oIEIInrlRZbFiU3d8EiGVv3sxz9deKtDsRJDKMsRNlbCu\nYHuiJ1KVaKdK2b7gn9yZ5ME7UniyxlJToGsav/HfX8FyAwxVouEETCYMZostXF+AaBNXQ5O5czpG\nWF8+0RqqjKGuf3L/1FsP8It/eYGq1Wba8ZDKD989CV6D/3a+wF8+ncVQZATwlYt5fujuKWaLKeq2\nx0PH03zirok1u+wbboOCVSBn5dqV2RX3zxaeJW/lcYPOBXOmL0bDjxKWU/zKE/t6hHblfdJIIktb\nJy3D9iGVOmSYyNpV5GFjt2ydtuMBa5pmz0JrWLgVZFUIsUdWd4g9sjpEbHcHG1bKVP+6+9FtIIrH\n4zuKSB02WR3GSUEIweLiIvV6nYmJiYFO2O1ioyF74TmIUgW/WCUoNQjKVrsqWg8I6uA3ZQJruXHG\nJ6AiNSnJZcpKkZJUoyhZVPsK3qrwyFDkmJRjjALj5BkjTyxoILWAFoh6uBf36EgGQo3ghccwUmME\nRmyASA5MG51oyL55qOaaeePZa9cYHx/fMGZWCEH+ep1L38pz+dwCzYqLokpMn0yy/84UP/X3L1K0\nNi4nysJnpnGFM7UL7Ldu4CNzOXyI5+OnuW5O7zgLfSU0GYIAak6Mr8w+yNeuv5v9sSu8ffo7vHni\nHO/Y9x1u1Cd47MZbeHz+Xuru1t0wLC9gvtJ2AViqOTwzV2EikScT1RmL6WSi7eAFWZL4H+7dxy8+\nOIPnC56eq+AFgmNjURIhlf/1r1+ibns4XkDMVPGRmEwa/NgDx1BEuzEmpVq4rsXP3TfCHzxZoNLy\nmUmH+d8/cpxHLub5z1+/iusHRAyF3/7ESSbimx9dATgzFeMPfuQM33iliKZIvPdEhvG4QT5f54lr\n1XYluCMjcX24WmjyHz5x6qbrjWgRIlqEA7ED6y4jhKDiVMi1cnxv/jqff+YiVbdIKt5kf9qlYOV5\nsfwiJbvESvM+VVIZNUcHSGy3attPaldKD26Vaf6rhWHaOt3MAzafz2/oAbsbuFXpVXsygJ1hj6ze\nhtjtlKmV6+4SKdu2WVhY2JVq4sp17zZ2u9oshKBareI4Dqqqrj/kLwJwmsvD3QND393pGtgNhF2H\npkO04uO3FBwvjG+b+E4U34vj+yl8McLyAHjvTVCkAg1pkZJUoqQ1KMgBBUmliNFrypEQjOoO+0IB\nmUi7CWEsESKRjCMbJwaJphHF6U5rYYQkk8/nqVQqTExMEI1Gmbt0icOHD+/aQXSjBJzSQpNL5/Jc\neSpPNW8hKxKTx+Lc86FR9p9KopntqsNno8f5559/fs31xN0qp2sXOFV7gXDQoqLG+HbqzVyInqSp\nbs7DdDsQSBxMhziYMqlaHr/+0eNE9bfy2KUP8Jtfu8jRxJO8dfLb/Mjxh/mhO/6Kp3Nn+Obc/Txf\nOIHYoKFKAsK6zKfu38+XLuaw3YCz03EOjoS4vFCghUGubvPyUoN8w+npULuQJRiN6AOE9k0HErzv\nZJqr+SbXii32pUL8j2/bTyykA/qAr+b0tMcDxydoNFu4jo1TyvLeAzrv+8kToOpk4uFtH4OOZCIc\nyay+8EtHtIHvEQhI76LhuyS1G7iSRpI7knfwo6ceXHM5L/AoWIWe1KD/Pm/luVq7yj/k/oG6W1/1\n2q70oCs7SGkpIkGEGX+mJ0cYNUfR1wky+H7DrQoF6GIrHrArLbS2c364Fd+v65iwh+1jj6zehhhm\n5GqXCC8sLNBqtZiYmBg4KOx03cP83Ju6OhUCfHv9xh6njtcoUS9k0YXNoVaV+CsSktNYTUadOjhN\npE4FJhAhfJHBF2m8zr1PujNvGl+kEaysQvkoegs5ZKGFHIxQlpbpU1RcinjkPZdc3aJQbeJ63bHu\nCIlEgkwmwx2ZDJlMpld9mJxcu7lno1+90WiQzWaJxWIDlfPdbgRbub7KUovLT+W5dC5HOdv2rJw6\nluQN793HwbMjSOrqis0DR0d5y6EET9+oYbkBkgg43LzKmdoFDrSuI5C4Gj7I+dgproX2I7YxbLtV\nCCGYLTTx/YDPvPdIT7/4A2cneOh4mufm70KRfhaNa/zt9/5v3jz+Xd40/gxlO8V3sm/hueIDvJSP\nIZZH6AEwNZkfvnuSTz1wkE89MGhQPzvLQNa8HwiKDYelmsNS3SFXszv3Dkt1m4WKzbM3ahSbKzXj\nJf7s3AKZqE4mpjMWNTr3OmOx7nSYTDpFVJd7tkRtn90KQRDsWlOMEIKfePMkT883qNvtbT0Z1vjJ\n+/dva307gSqrjIfHGQ+Pb7hc02u2pQcrCW1HfnC+cJ6clWtLD64OvjapJ5ertGs0h2VC25ce3EoM\n2zB/M1jPA7a7rZbL5W17wN4qGcBeZXVnkMRrxdH4NkS3I3KrWFhYIBaLbbkLfTOfp1AosLS0xOTk\nJMlkclcPQl2rpwMH1h+mWxOBv07Fcpk8lhfniJsyitda1djDSqJ5k8aeLoRq4ish5FACoSXx5Uk8\nxtvkM0jhewl8N0pgh/AtA+Gt1hzJUaVt35Q0ex6iju5j6z7RiSSFVpl8YdBE37Ks3usjkQiZTIZ0\nOs3Y2BjpdJp0Or1qKL1Wq9FsNhkf3/jk2g/P88hms/i+z+Tk5Kor+ytXrrB///5dq+DPzc1hyFHm\nL9a5fC5PYa4BEkzMxJm5O83hu0YJxdqfobtvrLX9lZsuv/tX56g8+zgH8s8T9RvUlAgXYid5PnaS\nhrr2fnEgZbBQtnF38YgmAXFTwQ0E9+xP8Ac/enbD5f/t37zE45eWuDP9HHdlvsnRxEVkCeZbp/n6\ntft4Nv8GWp7CO46O8MHTY7zj6Miav8Hs7OwAWd0sXD8gX3dYrDnk6jZLNYfcKnLrUFtDamGqMplY\nt1Jr9Cq2KUMmrgtiakBM9QlpCoZhEAqFbpor349cLkckEsFG44mrJUDi/sPJW5JQNEw0m03mS/MQ\nZUBDu7JqW7SLq6QHiqQwao6uqaHtv4+okVeNMG53W7zV6PeA7d424wFbr9exbZvR0dGhfbb5+XlS\nqRRjY8NNJnstY6+yehtiGJXVbnUtHA6j6zqp1A7ypoUArwV2baBiqbUqhBdmkQvhFVXKxpoEtEtM\nN9PYk2H9xh4Rm1jR0DPY2BMoUWpliUrRI6ylMYgSNGSCqksrV0etglij7VoKq20CmtFRO7ZNXU9R\nOaEjxzQkpe2A0J/qlL2SJZ/PDyQ7GYZBOp3mxIkTZDrV0kwms+mq9laqoEIIisUipVKJsbGxnp3M\nWuvcDTQqNleeKvDCE1nK823dZeZglPs+doiZu9NEkpvrmA+CgOvPPc3Fr/89+557imkgcvgU/1/z\nAJfMAwhJ5u7pGC8t1Wn0MVJJgp95Y4pPv/8sf/j4Nf7rP8zj+QJZbg8xHxoJka1alFseri+ImyqX\n8w0cvz2UnghrlJvuwPC0LLWHqE1NRpZlpCBgbBPej7/83iP8nirzxFWTvHc/Z45FyKiPoucfZur4\nH/KjJ+KkRj7IvokfIhze/ZOjpshMJkwmExvrTFuu36vK5nrV2uXHF7N1vl6zabmrj0NRQyEd0RgJ\nKaRMmaQhkY6oTCRCTKXCTI9EmUiEe04DXXS331RY4wOnXlsn7YSeIJPIcDRxdN1lvMCjaBUHSWxf\nk9i12jXO5c5Rc1eHZISU0ICGdq37UXMUQ3lt+ZNuBdv1gPU875ZoVoch63s9Ya+yOmTY9uaiE/uR\nz+dRFGVnhLIDx3FYXFwk8BwmUhEMyeX6Kxc4MD4CzjLZlOy1hsC7hLKxer7YHJkWWniZPK4kmis6\nxDdq7JnPV0llJgmtIHciEAR1l6Bn4WQvd9F3PEaDureqT1sy2xVRR/cJZWKoqeXKaJeQStrgAcz3\nfUql0kCVNJfLUSqVessoisLIyAixWIyDBw+STqfJZDLE4/EdkcNGo0GlUmFqamrD5ZrNJgsLC0Sj\nUTKZzIYH4dnZWaampralVbbqLleeKXD5XI6FS1UQEBvTmbl7lONvniKe3pgs9VdWG+UiL37za7zw\nza9SL+YJJZKceOBdnHj7g8TSmba+2PKIm21NWsP2+Lk/O8+FbANVkfjhuyb42BGFQwfb3fPfvlLm\n5aUGEwmD9xxPo6zhCesHghezda6VW4Q0hXsPxPne9RoLVYtC3cHyAh5+ZhEvEB1tqcLnfvwNW242\nWv6+AdXqE+TyD1MqPYoQLpHwKTKZTzAy8n5UdbAp63aoZgkhqNs+ubrDUs3u3K9dsXX91aeRuCGT\njmiMxQzG4yYx1WdqJMp0KtKr3I5G9VsWpzksNBoNWq0W6V2yrmp5rZ70IGetLT/It/I4wepRu4Se\n2JDQps00KTOFIm2+M/122BZ3E/0esJZl0Wi0LdHC4fCAhdZuEthr164xPT1NMpnctXW+3rBHVoeM\n7ZDVYrGIEGJHwxJdY/tqtcr+2jliX/65nvZyIwhF7yOPkRXksZ9QRhBGbIBoCj3CtWyRA3ec7jX2\nIG/frkMIgWh6+BWHwtVFTF9FbUkEFbtHRoOay6rOE01Gjmt4JvghifB4HGM0PEBGZaP9ua5fv04m\nkxmwU+kmd/UT0nw+T6FQ6AUqSJJEKpUaqJJmMhlSqRS2bVMsFpment72d1+JZrNJqVRad50r/XE3\n6sjv4tq1a0xMTGxa+G83PWafK3D5XJ4bL5URASTGQhy5J83MPWlaQYV4PL4pR4XA97nyzDkufv3v\nmX3me4ggYPrUWU6+8yEOveGN7WCBm6Bue6iyhKHKXL9+fevyk5sgX3d47FIRSYK3HxlZ0xB+O3C9\nMoX835DLP0yr9TKybJJKvYexzCeIRu9GkqRbThC8QPB3L+QoNFzu2hfn9OTmHQ2EEJRbXo/Q5mpt\ncrtYtchWLZZqNvm6S8nyV+2qEp0msY6ONhNrSxDa00ZvXiqsrWlndTvgVgwjr4QQgppbWya0a1h5\n5a08RatIsELRrkgKI8YI/+zMP+ODBz540/d6rZHVlSgWiyhKW9rSJbC77QF79epVDh061Kv47mHr\n2KtLDxnbaWJRFGVbWldY7nLP5XIkk0mOHDmCVAvjv+tfg2oi9CjZYp3xA0fXrHSyww5Wp/kKxG6e\n8COEQFj+gKF9rzJaXfYYxWv/dgrtVExXkTpJSjrawdjAsLySMJBiGmWrSqlUIp1Ok0gkNuxSt22b\n2dnZXqxsl5j2//7xeJxMJsPMzExPWzo6OrrusM520qZuhvW2IyEE5XKZQqFAOp1mampq0wfUzWyb\nru1z7XyRS+fyzF0sEfiC2KjBnQ9OM3NPhpGpcO/9WguVm66vWSlz8RuP8vzX/o5qbhEzGuPO932Y\nE29/kMT4xKY+dxdRo/37CyHWfd+q5fG5J+a4lGuwPxXix9+yj9FNks50VOdjb9jaZ9oMNDXJxMQ/\nZXz8n9BoPE8u/wUKhS9TKPw1pnmQdPpj+P7dwK0hCF4g+NSfPsuFhRp+IJAliX/zoTv4yNnN6aMl\nSSIV1kiFNY5v8JIb8wvYkk6u7rBQarJYtSi0PMo2lK2AharFs/M1SquaxECVJdLRtQjtsq1XJqr3\nqu+3Eq+GdZUkScT1OHE9zpHEkXWX8wKPkl1a1SBWsAqMhzavf38tY6UsoH/+bnnA7skAdo69X+82\nxGYjUVei1WqRzWbRdX0wIjU+hX///9RbrvrKK4wdWV9btRvoRn1uREaFs4LQSSDH2sRTnYygn0j1\niGklaGCMRoiPp9aM+oR29TGbvU44HObw4cMDQvquZ9/KIfxWa1kvGwqFGBsb4+zZs71KaTqd3lKK\nFyzbbO0m1lpnu2O7HYm78vtuBuuRVc/xuX6xzOWnclw7X8J3A8IJnVNvn2TmnjSZA9E1D9AbXRTc\nuHie849+hcvfe5LA95g6cYo3feyTHL7nzSg7tExbD34g+D++cokrhSYxQ+F71yrMlS1+6wdPoG9g\nan+rIEkS0egZotEzHNj/GYqlR8jlvsDc3O8BMp7/DjKZj5NMvA1JGt6h+usvF7i4UOvTpwr+3Zde\n5gfOjO0qCVNkialkhJnJ5QpkPyGwLAvHcfCFRFOo1FyZigvFZkeK0JEdXC20eHK2smaTmKHKvcaw\n/iaxfkI7FjMGQg52itvZZ1WV1bZPbCizrde/HgZe13MD2I4HrGmaa1po7ZHVnWPv1xsytltZ3Upl\nrn8IeGJiYmDnWu8z7cSuY72oz6BqE83VyVvfQ7RWk20pqqHEdZR0CH0m0R6O729YiupIytoHfTkf\nIFR5TaLa//3Hxsao1+tcuHBhgJxWq9Xe8pqmkclkOHbsGIZhMDU1xYEDBwiHw7ty0tltS6iV6/R9\nn6WlJVqtFpOTkzf9vze1Ti9g/sUyl57KM/tsEdf2MaMax+4b48g9acYPx9e9SFhrfQCtWo0XHvsq\nz3/1EcrZeYxIlLPv+QBn3v1ekpPT67oBbOd7rIV83WG22CQdaVc/TE1h2hUrDQAAIABJREFUqe4w\nV7aYSQ/Pl3U7UJQQmfRHyaQ/Sqt1lUuXP0ej/nXK5a+haRnS6Y+QSX8M09xdqQNAaUVzGYDjBXiB\nQFtnf9wuVv5X6xGC/o5uN+KiTemYZrxHCBRFoeX65NfQ0S7V2tMbNYlFdIVMTGe8Q2hX2np1K7Yb\nJXV18VomdK8Hy6WtnAu34gF748YNSqUSZ8+e3TV7rEceeYQvf/nL/M7v/A4ATz/9NJ/97GdRFIUH\nHniAT3/60zt+j9sVe2T1NsRmK6tdK6pyubylJp6NPEtXRX1WBqf9qoOorx6mk0IKcsIgCMsYR5K9\nzvkeGY3rSDuoZq0cWu/Gw165coX5+fme116pVOqdPGRZJp1Os2/fvgFdab80YHFxkVAotCvJVet9\n1t1cZ1dLOzIywsTExM7InoCFl6vcuHCDq88UsJseekjh8N2jzNydYeqOBPIWyUoQBMy/eJHzX/0K\nl777bXzXZeKO47znB3+Oo/fej6q3tbS3ohqlKVLb27STdy+EQARbz4a/1QiFDhGL/jj79/8Klco3\nyeUeZmHh/2Fh4Y+Ixd5IJv0JRkYeQpa31+y1EvfsTww8ViQ4Ph5FU3aXpGyW1K301Oy3JGo2mxSL\nxd7QbdQ0SWdMjH2xtY9nQtBw/DUaw9rOB0s1h6euV9ZtEkuE1GXJwZqk1kD1AtRdJvW3C24Hj9Vh\nY6eEfD0P2HK5zLe+9S3+4i/+gkKhwNGjRzlz5gxnz57lzJkzjIyMbOl9fv3Xf53HHnuMkydP9ub9\n6q/+Kr//+7/P/v37+Zmf+RkuXLjAqVM3T4P7fsQeWb0NsRlz/e1EpIpAIBouajHArhVxGsGAPrTd\nsOSwsg9L0uU28YzrGBPJjj60/bjXOd8ZVrt8+TIThw7u2tV4V4N7/fp1CoUCjUaDfD5PPp8fIPTd\nZqeTJ08ONDvdbGj8Vg3Z7xSu69JqtdA0bVDisUWIQLB4pcblp3JcOpfDbvhohsyBM6McuSfN9Ikk\nyjYuKuxGg1e+9TUuf+cxKtl59FCYU+98iNPvfh/p/a9Oc8ZIROfB42keeSGHLEkEgeD+mRTTN7F1\nul0gyxqp1IOkUg/iOIvk839FLv/fuHzlXzN77TcZHfkgmcwniERO3nxlG2AmHea3P36S/+2vX6Rm\neZyejPF7nzy9S99iENshPutZEnU7uqvVKrZtI4QYGI7tNsREDZWooW5YTRdCUGl5awYuLNXa0y/n\nGhTqDis5rQSkwirjcXNZU7uC0GaiOiOR27dJbD3sVVa3B1VVOXPmDGfOnMF1XWZnZ8lkMpw/f54n\nnniCP/zDP8SyLP7oj/5o04WSe+65h/e85z18/vOfB9qNfY7j9BpLH3jgAR5//PE9srqH7WE7B+eN\nZAC2bZPNZpFlmQMHDmyqkztoelQ+9wLeUgv8dsZSk0L7SVXqDcNrh2PtimivYalTETWVLTXtbHfn\nbzabqzSl+Xx+wFEhGo0Si8W44447OHjwIJOTk6TT6W1Hxd7KZqjtIAgCcrkc9XodTdO25TAghCB/\nvW3Uf/mpPI2yg6LJZGbanfx33DOJug0NnxCCxcsv8/yjj/DyE4/hOQ6jBw7z4E//C+54y9vQjFef\nFP7k/fs4ORFltthkKmHywJG1Tfhvd+j6OFNTn2Jy8qeo1b5HLvcFcvkvspT7c8Lh42TSH2d09EOo\n6tqeujfDu46N8s1ffOtQK967nZbWTdRKJNqV4bUaYjajJ+yuLxnWSIY1jo2tTx78QFBqugNWXtdy\nZQpNn7INizWb5xZqFBs3bxIb1NEuP341msTWw+uhsjrsBKsgCFAUhX379rFv3z4+8IEPbLj8n//5\nn/PHf/zHA/N+4zd+gw996EM88cQTvXn1en0gOCgSiXD9+vXd/fC3EfbI6m2ItSqrvu+Ty+VoNBpM\nTExsadha0mS0w3G0mQRKQqfs14lOJImMx5HCu3tg3Ize1rbtAT1pd7rrdwdgmiaZTIbTp0/3zPMl\nSUJRlA2N7reKYVRBd4usVqtVlpaWSKVSHDp0iKtXr276tUIISgtNLp3Lc/lcnlrBQlYk9p1Mcu9H\nDnHgTIpiOU8kEtkyUXVaLV769jc4/+gj5K9dQTNMjr/tnUzf/WbGDs1s2kvwVkgBZEnirTMp3jqz\nc8/i2wGSJBOP30s8fi8HvSqF4pfI5R5m9tpvce36f2Qk9RCZzMeJxd6EtI0Yz2H/H8Nc/830r2tl\nyncJ7GahdAhnOrpcJCgUdHRdH7Alcv2AQicetxu6sNSr2NrMFlt8d7ZC9SZNYpkVOtpuxXZ8l5vE\n1sPrpbI6zO3S9/0t/Yaf/OQn+eQnP3nT5aLR6MA5s9Fo7Np58XbEHlm9DdFPdvqtiUZGRhgfH9/y\njiVpMtH3LzdmVLICIjpyZPe7sPsrlZ7nUSwWV1VLK5VKb3lVVUmn0xw5cqTXfZ/JZIhGlzvO6/U6\n8/PzKIrC4cOHd/XgKUnStpwXhgnHcVhYWECWZQ4ePIimaRvaM/WjstTi0rkcl5/KU862kGSYOpbk\nrvft49Cdoxjh5V1+q6R66eplnv/qV3jp29/EtSzSBw7xrp/4GY7d/3b0UJh8Pr/p9TUaDXK53ECW\n92ZtYPbQhqrGGR/7EcbHfoRG44WOBdbfUih+CcPYRyb9g6TTH0XXbw+LolejEWktPWE30ajValEq\nlQiCYGA7NE1zS8eYtS66NEVmIm7eNETCcttOBysDF7qV2xcX63zjlY2bxFZ60nYrtGNbaBJbD6+H\nyioM9yJqWJXbaDSKpmlcu3aN/fv389hjj+01WO1h+9jJTtC2YsoSCoW2ZU20Hjajid0KgiCgXC6T\ny+W4fPkyjUaDYrHYCzfovufIyAhTU1O84Q1v6OlKk8nkur+R4zhks1kAxsfHaTQau77Ty7KM562u\nbrwaCIKAQqFApVJhYmJiYIhno+2oVrC4/FR7iL8w1wAJJmbivPWTkxx+wyih2NpSkc35rFq8/J3H\nOP/VR1i6/AqqrnPHfQ9w+sH3Mj5zx8Dn2sy23nVucF2X0dFRgiCg1WpRq9VwXXcVaditbf61jkjk\nBJHIr3Bg/y9QLP09udzDzN34v5i78QckEm8lk/44yeQ7kOXh2IRtFrcD8dkokrNWq/UuuvoN4Q3D\n2NCabbvfy9QU9qdC7E9t7OjRsL01dbTdeNyn56rkajbOOk1iXcuuTEeGsD8V4gfOjt20ie52tuX6\nfoEQYmjHsV/7tV/jM5/5DL7v88ADD/CGN7xhKO9zO2CPrN6GcF0Xx3FYWlpienp6U2lEW8FWrbG6\nEEJQr9fX1JX2E754PM74+DjHjx/vmeiPjIxseoftT9/qkrbuiWS3MQzN6nZQr9fJZrMkEolNNcw1\nKjZXnipw+ak8S1fbv0vmYJS3fPwwh+8aJZK8+Taz0Ukof32W57/6FV781jdwWk1Gpvfz9h/7aU68\n7Z0Y60hQNiK//SMEXecK13URQvRsYNbr+t4sadgDyLJJevTDpEc/jGVdJ5d/mHz+i7xy6ZdQ1RHS\n6R8gk/44odDhW/7ZbleLJ0mS0PX2UH53GDUIgl4DV7lcxrZtZFke2Ba7IwG3gtBFDJXDhsrh0Y2b\nxKqW16vQLq4gtLm6w6Vcg3y9HXhyYiLKyYnouuvrrvO1LgMYNrYqA9gI9913H/fdd1/v8V133cWf\n/dmf7cq6b3fskdUhYysHsX6SpqoqBw8eHMpBcDOV1VartSYptSyrt0wkEiGTyXD33Xf3KqVBEBCP\nx7etnem6HKwkbbtdDe5iGJrVrcB1XbLZLEEQ3LRhzmkFXHxsgUtP5cleqoKA0ekI937kIDN3p4mN\nbq2haSW59BybV578Nue/+hWyL7+Iomkcvfd+Tr/7fUweO7GpbXGt39K2bebn5zEMY8MRgvW6vrtN\nMytJQygU2rLm8PUE09zP/n0/x77pf06l8ji53MMsLv5XstnPEY3eRSb9MUZG3oei3DrP2e+XC43+\nxqwu1jKEVxQF3/dRVRVd11/VbVGSJBIhjURI446bNInZXrApzetrXQZwK4793QarPewMe0f52wBC\nCGq1GktLSySTSWZmZpidne0dBHcb/UPfjuP0rKD6iWm9Xu8tbxjGKluodDo9YIzcRS6X2xapXEun\n2Y9hVUCHRYJvBiEExWKRUqm0YcOY3fSYfbZdQZ17sQwiR2I8xD3v38/MPWmS49snGl2yWpqf4/xX\nH+GFx76G3aiTnJjibf/4xznxwLsJbSHLei0v3O62NDk5ueb2spl1rkUaVjbNeJ5HoVDYkw+sAUlS\nSSbfQTL5Dly30LHAepgrV/8ts9f+PaOjHyCT/jiRyJmhEpPbtbK6WaxlCO95HgsLCz3Jku/7O9K/\n3goosrTp5qzXemX1Vny/PbK6O9gjq68yupGZKyNStztUvx66eshcLseNGzdYWlqiWq1SLpd7y3Sb\nnQ4dOjRgoh+LxTZ9Etsq+esnNBu5HAyrAjpMGcB6w4PNZpOFhQWi0eiaQ/6u7XPtfJFL5/LMXSwR\n+ILYqMGBe8K88aFjjEztPGnLd11mn/our3zr6yxdeglZUTnypvs4/e73Mn1ye6Sl/zVdWUP34mu3\nHSdWmsbPzs6iaRqNRoNCobAlzeHrCZo2yuTkTzAx8ePU60/3mrJyub8kFDpKJv0xRkc/jKYNxz3h\ntfYfqKqKpmmkUikMwxjQv9br9S3rX283DNvW6dXGrfh+3Qa+PewMe2R1yFjvoOR5HktLS1iWtWZk\n5m5X/L74xS9y8eLF3meKx+NMTk5y9uzZXqU0lUrteMfdSvpWt5qcSqVuSmi+32QAa2nZ+puL9u3b\nN6BF9hyf6xfLXD6X49rzJXw3IJzQOfX2SY7ckyZ9IMqlS5cYnd5Z0lZlMcvzX3uEC994FKtWJTKS\n5v5/9GOcfMeDhOOJm69gA3SdFebm5vB9f9M+wDuFJEm9bbpboV5PPrAZz83XAyRJIha7m1jsbg4e\n+GUKhS+Tyz/Mtev/getzv0cq+S4ymY8Tj79lWxZYa+H7vbK6Hvr387X0r2tti/0jBrezE8ZrvbJ6\nq8jqXmV159gjq7cY/cO/6XSaycnJNQ9SmyV9m8V9993H0aNHe56llUqFffv27dr6u5BlGdddbYjd\nD9u2WVhYQFXVTacx7abR/sr1DpsECyEolUoUi8WBWFzfC7jxYpnL5/LMPlfEtX3MqMbxt4wxc3ea\n8cNxJHnnJzDf87jy1Hd5/tGvcP35Z5FkmcP33Muhe99K5sgxMmNjO36PbvNdrVZjamrqVff726x8\nQNO0nvbVMIzX5UlFUaKMjf0wY2M/TLP5Mrn8F8jn/4Zi6RF0fZJ0+qNk0j+IYUzt+L1uR0K2U9ys\nwWqtbTEIgt622K9/3a7/67DwWtes7pHV7x+8+nvD6wj1ep3FxcV1h3/7sdsygMnJSSYnJ4E2WRzW\n0PdGFdD+YIPtahh3G8OurLZaLf5/9t48yI3zvhY92LfBMtgxM5iNohaSIkXJWk1KlqzFu8TEinPv\nixP5pexsvjeW95dKYquercS5yavEfik/J1WJHdd7r65cERVHfo4pRZRkSY4cSyIpkpIobkNyBvsO\nNLZe3h/012pgsHQD3Y0GBqfKpYTkNBo93V+f7/c7v3NisRhvP6aDHhunCjj7Whrnj2ZQp2iYbQas\n7PVh2/UBRK5wQ98jZ1zK5HExncTJZ5/Gyef+HVQhjxmvHzf/6n/BNbffhZlZLwqFAhqNxtDflUhZ\n9Ho93G73yIlqN3SSD0xSy1YO2O3bsbT4RUQXPoNc/jBSqYPY2Pg7bGz8HVyuWxAIPIBZz53Q66VX\nzLdCZVUs9Hp9R/0rIbD5fB40TcNsNrfci2qTnkm3rlKDjE/JqjyYklWFodPpWvxCo9GoqNao3JVV\nIeQmwkJ0In8cx6FQKCCdTg8cbKAUlNSsxuNxNBoNRMIRFGJNvHzwPM6+lkGt3ITJosfStT6sXu/H\n/FUeGEQYd4uxyWEZBmtHX8XxZ36CtdePQAcdlvbsxa677sPi7uug1xs2HW9QEL0x2XzQNA2KokT9\nLMdxYBiGt3URuj6ohV4tW2IYLyWyc5Kg15vh894Hn/c+1OsbSKX/Ben0v+DMmS/BaPTA5/sgAv4D\nsNuvkHTcSbxuchE6o9GImZkZ3l+5fTOVyWR4KzeyobJYLIo+M1MZgDyfMSWrw2NKVhUGx3GIx+Pw\ner0tJu/9oDShVOvYpOpmsVhEt/zVhNyVVULMK5UKTLQL2bPAy987jkq+AYNJj8Wds1jd60d0x6zk\nmNNe5LKczeDkc/+Ok889jXI2A7tnFjd+5Fex44674fQHep7vICAWY7Ozs5crxjodyuVy3+NxHAeW\nZfmXBPlOZGPGMAxvoq3T6VR/UfaTDxQKBdA03SIf0OLEt5ywWOawMP97mJ/7FArFl5FOHUQy+T+R\nSPzfcDh2IRA4AJ/3PhgM4te3SYJS1cd++tdCocDrX4XdALPZLNv5TGUA8nzGlKwOD20xhwmETqfD\n0tKSZFKgZLKSktVEQlYZhkEymUS1Wu04QKYVyKmFrdVqOHXsAtJnGoi9UUa1kIfeoMPCNbO48cN+\nLO6ahdk6+CPXfq4sy+Di60dx/PAhnH/tFXDgsLhrD/b/xm9j+bobYOizMRjkuxNfWI7jOlqM9Toe\nIaXk5d6+cSEklmVZntSSf0+I7SgIrFT5gM1mk5UwaAU6nQEe923wuG9Ds5lFJvMjpNJP4Pz5/x0X\nLvwPeL33IuA/gJmZ6ybuu/eCmq3yXvrXer2ObDYrazdgWlkdHkomWG0lTMmqRqGkDEDJhVWn06Fe\nr+PcuXPw+XwIh8OyfZ5aaTFSkYtXcPyFC7h4vAAqx0CnB3yLVuy+ex5XvisCi12ex4xUgSv5HN54\n/hmcePZplNJJ2Fxu7P3g/dj5nrvhDoZFH08KWRUOBoZCId60v/143X6WkNBeZFMoBwDQQlrJ/wDw\nz8UoiCv53E6JR6Ti1Y0wTJJ9jcnkRTj8cYRCv4FK5ThSqceRyf4E6fQPYbUuI+B/AH7/h2Ey+UZ9\nqopj1FrcbvpXcj8KhwmlRhlvhcqq0t2+aWVVHkzJqgoYpIKlpAxAKVSrVWxsbICmaWzfvl32B5RU\nbbXw4JcyNZx9LY23/zOBfPxyqld4mwt77/Zj+To/8qU0XC6XbESVY1mkz5zC8Sf+J9aO/AIsw2Bh\nx7V4969/HCvX3wiDUToREntfkiExu93eczCw/XhCokn+XsqLj3yO8PfdTmAZhuH/22w2+Qqs2iRW\nr9fDZrO1dBAYhkG1Wm2RDwgHZiZBPqDT6TAzcy1mZq7F4uIXkM0eQip9EBcv/TUurf+f8LhvRyDw\nANzu20Z9qopCa4TOaDTCaDS2dAM6RRm3D3C1349aLA7ICbVkAFqTv40jpldQo1Cysio3iH9oo9HA\n3NwcNjY2FCGUoyarlXwd545cTpNKni8BANwRM266fwnbbgjA4X7HN7VQlkdeUC0W8MZPD+PEs0+h\nkIjDMjOD3fd+EDvfcw9mI8NZCfV7CQmlHHNzcy2tx24Q2nUJq6lyvfDaCWyxWOQH94R6aWH1dZTy\ngW4DM6VSiZcPCMnrOMsHDAY7AoEHEAg8gGr1LFLpJ5BO/yty+WdgMgVgNr0HtdpvwWqV3zJvit7o\nFmXcaDT46mu9XgeAFv3rpIcCKC1zIJvrcX2mtYQpWVUBg9yoSldW5Wipd/MPVaotpqTWthuq5SbO\nH0njzGtpxM8UAQ5whSxYvW0GO2+LIhT1yn6uHMdh462TOP7MIZz5xX+ApWnMXXUNrrjjHlx7x12Y\nccpjDdXrd1UsFpFMJuH1ekVLOYTDUoNWU8Wi2WwikUhAp9NhcXGxpXIhrL6S/wLaGN4SKx+gaRrl\nclkzfptSYbOtYjH6WSzM/zfk888jlT6IQuGfcez1H8DpvBGBwAF4Z++CXt9/AzSFMiCDWRaLBW73\n5UCQ9vuxXq9jfX19Yt0wlCbj5PiTTPjVwvitglsESmfWD1ulJJGhDocDKysrqlQ7lfJEBVrbXXWK\nxtqxDM68lsbGqTw4FnCHbNh1Vwj2CI3Isg9+v79v4pbUc62VS3jzhedw4vAh5GLrMNvt2HXXvdj5\nnnvgW1jE+vr6QO3+buhEVpvNJmKxGHQ63UDuDaRqaLPZFCFZHMchn88jl8shGAx2dNjoJR8ghJVI\nB4Q/oxX5AE3TuHDhQle/zXGSD+j1Jni974XX+16cPfsKLNZXkU4/gbNn/whrBid8vg8g4D8Ah+Pq\nUZ/qFNh8P66trWFubq5jmIZU/asWoRZZnWJ4TMmqRqG0DIAcX+oiQ9M04vE4aJreFBmqNJQi8Dqd\nDo0ajYsn8jj7WgqX3siDZTg4fVbsfu8CFq/1oK4rAADCYXERomIrzBzHIX76FI4/cwinf/4SmGYD\noW1X4r2f/ANccdO7YRJcX7mr1sLjcRyHTCaDfD7fdYCq13cgGx+fzweKonhPSDIdb7PZhjbYr9fr\niMfjsFqtWF5elvQSaCew7dXWXsNbar9sjEYjDAYD/H4/gMmRDxgMfszPfRJzkd9GqfQLpFIHkfql\nDZbdfg0CgQfg874fRqM2QyW2Kjq5YQyif9UilB4gG+QdO0VnTMmqChjkYVCyikiOL4X4CclMMBiE\n0+lU/eUoN1mlGwwunszhxAt5PH8+CabJwuExY+ftEazu9cMXdSCbzSKfT0kmcP1kAHWqgrdeeh4n\nDh9C5uIFmKw2XLP/Tuy66174F5cHOqZUCFO2NjY2RCWrCdE+QKXX6+FyuVo8IWu1GqrVKrLZLGq1\nGgwGA+9ParPZRE3IsyyLdDoNiqIQDodFaWf7oRMRbZcPaMn7Vax8QOj9qlX5gE6nh8t1E1yum7BE\nF5DJ/Bip1ONYW/szXLjwf8DrvRsB/wNwOt+leQK+FSFW/zoOG6ppZXV8oM3VbArFIYX4kZhYp9Mp\niswoZTElB1ljaBbrb+Vx9tU01l7PoFlnYbbrccWNfmx/VwihFSd0eh0oisK5c+ckEziCbtc3cfY0\nThw+hFM/ewF0o47A8iru/MTvYvut+2C29vailbuyyrIsqtUq4vE45ufnJZFAMQNUOp2uY4ubEFhh\ni5v8u/YWd6VSQTKZhNvtxtLSkqIvu27ygU7er+T7jWp4q5t8oFtcJ6lsa+3FaTS6EQr9OoLBj4Gi\n3kAqdRCZ7I+RyfwIFkuUt8Aym4OjPtUpekCM/lWLaXBTsjo+mJLVLQoxA1zEAJ5lWdExscA7pFIJ\n66pByBrLcIidLuDMqymsHcuiTtGw2I1YvT6A1b1+NC0FzM1FYDabL8scNoaXOQiJZaNWxds/ewHH\nDx9C6vxZGM0WXHnrfuy88x6EVsXHVcpFVjmO4weo9Ho9lpeXRb8whrWj6hQp2Wg0UK1WUSgUkEgk\nAFyeSG40GtDpdJifnxd978mNXt6vWpQPdLq2vaa9tVLt0ul0cDh2wOHYgWj0s8jl/h2p9EFcWv8W\nLq3/LTzufb+0wNoPvV47frWj9ljVMrrZubXrX41G4yYCqyamMoDxwJSsqoBhJ+6VeJh6VVZZlkUm\nk0GhUJDc/hYeWymfVTHgWA6Jc0WceTWNc0cyqJWbMFkMWNrtxepeP+av8sBgvEwmLl4sgWEYZLPZ\nTc4Gg0Kn0yF76QKOP/k43nrpeTRrVfiii7jjNz+JK2/bD4vdIfmYckhDGo0GYrEYDAYDFhcXsbGx\nIYmoChOo5LgvhRUZj8fDD1BlMhnYbDawLItLly7BaDTyLz6bzTayF4BY71fgHQI7quGtXtWuarWK\nTCaDRqMxcrLQDoPBBr//Q/D7P4Ra7QJvgZU//TxMRh/8/g/DHzgAm3VppOcJTLYPqRLfrV3/CoDX\nY5NuC8Mwmwa4xrU6qRVf8EnAlKxqGEr6inYjfiTz3e12D9T+7nXsYdHvuBzHIX2hjDOvpnH2tTSo\nQgMGkx6LO2exen0A0Ws8MJo3X0uWZbG+vo6ZmZmhnQ2a9TpO//xFHHv635A6dwYGkxlX3HQbdt11\nL8JXXDk0AR6UrHIch3Q6jUKhgHA4jJmZGZ54ivlZMQlUw6LRaCAej8NkMm36PTSbTVSrVVQqFaTT\nadmHt4aBlOGtUUfHipEPMAyjmWEZq3UR0YX/joX530e+8CJSqYOIxb+PWPy7cM5cD3/gAXhn74HB\nMJo450kmq2qlV3XSv/aKMyb35Dhc96kMQD5MyaoKGPShIq16Ncgqqbjp9fqOme/DHFsudCJrHMch\nu0Hh7C8JailTg96gw8I1s9h2vx+Lu7wwWTpfP4ZhkEgkUK1WEQqFMDs7O/C5Zdcv4vjhQ3jrhedQ\npypwhyLY85GP4sb3fQjWGWmV6W4YlKwSm7F2zXG/4w3b8hcLEuVaLBYRCoVaYiMJyAtN7uEtJdBv\neKs9OnaUw1uANPkAub4mk0nSvTBsR0CnM2LWcwdmPXeg0UghnXkSqdRBnDv3p1hb+wZ8vvf90gJr\np6okZpLJqtKG+d3QbaCQ3JP5fB71eh16vb6FwKp9T4oBcUmYYnhMyaqGQeyllHjp6vV6NJtNftK6\nVCohFAp19K0c5NhKV1bziXcIaj5RhU4PzF/pwd77FrB0ra9nzCnHcSgUCkin0/D5fPx0q1TQjQbO\n/OI/cOLwIWy89Qb0RiO2vesW7LrrXrgXllAqlWQjqoB0skrIeL1e76i/7XU8pRKo2lGtVpFIJOBw\nOLC0tCT65SjH8JaaECMfIBICjuN4yYWW5AOk+ppOp9FsNmEwGEYiHzCbA5iLfAKR8EMolV+9PJSV\n+RFSqX+GzbYdAf8D8Pk/CJPRo/i5TDJZVauyKgbCwSwChmH4Aa50Oi1Z0qIGGScb0SmGx5SsahhK\npljpdDpUq1WcPXsWHo8Hq6urskZiKnHeVL6J069k8OLbG8isVwAdENnmws7bI1i+zg/bTH/CWavV\nEIvFYLFY+FZzIpGQdL652AZOPPsU3vzpYdTKJbhDYdz2sY/jmv2y7N7GAAAgAElEQVR3wua6/HKv\nVquyXwOxbghCMu73+xGJRLpO63f6WTWqqSzLIpVKoVarIRKJyOLXK3Z4S6h9lVqNkROd5AONRgOJ\nRAJ2u11Tw1t6vR52u72l6i3cHORyub5em0q4g7icN8DlvAE0/SVksz9BKvU4Llz8H7h46a8xO3sX\nAv4DcLlugk6nzPWaZLKq9e9mMBi63pNCSUs3/asaZHyqWZUPU7KqAgZ9IJQiffV6ndf9LS8vy165\nlfO8K/k6zh3J4MyrKaTWygCA4LITtxxYwcpeHxxucSSHZVkkk0lQFIVIJNJSkRMzuMTQTZx95ec4\ncfgpXDr5OvQGA1auvwm77rwHCzuuha6NPCgROyuGrNbrdcRiMZhMJskJVEoMUHVCuVxGMpnE7Ows\ngsGgYp/TPrwFvFMhrFarSCaTfDVm1MNbJLq4XQqhVe9XoL98oFartfwOlMxJNxqdCAY/imDwo6Co\nU0ilDiKd+RGy2Z/AbJ5DwH8//P77YbGEZf1crRO6YTAqGcAw6HRPdtO/Go1Gvouh1O9wSlblw5Ss\nqoRByIvcKVaEsFUqFXi9XlAUpZjEYBiyWi03ce5IGmdfTSN+tghwgG/BgevePwdXVIcrdy6LPhbH\ncSiVSnzOfSgU2rQw9TrfQjKOE88+jTeefwbVYgFOfxC3fPS/4prb74LD013jqhRZ7XZMoZwjHA63\nTNv2g1oDVDRN89XNxcXFkUydd6oQjnp4i2ww7Hb7JinEOHm/9pIPVKtV0DSNtbW1llatEpsDu/1K\nLC19CdHoZ5DLHUYqfRDrG9/G+sb/Bbf7NgT8D8DjeY9sFliTSla1JAMYFJ30rxzHoV6vo1Qq8dHG\nOp2upfoqV8dlSlblw5SsahhyyQCIr2YqlcLs7CxWV1fRaDRQLpdlOMvNGMRiqU7ROH8sg7OvpbFx\nKg+OBTwhG254/yJW9/rhDtpQr9eRTCZFH1No09SrythesWQZBude+wVOHD6EC8ePQgcdlvfegF13\n3ovotXug1/dffOROmyLH7HRdK5UK4vE4XC4XVlZWJCVQkcqDkOTIDWJHlcvlEAgEJFuhKQ2xw1tC\nAivHJo84NFQqFUnJXOPk/Uo2BxaLBRRFIRqNtlgViZEPDP7ZFvh874PP9z7U6+tIpf8F6dS/4PSZ\nL8BonIXf9yEEAg/AZts28GdMAqHrhnGsrIoBIabkeQkGg4ppslmWHbkV3KRgehU1DDkqq0SjaTab\nWwibUhIDcmyapvv+u0aNxoXjOZx9LYVLb+TBMhxcfit2v3cB2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GF9fX3kw1BiIZQXMAyD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\n2tDQACB+TKzT6UQ4HEZRURGKi4sxd+5czXq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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "visualize_data_fit(X_train, y_train, β_fixed_effects, α, 'Prior', n_samples=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Visualize data fit given parameter posteriors" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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LyzFjxgw8++yzAIYE3A9+8AO8++67ADDsGB1++OF47rnnwBhDKBTCj370I/zpT39Kuo1A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\nkbuTk5MNEblbiGw2i/HxcUnUK/E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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "visualize_data_fit(X_train, y_train, qβ_fixed_effects, qα, 'Posterior', n_samples=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It appears as if our model fits the data along the first two dimensions. This said, we could improve this fit considerably. This will become apparent when we compute the MAE on our validation set." ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "#### Inspect residuals" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def compute_mean_absolute_error(y_posterior, X_val_feed_dict, y_val=y_val):\n", " data = {y_posterior: y_val}\n", " data.update(X_val_feed_dict)\n", " mae = ed.evaluate('mean_absolute_error', data=data)\n", " print(f'Mean absolute error on validation data: {mae:1.5}')\n", " \n", "def plot_residuals(y_posterior, X_val_feed_dict, title, y_val=y_val):\n", " y_posterior_preds = y_posterior.eval(feed_dict=X_val_feed_dict)\n", " plt.figure(figsize=(9, 6))\n", " plt.hist(y_posterior_preds - y_val, edgecolor='white', linewidth=1, bins=30, alpha=.7)\n", " plt.axvline(0, color='#A60628', linestyle='--')\n", " plt.xlabel('`y_posterior_preds - y_val`', fontsize=14)\n", " plt.ylabel('Count', fontsize=14)\n", " plt.title(title, fontsize=16)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "param_posteriors = {\n", " β_fixed_effects: qβ_fixed_effects.mean(),\n", " α: qα.mean()\n", "}\n", "X_val_feed_dict = {\n", " fixed_effects: X_val\n", "}\n", "y_posterior = ed.copy(y, param_posteriors)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean validation `logerror`: 0.012986094738549725\n", "Mean absolute error on validation data: 0.089943\n" ] } ], "source": [ "print(f'Mean validation `logerror`: {y_val.mean()}')\n", "compute_mean_absolute_error(y_posterior, X_val_feed_dict)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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3DTClS5fWCy+8IEmqUqWKunbtKm9v7yIpDAAAIDd5fo26R48eSkhI0A8//KDM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\nYDr/H2XBh0zb8rIeAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_residuals(y_posterior, X_val_feed_dict, title='Linear Regression Residuals')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"The residuals appear normally distributed with mean 0: this is a good sanity check for the model.\"1 However, with respect to the magnitude of the mean of the validation `logerror`, our validation score is terrible. This is likely due to the fact that three predictors are not nearly sufficient for capturing the variation in the response. (Additionally, because the response itself is an *error*, it should be fundamentally harder to capture than the thing actually being predicted — the house price. This is because Zillow's team has already built models to capture this signal, then effectively threw the remaining \"uncaptured\" signal into this competition, i.e. \"figure out how to get right the little that we got wrong.