From 5fbe1de1a32758b277e5e85b23eb81391bca62a7 Mon Sep 17 00:00:00 2001 From: Max Margenot Date: Thu, 20 Jul 2017 12:21:39 -0400 Subject: [PATCH 1/4] First draft --- .../notebook.ipynb | 635 ++++++++++++++++++ 1 file changed, 635 insertions(+) create mode 100644 notebooks/lectures/Combining_Independent_Signals/notebook.ipynb diff --git a/notebooks/lectures/Combining_Independent_Signals/notebook.ipynb b/notebooks/lectures/Combining_Independent_Signals/notebook.ipynb new file mode 100644 index 00000000..8a9c7df8 --- /dev/null +++ b/notebooks/lectures/Combining_Independent_Signals/notebook.ipynb @@ -0,0 +1,635 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#Model Combining\n", + "By Chris Fenaroli, Delaney Granizo-Mackenzie, and Max Margenot \n", + "\n", + "Part of the Quantopian Lecture Series:\n", + "\n", + "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n", + "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n", + "\n", + "Notebook released under the Creative Commons Attribution 4.0 License.\n", + "\n", + "---" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "import matplotlib.cm as cm\n", + "import scipy.stats as stats\n", + "import scipy.linalg as linalg\n", + "from statsmodels import regression\n", + "import statsmodels.api as sm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## What is Model Ensembling?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Model ensembling is the name for a variety of methods which combine information from many prediction models to obtain results with more predictive power than any of its components alone. An model ensemble takes these component predictions and uses some logic to combine them into a final prediction. There are many methods used to aggregate the predictions, the simplest of which would be to find the equally weighted average of the predictions. \n", + "\n", + "### Why Combine Models?\n", + "\n", + "A common approach to model selection is a \"winner takes all\" process where the best single model is chosen to make predictions. A OLS fitted simple linear regression, for example, returns a single set of coefficients that minimizes the sum of squared residuals with the training set. This model is simply an estimate. It will usually have bias (difference betwen model expected value and true value) and variance (sensitivity to small changes in the training set). \n", + "\n", + "Let's define a identical standard normal toy models `m_1` and `m_2`, and see what happens to their mean and standard deviation when we average their predictions over 1000 trials." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "---- Mean ---- ---- Variance ---- \n", + "Model 1: -0.019 Model 1: 0.996 \n", + "Model 2: -0.003 Model 2: 1.011 \n", + "Combined: -0.011 Combined: 0.526 \n", + "\n", + "Covariance between models: 0.0478288505058\n" + ] + }, + { + "data": { + "image/png": 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cxnEcBQIBnXfeebrjjjvi2j322GOxYzaspbFjjz1We/fu1euvv66zzz67xXbh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\nCDR1zlUymew4rpgvyDAMpV0pqAR6//UTcmy7T1U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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "mu = 0\n", + "sigma = 1\n", + "\n", + "# Create two identical models\n", + "m_1 = np.random.normal(mu,sigma,1000)\n", + "m_2 = np.random.normal(mu,sigma,1000)\n", + "\n", + "# Combine them\n", + "m_cm = (m_1 + m_2)/2\n", + "\n", + "# Plot their distribution over 1000 trials\n", + "plt.hist(m_1, bins=50, alpha=0.2);\n", + "plt.hist(m_2, bins=50, alpha=0.2);\n", + "plt.hist(m_cm, bins=50, alpha=0.6);\n", + "plt.legend(['Model 1', 'Model 2', 'Combined Model'])\n", + "plt.title('Histogram of Model Outputs over 1000 Trials')\n", + "\n", + "print \"%-39s %-24s\" % ('---- Mean ----', '---- Variance ----')\n", + "print \"%-15s %-24s %-15s %-15s\" % ('Model 1:', \n", + " np.round(np.mean(m_1),decimals=3), \n", + " 'Model 1:', \n", + " np.round(np.std(m_1)**2,decimals=3))\n", + "print \"%-15s %-24s %-15s %-15s\" % ('Model 2:', \n", + " np.round(np.mean(m_2),decimals=3), \n", + " 'Model 2:', \n", + " np.round(np.std(m_2)**2,decimals=3))\n", + "print \"%-15s %-24s %-15s %-15s\" % ('Combined:', \n", + " np.round(np.mean(m_cm),decimals=3),\n", + " 'Combined:',\n", + " np.round(np.std(m_cm)**2,decimals=3))\n", + "print \"\\nCovariance between models:\", np.cov(m_1, m_2)[1][0]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "When the identical models are aggreagated, the mean stays the same while the variance of results decreases. How can this be explained? First, let's approach it symbolically:\n", + "\n", + "\n", + "\n", + "Consider two models with the same mean $m$, the same variance $v$, and zero covariance:\n", + "\n", + "$$ models = \\hat{\\theta_1} \\: , \\: \\hat{\\theta_2}$$\n", + "\n", + "$$E[\\hat{\\theta_1}]=E[\\hat{\\theta_2}]=m \\:\\:\\:\\:\\:\\:\\:\\: Var[\\hat{\\theta_1}] = Var[\\hat{\\theta_2}] = v \\:\\:\\:\\:\\:\\:\\:\\: Cov[\\hat{\\theta_2},\\hat{\\theta_2}] = 0$$\n", + "\n", + "When averaged, $\\hat{\\theta_{cm}} = \\frac{\\hat{\\theta_1} + \\hat{\\theta_2}}{2}$, \n", + "\n", + "$$\\hat{\\theta_{cm}} = \\frac{E[\\hat{\\theta_1}]+E[\\hat{\\theta_2}]}{2} = m$$\n", + "\n", + "$$Var[\\hat{\\theta_{cm}}] = \\frac{Var[\\hat{\\theta_{1}}]+Var[\\hat{\\theta_{2}}]+2Cov[\\hat{\\theta_{1}},\\hat{\\theta_{2}}]}{4} = \\frac{v}{2}$$\n", + "\n", + "\n", + "\n", + "*Resulting in the combined model keeping the same mean $m$ as its components but seeing a sublinear reduction in variance.*\n", + "#### Caveats\n", + "\n", + "Should the models being aggregated have a covariance = 1, the variability-reducing effect no longer applies. Instead, the $2Cov[\\hat{\\theta_{1}},\\hat{\\theta_{2}}]$ term becomes equal to 2 and makes variance equal to it's original value $v$.\n", + "\n", + "### Averaging $n$ Models\n", + "\n", + "Let's see what happens to the mean and standard deviation when we increase the number of models being combined:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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TNGfOHDVq1Ei5ubklju3fv79+//13DRw4ULVq1VJhYaEmTJhQYnW2a/UUrVy5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\nvQ/k9des/f6ZzfXVjGbA0Dv9Teq0jZpuFLwXO+/RmayBdFa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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Number of identical models\n", + "n = 100\n", + "\n", + "# Initizalize n models\n", + "models = np.array([np.random.normal(mu,sigma,1000) for _ in range(n)])\n", + "\n", + "combined_models = [np.mean(models[0:i+1], axis=0) for i in range(n)]\n", + "means = np.mean(combined_models,axis=1)\n", + "stds = np.std(combined_models,axis=1)\n", + "\n", + "plt.plot(means);\n", + "plt.plot(stds);\n", + "plt.legend(['Model Avg Mean', 'Model Avg STD']);\n", + "plt.xlabel('Number of Models Combined');\n", + "plt.title('Mean and STD vs. Number of Models Combined');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As more models are added the mean predicted value is stationary and the prediction variability decreases. \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Intuition: Perspective\n", + "\n", + "The theory and simulation above demonstrate the benefits of simply averaging uncorrelated models; in both cases, as more models are averaged the mean stays the same but variance decreases sublinearly. Model combination gets its power from the diversity of uncorrelated models ensuring that different features of the problem are represented. But what are these \"features\" that data apparently has? And how do combinations of diverse models help reveal them?