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Inspect parameter posteriors" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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+QPmtSD7++GN89NFHsLa2hpubG7Zu3YpJkybh1KlTlS4gVMHc3BwbNmzA0qVL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\nw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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# draw samples from posteriors\n", "qβ_fixed_effects_samples = qβ_fixed_effects.sample(1000).eval()\n", "qα_samples = qα.sample(1000).eval()\n", "\n", "# plot samples\n", "plt.figure(figsize=(16, 10))\n", "\n", "for dimension in range(D):\n", " subplot = plt.subplot(221 + dimension)\n", " plt.hist(qβ_fixed_effects_samples[:, dimension], edgecolor='white', linewidth=1, bins=30, alpha=.7)\n", " plt.axvline(0, color='#A60628', linestyle='--')\n", " title = f'Posterior Distribution of `{fixed_effect_predictors[dimension]}` Effect'\n", " plt.ylabel('Count', fontsize=14)\n", " plt.title(title, fontsize=16)\n", " \n", "subplot = plt.subplot(221 + dimension + 1)\n", "plt.hist(qα_samples, edgecolor='white', linewidth=1, bins=30, alpha=.7)\n", "plt.axvline(0, color='#A60628', linestyle='--')\n", "title = f'Posterior Distribution of Fixed Intercept α'\n", "plt.ylabel('Count', fontsize=14)\n", "plt.title(title, fontsize=15)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In keeping with the definition of multivariate linear regression itself, the above parameter posteriors tell us: \"conditional on the assumption that the log-error and fixed effects can be related by a straight line, what is the predictive value of one variable once I already know the values of all other variables?\"2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bayesian linear regression with random effects\n", "Random effects models — also known as hierarchical models — allow us to ascribe distinct behaviors to different \"clusters\" of observations, i.e. groups that may each act in a materially unique way. Furthermore, these models allow us to infer these tendencies in a *collaborative* fashion: while each cluster is assumed to behave differently, it can learn its parameters by heeding to the behavior of the population at large. In this example, we assume that houses in different zipcodes — holding all other predictors constant — should be priced in different ways.\n", "\n", "For clarity, let's consider the two surrounding extremes:\n", "1. Estimate a single set of parameters for the population, i.e. the vanilla, [scikit-learn linear regression](http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html), Bayesian or not. This confers no distinct behaviors to houses in different zipcodes.\n", "2. Estimate a set of parameters for each individual zipcode, i.e. split the data into its cluster groups and estimate a single model for each. This confers maximally distinct behaviors to houses in different zip codes: the behavior of one cluster knows nothing about that of the others.\n", "\n", "Random-effects models \"walk the line\" between these two approaches — between maximally *underfitting* and maximally *overfitting* the behavior of each cluster. To this effect, its parameter estimates exhibit the canonical \"shrinkage\" phenomenon: the estimate for a given parameter is balanced between the within-cluster expectation and the global expectation. Smaller clusters exhibit larger shrinkage; larger clusters, i.e. those for which we've observed more data, are more bullheaded (in typical Bayesian fashion). A later plot illustrates this point.\n", "\n", "We specify our random-effects functional form as follows:\n", "\n", "``` python\n", "μ_y = α + α_random_effects + ed.dot(fixed_effects, β_fixed_effects)\n", "y = Normal(loc=μ_y, scale=tf.ones(N))\n", "```\n", "\n", "With respect to the previous model, we've simply added `α_random_effects` to the mean of our response. As such, this is a *varying-intercepts* model: the intercept term will be different for each cluster. To this end, we learn the *global* intercept `α` as well as the *offsets* from this intercept `α_random_effects` — a random variable with as many dimensions as there are zipcodes. In keeping with the notion of \"offset,\" we ascribe it a prior of `(0, σ_zc)`. This approach allows us to flexibly extend the model to include more random effects, e.g. city, architecture style, etc. With only one, however, we could have equivalently included the global intercept *inside* of our prior, i.e. `α_random_effects ~ Normal(α, σ_zc)`, with priors on both `α` and `σ_zc` as per usual. This way, our random effect would no longer be a zip-code-specific *offset* from the global intercept, but a vector of zip-code-specific intercepts outright.\n", "\n", "Finally, as Richard McElreath notes, \"we can think of the `σ_zc` parameter for each cluster as a crude measure of that cluster's \"relevance\" in explaining variation in the response variable.