\n", + "\n", + "An interesting analogy is to think of a model as a specific \"view\" of the world, having its own perspective and unique insights into the problem at hand. Data can have many \"dimensions\" and rarely will one model encapture every single one; only by approaching it from many \"views\" can we understand its structure.\n", + "\n", + "Consider a 3-dimensional object, such as a cylinder. To fully understand what this object is we require multiple perspectives from distinct viewpoints, as from each viewpoint alone you only see a 2-d projection of the space the cylinder takes up. To illustrate the limitations of attempting to understand a multi-dimensional structure from a single \"view\", imagine looking at a cylinder from a specific viewpoint to the side and trying to decipher what it could be:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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AAKCaqLKBVFBQEJtvvnm+xwAAAKqRmvkeYH0qKSnJ9wjVnjWoGqxDfi1atCgi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\nAJAIJAAAgOT/A7BsFUyIEMnLAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.fill_between([-1,0,1], -2, 2, facecolor='blue', alpha = 0.4);\n", + "plt.xlim(-4,4);\n", + "plt.ylim(-3,3);\n", + "plt.xlabel(\"X\", fontsize=20);\n", + "plt.ylabel(\"Z\", fontsize=20);\n", + "plt.title('View of Object from the Side', fontsize=20);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From this perspective alone we have no information on the object's presence in the $Y$ dimension; our only conclusion can be that the 3-d object is constrained in the $X$ and $Z$ dimensions by [-1,1] and [-2,2]. \n", + "\n", + "Beyond that, we can not tell if the shape is a prism, cylinder, or any number of possible objects that fit those constraints. The \"variability\" of our understanding is high, and can only be diminished by supplementing our current perspective with an additional \"view.\" \n", + "\n", + "Let's add another view by looking at the same object, this time from above instead of from the side:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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miIi9SkkxlZpqKCOjvaKjo+yOCgA4RyFbkAAALZff79f27YXavdunggKpujq5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\nTcXFMbwOQMtEQQKAIKIgoS2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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X = np.linspace(-1,1,50)\n", + "plt.fill_between(X, -np.sqrt(1-X**2), np.sqrt(1-X**2), facecolor='blue', alpha = 0.4);\n", + "plt.xlim(-4,4);\n", + "plt.ylim(-2.5,2.5);\n", + "plt.xlabel(\"X\", fontsize=20);\n", + "plt.ylabel(\"Y\", fontsize=20);\n", + "plt.title('View of Object from Above', fontsize=20);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After adding this second view we can be positive that the shape, if not a cylinder, is restricted to the space of\n", + "a cylinder with a unit circle base an height ranging from [-2,2].\n", + "\n", + "Individually, neither of these perspectives would provide a particularly enlightening idea of the shape being looked at. With the first view, we had no information on the object in the $Y$ dimension, and in the second view we gained no information on the $Z$ dimension. When combined, however, we can make conclusions based on all three dimensions and the size of the set of possible shapes is drastically reduced. \n", + "\n", + "This is the idea behind model ensembling; the aggregation of multiple perspectives yields a more complete view than any of them alone.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multifamily Real Estate Example\n", + "\n", + "Let's bring this analogy of uncorrelated models providing \"perspectives\" to one involving data. Where the cylinder above was a function of space in the $X$,$Y$, and $Z$ dimenseions, let's consider house pricing data, with possible explanatory variables `Number Of Stories`, `Total area`, `Type`, and `Year Built`. Note that `Type` is a classifier.\n", + "\n", + "The data was aggregated by user 'dmikebishop' on [DataWorld](https://data.world/dmikebishop/commercial-real-estate-for-sal). To use exterior data, store it as a CSV in the `data` folder in research and use the `local_csv` function to pull it into a Pandas DataFrame." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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TU15dcHCwwsPDm72f7OzsFunHmdr6GNv6+CTG2BY0d7HHJXMAAFymT58+ysjI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\nD+mWW25RYmKiZsyYofT0dOXl5WnOnDmOzgt0q62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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Pulling in DataFrame and dropping blank values\n", + "fields = ['Price', 'Number Of Stories', 'Total area', 'Type', 'Year Built']\n", + "data = local_csv('loopnetlistingswithbrokers (3).csv')[fields]\n", + "data = data[data != ' '].dropna()\n", + "\n", + "# Formatting values into integers\n", + "data['Total area'] = data['Total area'].str.replace(' SF', '').str.replace(',','')\n", + "data['Price'] = data['Price'].str.replace(',','').str.replace('$', '')\n", + "data = data[[i.isdigit() for i in data['Price']]]\n", + "for i in [0,1,2,4]:\n", + " data[fields[i]] = data[fields[i]].astype(int)\n", + "\n", + "# Restricting the real estate to only multifamily properties\n", + "data = data[data['Type'] == 'Multifamily']\n", + "\n", + "# Using log price transforms the price distribution to a more normal one\n", + "# Normally distributed independent variables are a linear regression assumption\n", + "data['log Price'] = np.log10(data['Price'])\n", + "\n", + "data.ix[:, data.columns != 'Price'].hist(bins=10);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's begin by attempting to model `log Price` using only `Year Built` as our explanatory variable. We'll also define a linear regression plotting function to make this step simpler as we repeat it for the other data dimensions." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rsquared 0.0190269927541\n" + ] + }, + { + "data": { + "image/png": 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XD530/PPSVVcVvaxOKMXwT6CB3UrrlwBAQRh+4AyrLgBqplFh1VlnM420hgaf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\nATOcHlYHwFn8MgAAXMWOEOOFngI4j94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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def linreg_r2(X,Y, plot):\n", + " # Running the linear regression\n", + " Xc = sm.add_constant(X)\n", + " model = regression.linear_model.OLS(Y, Xc).fit()\n", + " params = model.params\n", + " Y_hat = np.sum(params*Xc, axis = 1)\n", + " \n", + " # Plot results\n", + " if plot:\n", + " plt.scatter(X, Y, alpha=0.3) # Plot the raw data\n", + " plt.plot(X, Y_hat, 'r', alpha=0.9); # Add the regression line, colored in red\n", + " return model.rsquared, Y_hat\n", + "\n", + "print 'rsquared', linreg_r2(data['Year Built'], data['log Price'],plot=True)[0]\n", + "plt.xlabel('Year Built');\n", + "plt.ylabel('log Price');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using only `Year Built` in our model explained only 1.9% of the variation on `log Price`. Using only one dimension to try and understand a multi-dimensional dataset is equivalent to trying to categorize a 3-d object as a cylinder by only approaching it from a single perspective. It can not be done. In this model alone we ignore many features of the data and it can be improved by adding another dimension or 'view'.\n", + "\n", + "Let's see what `log Price` looks like from the perspective of `Number Of Stories`:" + ] + }, + { + "cell_type": "code", + "execution_count": 145, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rsquared 0.0561128798813\n" + ] + }, + { + "data": { + "image/png": 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SDJk2rUTr1m1WPO5XZWVUixdb/5yKsrJBvflmWLt29WtoKKz5862+1TXOyS9+\nId1xh9lVnNpZdmEAADgXhB8T2O1T+A9+sEFbt27X4KBHZWVpffCD1g1ykrRz55AymZmSvMpkktq5\n8x2zSzJscHBIGzf2KxzOqbu7VxdfbO2zmBwtGh1ea5LNml3JqT31lLRwodlVAABwSta+67ao4d3E\nDikaLZPfP6Rrr/XKyruJvfvuAU2c+GcqL++X3z9B775bhIf1nYW33krI4/mgPJ789WZzCxoDzz13\nSBUVC1RX16uKijo999wG/emfWnfTA1tMHX3sMemuu477kqlbKb9XU9PwVDIPbxEAAHvhnc0E27ZF\nlEhcoGy2RIlEVtu27VZbm9lVnbtZs6ZoYGCH4vGEfL5yzZo1xeySDKmpKVU8fmzNT01NEdyMGpRK\n5c54bTVFM3V0YGB4LUyx+sUvpNZWs6sAAKBoEH5MMDDg19Spde+57jGxGuMmTkyrvv585XJ9qq+v\n0cSJ280uyZBPfCKg3/2u9+hW1yl94hMBs0sybO5crzo6wnK5IiovT2juXGsfRBuJSFu39iqRKFF5\neVZz5hh8wp/+VPr7vx+T2sYcXRgAAMYM76YmqKlJqLv7+Gsrmz07oG3bdkmKqbz8sGbPtnZY+NKX\nLtK+fa+rt9enurqYvvSlj5hdkmFf/vJcrVq1XVu29Gru3KRuuWWu2SUZ0tnZo1isSdLwcTCdnR3S\nwITi7sL87GfS4sVn/Ba2UgYAoLAIPya45ZZZWrWqQ3195aqpSeiWW4r4hu19yGYn6OqrZ2rnzp2a\nMWOGstnu0X+oiL3xRp/OP/8SBQLDXYU33ujTokXVZpdliN9fqdtua1J7e7uam5vMLufM3kcX5suJ\njFJpl5ST5JJKPTnpn8Zhl7ApU6QNG+jCAABgUbyDmyB/I2oXdjudvr09qlhsmqThrkJ7e5cWLTK3\nJqPyGwR0dMQVj4cLv0FAgdfCuEpcKi09tgW5y3WWO5+9jy4MAACwH8IPDLPf6fQnbgZg7c0BJGn9\n+rA2bSrVrl0+xeNSKhXWokXTRv/BIl0L4/WWKFod1IZ/+S/5qof/Dspqu70BAIBxR/iBYUV/Ov1Z\nuuSScv2f/9OhaLRcfn9CCxf6zS7JmFhMzZ/9uOalpWw2q5KSEpW40pK/SP75//u/Dx9weRZckqok\nfbIgBQEAALsqkrsfWNm4T6kqsHQ6q64utwYG3KqqciudLpLDJH/xC+mOO87pR0syKaUzbmWzWeVy\nksszxt1yqyL/AAAgAElEQVSsyZOll18ujjNqgDFmt99xAOBkhB8YtnZtp/7zP13q7KzS1q0JDQ52\nasmSGWaXdc7WrDmgaHSuMpkSRaNZrVmzZewOBI3FpIsuklKpsXm+98nlGu76ZLOSlJXLdZpvPIcu\nDGB3+XOlMplBRSIN5p0rBQAwjPADw1av7lYkskDZbK8ikTqtXr3B0uFn375+HTokpdPDm3qVl/ef\n/E0GujAFd/HF0n/913E7kj34/3Ro27bpOnCgT+efX6PZs3fp7/7OPptuAIUUjXrOeA0AsA5+g8Ow\naDShd97ZpSNHMqqujmjOHIucW3SaLsz/e3hImcyxKS3uHSlpctl4Vyc98YR0xRVj8lTpdE7d3TEd\nPJiRyxXTzJnW38QBGC9229ESAJzsfYWftWvXat++fVq6dKn27NmjKVOmyHXaeTNwmv7+XkUitYrH\nXcrlcurv7x3fAp56Svrrvx6zp/N6S5RManhtjGv4+pxdfLH03HOmr4Xp6TmkZLJRuVxSyaRXPT2H\nTK0HsBL77WgJAM41avj5l3/5F3V2dmr//v1aunSpnn32WR0+fFh33333eNRnS/nFs9GoR35/2vKL\nZzOZUu3dG1U67ZfHE9VFF53Da4nFpLlzpaGhsS/wLHk8Lg0lUsrmSlTiysrjcUuPPy79j/9hdmnn\nrKqqTl7vHpWUpOT1HlZVVZ3ZJQGWYbcdLQHAyUYNP6+++qqeeuopLVu2TJJ066236qabbip4YXaW\nXzwrSZGILL949g9/6FFJyWfk8WR0fe4/9cCv/1yafKvZZZ3swgulF14YtQvz1S/+p9asmapk0i+v\nN6prPr1H/27h4CNJsVi/qquvVDbbq+rqOsViL5ldEgAAwLgbNfyUlQ2vdchPc8tkMspkMoWtyuaK\nfvHs4KD0hS9Ir7zyvr59R2xQudzdGj595ehcsUL6+c+lK68s2NP/5jcJZbOXyeORslnpN7/ZUbA/\na7xceul5+t3vnlNvb7nq6hK66qppZpcEAAAw7ka96/7IRz6iv/u7v1NPT49++tOf6oUXXtD8+fPH\nozbbGrfFs7/7nXTzzYV57vfI5TKSSk+4HsWsWdKLL5q+FuZUUqmskskB5XIlcrmycruL5JwfA9as\neUeDg1cql8tocNCtNWte0i23zDW7LAAAgHE1avi544479Pzzz6uiokIHDhzQl770JS1ZsmQ8arOt\n/OLZ9675Oa3BQemmm6RXXx2/As/Gs89q7p90qK9vtiSfpJhqarbp8P4vm13ZOauu7tfg4LuSyiUl\nVF19iq2uLWbPnjJlMiWSMspkSrRnjwm71wEAAJhs1PATj8eVzWa1YsUKSdITTzyhWCwmn89X8OLs\nbOqq76n+6f+QyyWVGtlNbCxce630/e8fdy7M2RgaCkmaJMkraYKGht4cy+rG3ac+dZGeeGKLhobq\nVFbWq0996iKzSzLM6x1SZeUElZTEVV5eKa/X/I0lYF9229QFAGAfo97tfvOb39Rll102cj04OKhv\nfOMbeuihhwpamJ2tXx/WZb/8D6VyGl4mo4zKvG7jT/zcc9JHPmL8ec5SKpWSFFa+85M64dwcq+np\nOaIpU65VJiO53VJPz2/MLsmwq6+u0X/8x4uKx8tUVjakq6+uMbsk2JjdNnWxG8IpACcbNfxEIhHd\n/J51I1/60pf00kvsFGVEKHRYtRPmqLF369Hwkz0Wfq6/XnrggXPuwpihpMQr6cOSSiRlVVKyxeSK\njKmsrJPHc1jZrEceT1qVldbfFnrevAbt2ZNUZ2dMjY0TNW+e1+ySYGNFv6mLwxFOATjZqO9IqVRK\nu3bt0vTp0yVJW7Zssfwn+2b77/8+ojs/9JTS6RJ5PFnNmPFHPfJI4XYvK7Rs1ispouFpb8mj19bl\n8+U0c+ak91y/Y2I1YyObnaCrr67Xzp07NWPGDGWz3WaXBBsbt01dxkm+U9LREVc8HrZ8p4RwCsDJ\nRv2N961vfUvLly/XwMCAMpmMamtr9c///M/jUZtt5XIuRSIuJZMl8npzyuUKvDV0gVVWxnTkiEeS\nW5JHlZUxs0syZMmSat1//3+pv79aEyYc0U03fcDskgyz280oittZbepiAflOSSYzqEikwfKdEn4f\nAHCyUcPPhz/8Yb3wwgvq6+uTy+VSIBAYj7psLZMZ0sDAXiWT5fJ6E8pkrL34vKysQm53hzKZCXK7\n+1VWVmF2SYZ0diY1Y8ZHj4bTrDo7d5tdkmH5m1G3u0uBQIXlb0btxm6dBa+31NLh4ER265TYLZwC\nwNk47W/wH//4x/qLv/gL/e3f/u3IAafvdd999xW0MDs7cCCubNavXM6rbNajAwfiZpdkSHW1V7HY\nQqXTw0uVqqufNrskQ/r6yiQlNPzPI3302tryN6OVlQfU3Gyfm1K7sFtnwW7s1imxWzgFgLNx2vBz\n0UXD2/t+/OMfH7dinCKTKZNUKZfLI8lz9Nq6Jk3yad++PyqT8amkJKZJk6y9Dfrevbv161+7NTRU\nqbKyuD796d2SLjG7LNiY3ToLdkPnFOOJ3fiAwjrtO2xra6sk6cCBA/ra1742bgU5gdeblc9XO7KV\nstebNbskQ3p6DimV+qgymeFOSU/PVrNLMmT9+sM6cmRQ2ayUSAxq/frDZpdkWDQa16pV27VlS59e\nfrlDt9wyS35/pdll4Si7dRbshs4pxhO78QGFNerHi7t27VJnZ6caGxvP6Q945pln9JOf/EQej0d/\n9Vd/pSuuuGLksUWLFmny5MlyuVxyuVy6//77FQza/xO1lpagUqlODQ6WqqIiZflPEbu6ypTN7lcu\nV65sNqGuLmt3srq6XHK5Piy3O3+92dyCxsCqVdvV3d2kdHq/ursna9WqDt12W5PZZeEoOgsA8ugE\nA4U16r+o7du360//9E9VXV2t0tJS5XI5uVwurV27dtQnj0Qieuihh/T0008rFovpX//1X48LPy6X\nS48++qjKy8sNvQir+fjHg/J4SpVIeFRentb8+dbeGnpoaFDZ7MWSXMpmcxoaes3skgxxubJKpw8p\nv+anrMzanTlJOniwVHv29Kqra1CpVK9KSphCUUzoLADIoxMMFNao4edHP/rROT/5xo0btWDBAlVU\nVKiiokIrV6487vFcLqdcLnfOz29VCxc2qLS0R9Go5PdLLS3WvtlJpyWpU/lzftIW/z1dX59VZ+dB\n5XLlcrkSqq+3fvg5cuSgEom5kqREok5HjvzR5IoAAKfCbnxAYZ0x/PzhD3/Q7t271dzcrEsuOfsF\n3+FwWIODg/ra176mgYEB3XrrrfrYxz523PesWLFC+/bt07x583TnnXee9Z9hRXbbaaey0qX+/j2S\nqiUdUWWltc8tmj9/mqRBJZOS1zt49NraPvaxKfr5zzeptzet8nKPPvaxKWaXBAA4BbvdIwDF5rTh\n54c//KE2bNigpqYm3XXXXfryl7+sP/uzPzurJ8/lcopEInr44Ye1b98+3XzzzXrppZdGHr/99tvV\n2tqqQCCg5cuX68UXX9SSJUvO/dXAFOl0TNIsSaWSzlc6be2uwmWXVcvjaVAy6ZHXm1ZTU9jskgzr\n6upTTc2FGhrqU01Njbq6tptdEgAAwLg7bfhZv369fv7zn8vj8WhgYEB/+Zd/edbhZ+LEiWpqapLL\n5dKUKVPk8/l0+PBh1dbWSpKuueaake+9/PLLtWPHjlHDT3t7+1nVUIxSqbS2bIkqHveqsjKpuXP9\nKi218oLGgKQuSX5JUUkBS4/TJZcMatOmdTpypFqBwBFdcskkS78eSdq+vUvvvCMNDZVpYKBHlZVd\nln9NdsW4FDfGp7gxPsWN8SluThmf095xe71eeTzDD1dVVSmTyZz1ky9YsEDf/va39ZWvfEWRSETx\neHwk+ESjUX31q1/VT37yE5WVlem1115TW1vbqM/Z3Nx81nUUm3XrwqqvP9bSTqXC+uhHrdviTqXW\nqaTko8rlMnK53EqlXrH0OK1bF9bnPndsY47S0rDlF6E/+mhcU6Zcpr6+XtXU1ElaZ+kxsqv29nbG\npYgxPsWN8SlujE9xs9v4nCnInTb8uFyuM16/H/X19Wpra9MNN9wgl8ulu+++W6tXr1ZVVZUWL16s\ntrY23XjjjfL5fJo9e/b7Cj92YLdtLKurgzp8+DXlchVyuQZVXW3txZl2Gx9JmjrVp3g8LJcrovLy\nhKZOtfZBtAAAAOfitHd1u3bt0je+8Y3TXt93333v6w+44YYbdMMNN5zysWXLlmnZsmXvt1bbsNs2\nljNnpvT22+crmXTJ663WzJnWPuTUbuMjSS0ttXK5JK93SNOnS/Pn15pdEgAAwLg7bfj5m7/5m+Ou\nT9ylDeeuqalGq1Z1qK+vXDU1CV155SyzSzLkjjsu0Xe+84Z6e8tVV5fQHXec/c6AxcSO24zmt1ev\nrIypqcn626sDAACci9OGn8985jPjWYejdHT0qbGxSY2N+euwWlsrzS3KAL9/sv73/27Szp07NWPG\nDHk83WaXZIgdtxnlEE0AAACpxOwCnMhua0pOnBZmh2liAAAAsB/CjwnsFhZaWoIKBMJyu7sUCIRt\nMU0MAAAA9mPtloNF2W1NCVOqAAAAYAWjhp+5c+eedMaP2+3WtGnTtGLFCl122WUFK86u7LamJJlM\nKRTqUUdHXPH4cOfH6y01uywAAADgOKOGn29961vyer1avHixcrmcfv/732tgYEDz5s3TP/7jP+qp\np54ajzpRxEKhHkUiDcpkBhWJNCgUCtsq3AEAAMAeRl3z8/zzz+v6669XTU2Namtrdf3112vdunW6\n5JJL5PEwaw7228ABAAAA9jTqXerQ0JCeeOIJNTc3q6SkRJs3b1Zvb6/efPPNk6bDwZnseCgoAAAA\n7GfU8HPffffphz/8oR5//HFls1lNnz5d9913n9LptO69997xqBFFLr+Bw/BubxWW38ABAAAA9jRq\n+Jk2bZoeeOAB9fX1qaSkRNXV1eNRFwAAAACMqVHX/LS3t2vx4sX61Kc+pba2Nn3yk5/U5s2bx6M2\nWMSxDQ8mHd3woMfskgAAAICTjNr5+e53v6uHH35YH/rQhyRJb731lu699179/Oc/L3hxsAY2PAAA\nAIAVjNr5KSkpGQk+knTRRRfJ7XYXtChYy4kbHLDhAQAAAIrR+wo/L774oqLRqKLRqH79618TfnCc\nlpagAoH8hgdhNjwAAABAURp1ftJ3vvMd/cM//IP+/u//Xi6XS5deeqm+853vjEdtsAivt1StrQ2q\nrDyg5mYONwUAAEBxel+7vf3kJz8Zj1oAAAAAoGBOG34+//nPy+VynfYH2fAAAAAAgJWcNvz89V//\n9XjWAQAAAAAFddrwM3/+/PGsAwAAAAAKatTd3gAAAADADjiNEoZFo3GtWrVdW7b06eWXO3TLLbPk\n91eaXRYAAABwHDo/MGzVqu3q7m5SOn2RurubtGrVdrNLAgAAAE5C+IFhfX3lZ7wGAAAAigHT3mBY\nRUVEGzZsVU9PUsFgnxYv7je7JEOSyZRCoR5Fox75/Wm1tATl9ZaaXRYAAAAMovMDw4bPg/JL8kny\nn/F8KCsIhXoUiTQona5XJNKgUKjH7JIAAAAwBuj8wLB4vFqXXdaorq79mjRpsuLxuNklGRKNes54\nDQAAAGui8wPDamoSZ7y2Gr8/fcZrAAAAWBPhB4bdcsss1dd3yON5S/X1w1tdW1lLS1CBQFgeT7cC\ngbBaWoJmlwQAAIAxwHweGOb3V+q225rU3t6u5uYms8sxzOstVWtrg9llAAAAYIzR+QEAAADgCIQf\nAAAAAI7AtDcYlj8Xp6Mjrng8zLk4AAAAKEp0fmBY/lycTGYS5+IAAACgaBF+YBjn4gAAAMAKCD8w\njHNxAAAAYAWEHxiWPxfH7e7iXBwAAAAULeYnwbD8uTiVlQfU3Mz5OAAAAChOdH4AAAAAOALhBwAA\nAIAjEH4AAAAAOAJrfmDY4cNHtHLl69qxI6EPfegl3XPPR1RbW212WQAAAMBx6PzAsJUrX1dX15VK\np+erq+tKrVz5utklAQAAACch/MCw3l7fGa8BAACAYsC0NxMkkymFQj2KRj3y+9NqaQnK6y01u6xz\nVlNzRFu29KuvL6l0ul9z5x4xuyQAAADgJHR+TBAK9SgSaVA6Xa9IpEGhUI/ZJRmyZEmD/P43VVKy\nQ37/m1qyhLN+AAAAUHzo/JggGvWc8dpq3O46feUrF2nnzp2aMWOG3O5us0sCAAAATlLwzs8zzzyj\na665Rp/97Gf1hz/84bjHNm7cqOuvv1433XSTHn744UKXUjT8/vQZr63Gbq8HAAAA9lTQ8BOJRPTQ\nQw/pySef1I9//GP9/ve/P+7xe++9Vw8++KCeeOIJbdiwQbt27SpkOUWjpSWoQCAsj6dbgUBYLS1B\ns0syJP963O4uW7weAAAA2FNB51tt3LhRCxYsUEVFhSoqKrRy5cqRx/bu3atAIKD6+npJ0hVXXKFX\nXnlF06dPL2RJRcHrLVVrq33WxeRfT2XlATU32+d1AQAAwF4KGn7C4bAGBwf1ta99TQMDA7r11lv1\nsY99TJJ06NAh1dbWjnxvbW2t9u7dW8hyiobddnsDAAAArKCg4SeXyykSiejhhx/Wvn37dPPNN+ul\nl1467fe+H+3t7WNZoik6OiIaGGgcud6+/f9TU1PAxIrGjh3Gx+4Yo+LG+BQ3xqe4MT7FjfEpbk4Z\nn4KGn4kTJ6qpqUkul0tTpkyRz+fT4cOHVVtbq2AwqIMHD458b3d3t4LB0deKNDc3F7LkcdHT0610\nun7k2uOpUnNz/Rl+whra29ttMT52xhgVN8anuDE+xY3xKW6MT3Gz2/icKcgVdMODBQsWKBQKKZfL\nqa+vT/F4fGSqW0NDg2KxmPbv3690Oq21a9dq4cKFhSynaLA7GgAAADD+Ctr5qa+vV1tbm2644Qa5\nXC7dfffdWr16taqqqrR48WKtWLFCd955pyTp6quvVmNj4yjPaA8tLUGFQuHj1vwAAAAAKKyCn655\nww036IYbbjjlY/PmzdOTTz5Z6BKKjt12e8tv4NDREVc8HmYDBwAAABSlgh9yCvsLhXoUiTQok5mk\nSKRBoVCP2SUBAAAAJyl45wf2F4lIW7f2avfuIQ0N9WrOHLMrAgAAAE5G5weGdXb2KBarUzZbo1is\nTp2ddH4AAABQfOj8wLCpU89TNBqWy9Utny+nqVPPM7skAAAA4CR0fmAYW3cDAADACgg/GCPlcrnK\nJJWbXQgAAABwSoQfGBaNeiQllMsNSUocvQYAAACKC3epJsifi/PeQ06tfC7Onj0HFYs1KZdzKRab\nrD17OiR9wOyyAAAAgOPQ+TFB/lycdLreFufiNDYG5fP1qqSkTz5frxobg2aXBAAAAJyE8GOCE6eF\nWX2amM+XOuM1AAAAUAwIPyaw5+5ox9b8AAAAAMWI8GOCpqYadXZ26I03tqmzs0NNTTVml2SI3TpZ\nAAAAsCfCjwk6OvrU2NikSy+drcbGJnV09JldkiHDGx40KJc7X7FYg/bsOWh2SQAAAMBJ+IjeBHbr\nlDQ2BhWN5jc8KGPDAwAAABQla991W5Tfn1Ykcvy1lQUC0pw5dSor69OMGXUKBMJmlwQAAACchGlv\nJmhpCSoQCMvj6VYgEFZLi7U7Jfk1TNu3v2uLNUwAAACwJzo/JvB6S9Xa2mB2GWMmv4YpldqpxsYZ\n6ugIq7W10uyyAAAAgOPQ+YFhdlvDBAAAAHsi/MAwe55bBAAAALsh/MCw/Bomt7vLFmuYAAAAYE/M\nT4Jh+TVMlZUH1Nxsn7VMAAAAsBc6PwAAAAAcgc6PCZLJlEKhHkWjHvn9abW0BOX1lppdFgAAAGBr\ndH5MEAr1KBJpUDpdr0ikQaFQj9klGZJMprRuXVgbNsS1bl1YyWTK7JIAAACAk9D5MYHdtobOh7lM\nZvBomAtb+hwjOnMAAAD2ROfHBHbbGtquYc4unTkAAAAMI/yYIL81tMfTbYutoQlzAAAAsALu6kyQ\n3xraLlpaggqF8uf8VNgizEUix18DAADA+gg/MMxu5/zkw9x71/wAAADA+gg/wAns1pkDAADAMNb8\nAAAAAHAEwg8AAAAARyD8AAAAAHAEwg8AAAAARyD8AAAAAHAEwg8AAAAARyD8AAAAAHAEwg8AAAAA\nRyD8AAAAAHAEwg8AAAAARyD8AAAAAHAEj9kFOFEymVIo1KNo1CO/P62WlqC83lKzywIAAABsjc6P\nCUKhHkUiDUqn6xWJNCgU6jG7JAAAAMD2CD8miEY9Z7wGAAAAMPa46zZBWdmg3nwzrETCo/LytObP\nT5ldEgAAAGB7hB/TlGu48eaRZO3wk1/D1NERVzweZg0TAAAAihLhxwRDQxWaM6fuPddpE6sxbv36\nsDZtqtLu3bWKx8uVSoW1aNE0s8s6Z2xIAQAAYE8FDT+bNm3S7bffrpkzZyqXy2nWrFm66667Rh5f\ntGiRJk+eLJfLJZfLpfvvv1/BYLCQJRUFvz+tSOT4aytrb48qFpumbHZIsVid2tu7tGiR2VWdu/yG\nFJIUiUihUFitrQ0mVwUAAACjCt75mT9/vn7wgx+c8jGXy6VHH31U5eXlhS6jqLS0BBUKhY/rLFhb\nbpRra2FDCgAAAHsq+F1dLnf6G+FcLnfGx+3K6y21VSehublKmzaF5XJ1y+fLqbm5yuySDCkp6ddz\nzx1SNFomv39I117rlVRvdlkAAAAwqOBbXe/atUvLly/XF77wBW3cuPGkx1esWKHPf/7z+u53v1vo\nUlAgCxc2aMEC6eKLY1qwYPjayrZtiyiROF/ZbJ0SifO1bVtk9B8CAABA0XPlCth66e7u1uuvv66r\nrrpKe/fu1c0336zf/va38niGG05r1qxRa2urAoGAli9frmuvvVZLliw57fO1t7cXqlRgxL/9W5/S\n6YtGrj2et/SVr9SYWBEAAADORnNz8ym/XtBpb/X19brqqqskSVOmTNHEiRPV3d2thobhzsA111wz\n8r2XX365duzYccbwI53+hcB87e3tthifl1/uUHf35JHr+vpuNTc3mVjR2LHLGNkV41PcGJ/ixvgU\nN8anuNltfM7UMCnotLdnn31WDz74oCSpt7dXhw8fVn398NqJaDSqpUuXamhoSJL02muvaebMmYUs\nBwUSjcb14IMd+rd/69ODD3YoGo2bXZIht9wyS/X1HfJ6t6m+vkO33DLL7JIAAAAwBgra+Vm0aJG+\n/vWv63Of+5xyuZxWrFihZ599VlVVVVq8eLHa2tp04403yufzafbs2WpraytkOSiQVau2q7u7Sen0\nfnV3T9aqVR267Tbrdkr8/kpL1w8AAIBTK2j48fl8+tGPfnTax5ctW6Zly5YVsgSMg76+8jNeAwAA\nAMWg4Lu9wf5qahJnvAYAAACKAeEHhuXXyHg8b7FGBgAAAEWLo+thWH6NzPBOIayVAQAAQHGi8wMA\nAADAEQg/AAAAAByBaW8wLJlMKRTqUUdHXPF4WC0tQXm9pWaXBQAAAByHzg8MC4V6FIk0KJOZpEik\nQaFQj9klAQAAACch/MCwaNRzxmsAAACgGBB+YJjfnz7jNQAAAFAMCD8wrKUlqEAgLLe7S4HA8Jof\nAAAAoNgwPwmGeb2lam1tUGXlATU3N5hdDgAAAHBKdH4AAAAAOALhBwAAAIAjEH4AAAAAOALhBwAA\nAIAjEH4AAAAAOALhBwAAAIAjEH4AAAAAOALhBwAAAIAjEH4AAAAAOALhBwAAAIAjEH4AAAAAOALh\nBwAAAIAjEH4AAAAAOALhBwAAAIAjEH4AAAAAOALhBwAAAIAjEH4AAAAAOALhBwAAAIAjEH4AAAAA\nOALhBwAAAIAjEH4AAAAAOALhBwAAAIAjEH4AAAAAOALhBwAAAIAjEH4AAAAAOALhBwAAAIAjEH4A\nAAAAOILH7AJgfclkSqFQjzo64orHw2ppCcrrLTW7LAAAAOA4dH5gWCjUo0ikQZnMJEUiDQqFeswu\nCQAAADgJ4QeGRaOeM14DAAAAxYDwA8P8/vQZrwEAAIBiQPiBYS0tQQUCYbndXQoEhtf8AAAAAMWG\n+UkwzOstVWtrgyorD6i5ucHscgAAAIBTovMDAAAAwBEIPwAAAAAcgfADAAAAwBEKuuZn06ZNuv32\n2zVz5kzlcjnNmjVLd91118jjGzdu1Pe+9z253W5dfvnlWr58eSHLAQAAAOBgBd/wYP78+frBD35w\nysfuvfdePfbYYwoGg1q6dKna2to0ffr0QpcEAAAAwIEKPu0tl8ud8ut79+5VIBBQfX29XC6Xrrji\nCr3yyiuFLgcAAACAQxU8/OzatUvLly/XF77wBW3cuHHk64cOHVJtbe3IdW1trXp6egpdDgAAAACH\nKui0t8bGRt1222266qqrtHfvXt1888367W9/K4/n5D/2dB2iE7W3t491mRhDjE/xY4yKG+NT3Bif\n4sb4FDfGp7g5ZXwKGn7q6+t11VVXSZKmTJmiiRMnqru7Ww0NDQoGgzp48ODI93Z3dysYDI76nM3N\nzQWrF8a0t7czPkWOMSpujE9xY3yKG+NT3Bif4ma38TlTkCvotLdnn31WDz74oCSpt7dXhw8fVn19\nvSSpoaFBsVhM+/fvVzqd1tq1a7Vw4cJClgMAAADAwQra+Vm0aJG+/vWv63Of+5xyuZxWrFihZ599\nVlVVVVq8eLFWrFihO++8U5J09dVXq7GxsZDlAAAAAHCwgoYfn8+nH/3oR6d9fN68eXryyScLWQIA\nAAAASBqH3d4AAPj/27v3oKjqBozjz4IsIqhochkvaWKG+UeZ4y0yUBFsxkbMMcGE0ZoxRWvKkQbx\n7pAK3hXJuwGWCJlE1gym0zA6MJg2meVokWRpAspF5ZKI7PvHmzuAaG/zuh30fD9/sefs/vY5/IbL\ns7+zZwEAaA0oPwAAAABMgfIDAAAAwBQoPwAAAABMwaEXPEDL6upuqaCgVFVVbeThUa8hQ7xltboY\nHfYd3psAAA6ZSURBVAsAAAB4pLHyY4CCglJVVnZTfb2PKiu7qaCg1OhIAAAAwCOP8mOAqqo2970N\nAAAA4MGj/BjAw6P+vrcBAAAAPHiUHwMMGeItT89LatOmRJ6elzRkiLfRkQAAAIBHHudbGcBqddHw\n4d2MjgEAAACYCis/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/\nAAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADA\nFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMA\nAADAFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB\n8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/AAAAAEyB8gMAAADAFCg/AAAA\nAEyhjaOf4ObNmxo7dqxmzZqlsLAw+/aRI0eqa9euslgsslgsWr16tby9vR0dBwAAAIBJObz8JCcn\ny9PT867tFotFO3bsUNu2bR0dAQAAAAAce9rb+fPnVVRUpMDAwLv22Ww22Ww2Rz49AAAAANg5tPwk\nJiYqNjb2nvsXL16syZMna+3atY6MAQAAAACy2By0/JKVlaWysjK98cYbSkpKUrdu3TR+/Hj7/s8+\n+0zDhw+Xp6enoqOj9corrygkJOS+Y548edIRUQEAAAA8QgYOHNjidoe95yc3N1cXL17UoUOHVFxc\nLFdXV/n6+mrYsGGSpHHjxtnv++KLL+qnn3762/Jzr4MAAAAAgL/jsPKzbt06+9dJSUnq3r27vfhU\nVVVpxowZ2rlzp1xdXXXixAmFhoY6KgoAAAAAOP5qb40dOHBA7du3V3BwsEJDQzVp0iS5u7urX79+\nlB8AAAAADuWw9/wAAAAAQGvi0Ku9AQAAAEBrQfkBAAAAYAqUHwAAAACm8NCUnxUrVig8PFwRERE6\nffq00XHQTGJiosLDwzVx4kR99dVXRsdBC27evKnRo0crKyvL6ChoJjs7W+PGjdOECROUm5trdBw0\nUlNTo7feektRUVGKiIjQsWPHjI6Ev5w9e1ajR4/WRx99JEkqLi5WZGSkpkyZonfffVe3bt0yOKG5\nNZ+fy5cva9q0aYqMjNTrr7+usrIygxOaW/P5uePo0aPy9/c3KNW/46EoP998840uXLig9PR0xcfH\n6/333zc6EhopKChQYWGh0tPTtX37di1fvtzoSGhBcnKyPD09jY6BZiorK7V582alp6dr69atOnLk\niNGR0MiBAwfUu3dvpaamasOGDfz9aSVqa2uVkJCggIAA+7YNGzYoMjJSe/bs0eOPP679+/cbmNDc\n7jU/r776qtLS0jRq1Cjt2rXLwITm1tL8SFJdXZ22bdsmb29vg5L9Ox6K8pOfn6/g4GBJkp+fn65f\nv67q6mqDU+GOQYMGacOGDZKkDh06qLa2VlxEsHU5f/68ioqKFBgYaHQUNJOXl6eAgAC5ubmpS5cu\nWrZsmdGR0Ejnzp1VUVEhSbp27Zo6d+5scCJIkqurq7Zu3aouXbrYtx0/flwjRoyQJI0YMUJ5eXlG\nxTO9luZn8eLF9o816dy5s65du2ZUPNNraX4kacuWLYqMjJSLi4tByf4dD0X5uXr1apM/OJ06ddLV\nq1cNTITGnJyc5ObmJknKzMxUYGCgLBaLwanQWGJiomJjY42OgRZcunRJtbW1mjlzpqZMmaL8/Hyj\nI6GRl156ScXFxQoJCVFUVBQ/R62Ek5OTrFZrk221tbX2f9oee+wxXblyxYhoUMvz4+bmJicnJzU0\nNOjjjz/W2LFjDUqHluanqKhIhYWFCgkJeeRfwP5XP+