\"3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fit model" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "n_zip_codes = len(set(zip_codes))\n", "\n", "# random-effect placeholder\n", "zip_codes_ph = tf.placeholder(tf.int32, [N])\n", "\n", "# random-effect parameter\n", "σ_zip_code = tf.sqrt(tf.exp(tf.Variable(tf.random_normal([]))))\n", "α_zip_code = Normal(loc=tf.zeros(n_zip_codes), scale=σ_zip_code * tf.ones(n_zip_codes))\n", " \n", "# model\n", "α_random_effects = tf.gather(α_zip_code, zip_codes_ph)\n", "μ_y = α + α_random_effects + ed.dot(fixed_effects, β_fixed_effects)\n", "y = Normal(loc=μ_y, scale=tf.ones(N))\n", "\n", "# approximate random-effect distribution\n", "qα_zip_code = Normal(\n", " loc=tf.Variable(tf.random_normal([n_zip_codes])),\n", " scale=tf.nn.softplus(tf.Variable(tf.random_normal([n_zip_codes])))\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Infer parameters" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "250/250 [100%] ██████████████████████████████ Elapsed: 6s | Loss: 34898.613\n" ] } ], "source": [ "latent_vars = {\n", " β_fixed_effects: qβ_fixed_effects,\n", " α: qα,\n", " α_zip_code: qα_zip_code\n", "}\n", "\n", "sess.run(INIT_OP)\n", "inference = ed.KLqp(latent_vars, data={fixed_effects: X_train, zip_codes_ph: zip_codes[train_index], y: y_train})\n", "inference.run(n_samples=5, n_iter=250)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Criticize model" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "param_posteriors = {\n", " β_fixed_effects: qβ_fixed_effects.mean(),\n", " α: qα.mean(),\n", " α_zip_code: qα_zip_code.mean()\n", "}\n", "X_val_feed_dict = {\n", " fixed_effects: X_val,\n", " zip_codes_ph: zip_codes[val_index]\n", "}\n", "y_posterior = ed.copy(y, param_posteriors)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean absolute error on validation data: 0.084635\n" ] } ], "source": [ "compute_mean_absolute_error(y_posterior, X_val_feed_dict)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "#### Inspect residuals" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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m5mb02nNychrkuKaAbVO1x6VdrhWUQCGX13j7dru3Q61W469XX4dMZlarfe9n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\nRFdXF9asWQMrKysolUqNWYn29nYMDQ3BysoK5eX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_residuals(y_posterior, X_val_feed_dict, title='Linear Regression with Random Effects Residuals')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### Plot shrinkage\n", "To illustrate shrinkage we'll pare our model down to intercepts only (removing the fixed effects entirely). We'll first fit a random-effects model on the full dataset then compute the cluster-specific-intercept posterior means. Next, we'll fit a separate model to each individual cluster and compute the intercept posterior mean of each. The plot below shows how estimates from the former can be viewed as \"estimates from the latter — shrunk towards the global-intercept posterior mean.\"\n", "\n", "Finally, blue, green and orange points represent small, medium and large clusters respectively. As mentioned before, the larger the cluster size, i.e. the more data points we've observed belonging to a given cluster, the *less* prone it is to shrinkage towards the mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimate random-effects intercepts" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 34515.773 0s | Loss: 34524\n" ] } ], "source": [ "# model\n", "μ_y = α + α_random_effects\n", "y = Normal(loc=μ_y, scale=tf.ones(N))\n", "\n", "latent_vars = {\n", " α: qα,\n", " α_zip_code: qα_zip_code\n", "}\n", "\n", "# infer parameters\n", "sess.run(INIT_OP)\n", "inference = ed.KLqp(latent_vars, data={zip_codes_ph: zip_codes[train_index], y: y_train})\n", "inference.run(n_samples=5, n_iter=250)\n", "\n", "# compute global intercept posterior mean\n", "global_intercept_posterior_mean = qα.mean().eval()\n", "\n", "# compute random-effects posterior means\n", "random_effects_posterior_means = global_intercept_posterior_mean + qα_zip_code.mean().eval()\n", "random_effects_posterior_means = pd.Series(random_effects_posterior_means, index=range(0, n_zip_codes),\n", " name='random_effects_posterior_means')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Estimate within-cluster intercepts" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 407.149\n", "250/250 [100%] ██████████████████████████████ Elapsed: 3s | Loss: 339.477\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 314.130\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 306.847\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 276.160\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 267.080\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 253.680 1s |\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 236.092\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 240.532\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 233.505\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 232.273\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 229.171 0s | Loss\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 217.063\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 211.964\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 211.962\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 207.407\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 199.322\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 199.557\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 197.278\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 195.386\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 191.565\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 187.577\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 190.232\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 185.698\n", "250/250 [100%] ██████████████████████████████ Elapsed: 4s | Loss: 188.302\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 138.870\n", "250/250 [100%] ██████████████████████████████ Elapsed: 6s | Loss: 135.920\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 135.151\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 136.043\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 136.001\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 136.464 1s | Loss:\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 134.585\n", "250/250 [100%] ██████████████████████████████ Elapsed: 6s | Loss: 133.699\n", "250/250 [100%] ██████████████████████████████ Elapsed: 6s | Loss: 132.002\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 131.619\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 130.199 0s | Loss: 130.0\n", "250/250 [100%] ██████████████████████████████ Elapsed: 6s | Loss: 129.326\n", "250/250 [100%] ██████████████████████████████ Elapsed: 5s | Loss: 129.478\n", "250/250 [100%] ██████████████████████████████ Elapsed: 6s | Loss: 128.817\n", "250/250 [100%] ██████████████████████████████ Elapsed: 6s | Loss: 132.139\n", "250/250 [100%] ██████████████████████████████ Elapsed: 7s | Loss: 128.637 2s | Los\n", "250/250 [100%] ██████████████████████████████ Elapsed: 6s | Loss: 128.923\n", "250/250 [100%] ██████████████████████████████ Elapsed: 7s | Loss: 126.815 3s | Loss: E\n", "250/250 [100%] ██████████████████████████████ Elapsed: 6s | Loss: 126.686\n", "250/250 [100%] ██████████████████████████████ Elapsed: 6s | Loss: 132.182\n" ] } ], "source": [ "# select a few clusters of varying size\n", "zip_codes_df = pd.DataFrame({'cluster_size': zip_codes[train_index].value_counts()})\n", "zip_codes_df['cluster_size_group'] = pd.cut(zip_codes_df['cluster_size'], 3, labels=['small', 'medium', 'large'])\n", "zip_codes_df = zip_codes_df.groupby('cluster_size_group').head(20)\n", "\n", "# build individual models for each cluster\n", "within_cluster_posterior_means = {}\n", "\n", "for zip_code in zip_codes_df.index.unique():\n", " # compute mask, number of observations\n", " mask = zip_codes[train_index] == zip_code\n", " N_ = mask.sum()\n", " \n", " # instantiate model for current cluster\n", " fixed_effects = tf.placeholder(tf.float32, [N_, D])\n", " μ_y = α\n", " y = Normal(loc=μ_y, scale=tf.ones(N_))\n", " \n", " # fit model\n", " sess.run(INIT_OP)\n", " inference = ed.KLqp(latent_vars, data={y: y_train[mask]})\n", " inference.run(n_samples=5, n_iter=250)\n", " \n", " # compute mean of qα for this zip code\n", " within_cluster_posterior_means[zip_code] = qα.mean().eval()[0]\n", " \n", "within_cluster_posterior_means = pd.Series(within_cluster_posterior_means, name='within_cluster_posterior_means')" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# prepare for plotting: join, give colors, sort, reset index\n", "zip_codes_df = zip_codes_df\\\n", " .join(within_cluster_posterior_means)\\\n", " .join(random_effects_posterior_means)\n", "zip_codes_df['cluster_size_color'] = zip_codes_df['cluster_size_group'].map({'small': '#377eb8', 'medium': '#4daf4a', 'large': '#ff7f00'})\n", "zip_codes_df = zip_codes_df\\\n", " .sort_values(by='cluster_size')\\\n", " .reset_index(drop=True)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "scrolled": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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//z1Dhw4lNze3SHn4osqcF7FtiYmJdO7cGUdHR6W+e5a6qiTvvvsuLi4urF27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7B5/V6+LPmciwoubvU7JcYZw48GXsD729+zMJ18H6Zp8tSqf3D3l3/E4/SQm9ifhcULuH7OtZQ1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\nBgMDBw7khx9+MNXZu3cvfn5+NGjQgM6dO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot shrinkage\n", "plt.figure(figsize=(14, 10))\n", "plt.xlim(-1, len(zip_codes_df) + 1)\n", "\n", "plt.scatter(zip_codes_df.index, zip_codes_df['random_effects_posterior_means'], facecolors='none',\n", " edgecolors=zip_codes_df['cluster_size_color'], s=50, linewidth=1, \n", " alpha=1, label='Random-Effects-α Posterior Mean')\n", "plt.scatter(zip_codes_df.index, zip_codes_df['within_cluster_posterior_means'], c=zip_codes_df['cluster_size_color'], \n", " s=100, alpha=.7, label='Within-Cluster-α Posterior Mean')\n", "plt.axhline(global_intercept_posterior_mean, color='#A60628', linestyle='--', label='Global-α Mean')\n", "plt.xticks([])\n", "plt.xlabel('Cluster \\n(In Order of Increasing Cluster Size)', fontsize=14)\n", "plt.ylabel('α', fontsize=14)\n", "plt.title('Shrinkage in Mean-α Estimates from Within-Cluster vs. Random Effects Linear Regression', fontsize=16)\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Neural network with random effects\n", "Neural networks are powerful function approximators. Keras is a library that lets us flexibly define complex neural architectures. Thus far, we've been approximating the relationship between our fixed effects and response variable with a simple dot product; can we leverage Keras to make this relationship more expressive? Is it painless? Finally, how does it integrate with Edward's existing APIs and constructs? Can we couple nimble generative models with deep neural networks?\n", "\n", "While my experimentation was brief, all answers point delightfully towards \"yes\" for two simple reasons:\n", "1. Edward and Keras both run on TensorFlow.\n", "2. \"Black-box\" variational inference makes everything scale.\n", "\n", "This said, we must be nonetheless explicit about what's \"Bayesian\" and what's not, i.e. for which parameters do we infer full (approximate) posterior distributions, and for which do we infer point estimates of the posterior distribution.\n", "\n", "Below, we drop a `neural_network` in place of our dot product. Our latent variables remain `β_fixed_effects`, `α` and `α_zip_code`: while we will infer their full (approximate) posterior distributions as before, we'll only compute *point estimates* for the parameters of the neural network as in the typical case. Conversely, to the best of my knowledge, to infer full distributions for the latter, we'll need to specify our network manually in raw TensorFlow, i.e. ditch Keras entirely. We then treat our weights and biases as standard latent variables and infer their approximate posteriors via variational inference. Edward's documentation contains a straightforward [tutorial](http://edwardlib.org/tutorials/bayesian-neural-network) to this end." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Fit model" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "def neural_network(fixed_effects, λ=.001, input_dim=D):\n", " dense = Dense(5, activation='tanh', kernel_regularizer=l2(λ))(fixed_effects)\n", " output = Dense(1, activation='linear', name='output', kernel_regularizer=l2(λ))(dense)\n", " return K.squeeze(output, axis=1)\n", "\n", "# model\n", "fixed_effects = tf.placeholder(tf.float32, [N, D])\n", "μ_y = α + α_random_effects + neural_network(fixed_effects)\n", "y = Normal(loc=μ_y, scale=tf.ones(N))" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1000/1000 [100%] ██████████████████████████████ Elapsed: 18s | Loss: 34446.191\n" ] } ], "source": [ "latent_vars = {\n", " β_fixed_effects: qβ_fixed_effects,\n", " α: qα,\n", " α_zip_code: qα_zip_code\n", "}\n", "\n", "sess.run(INIT_OP)\n", "inference = ed.KLqp(latent_vars, data={fixed_effects: X_train, zip_codes_ph: zip_codes[train_index], y: y_train})\n", "optimizer = tf.train.RMSPropOptimizer(0.01, epsilon=1.0)\n", "inference.initialize(optimizer=optimizer)\n", "inference.run(n_samples=5, n_iter=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Criticize model" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true }, "outputs": [], "source": [ "param_posteriors = {\n", " β_fixed_effects: qβ_fixed_effects.mean(),\n", " α: qα.mean(),\n", " α_zip_code: qα_zip_code.mean()\n", "}\n", "X_val_feed_dict = {\n", " fixed_effects: X_val,\n", " zip_codes_ph: zip_codes[val_index]\n", "}\n", "y_posterior = ed.copy(y, param_posteriors)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean absolute error on validation data: 0.081484\n" ] } ], "source": [ "compute_mean_absolute_error(y_posterior, X_val_feed_dict)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "#### Inspect residuals" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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giMggBhgikq3TkYO5DgwRGcRJvERERGRyGGCISLZapq6C56Y0qcsgIhniEBIR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\nBoaIiIgshw0MERERWc5vtAORsMKyk0wAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_residuals(y_posterior, X_val_feed_dict, title='Neural Network with Random Effects Residuals')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Future work\n", "We've now laid a stable, if trivially simple foundation for building models with Edward and Keras. From here, I see two distinct paths to building more expressive probabilistic models using these tools:\n", "1. Build probabilistic models in Edward, and abstract deep-network-like subgraphs into Keras layers. This allows us to flexibly define complex neural architectures, e.g. a [video question answering model](https://keras.io/getting-started/functional-api-guide/#video-question-answering-model), with a nominal amount of code, yet restricts us from, or at least makes it awkward to, infer full posterior distributions for the subgraph parameters.\n", "2. Build probabilistic models in Edward, and specify deep-network-like subgraphs with raw TensorFlow — ditching Keras entirely. Defining deep-network-like subgraphs becomes more cumbersome, while inferring full posterior distributions for the subgraph parameters becomes more natural and consistent with the flow of Edward code.\n", "\n", "This work has shown a few basic variants of (generalized) Bayesian linear regression models. From here, there's tons more to explore — varying-slopes models, Gaussian process regression, mixture models and probabilistic matrix factorizations to name a random few. \n", "\n", "Edward and Keras have proven a flexible, expressive and powerful duo for performing inference in deep probabilistic models. The models we built were simple; the only direction to go, and to go rather painlessly, is more.\n", "\n", "Many thanks for reading." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# References\n", "1. [Edward - Linear Mixed Effects Models](http://edwardlib.org/tutorials/linear-mixed-effects-models)\n", "2. McElreath, Richard. \"Chapter 5.\" Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Boca Raton, FL: CRC, Taylor & Francis Group, 2016. N. pag. Print.\n", "3. McElreath, Richard. \"Chapter 12.\" Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Boca Raton, FL: CRC, Taylor & Francis Group, 2016. N. pag. Print.\n", "4. [The Best Of Both Worlds: Hierarchical Linear Regression in PyMC3](http://twiecki.github.io/blog/2014/03/17/bayesian-glms-3/)\n", "5. [Keras as a simplified interface to TensorFlow](https://blog.keras.io/keras-as-a-simplified-interface-to-tensorflow-tutorial.html)\n", "6. [Mixture Density Networks with Edward, Keras and TensorFlow](http://cbonnett.github.io/MDN_EDWARD_KERAS_TF.html)\n", "7. [Use a Hierarchical Model](http://sl8r000.github.io/ab_testing_statistics/use_a_hierarchical_model/)\n", "8. McElreath, Richard. \"Chapter 14.\" Statistical Rethinking: A Bayesian Course with Examples in R and Stan. Boca Raton, FL: CRC, Taylor & Francis Group, 2016. N. pag. Print." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }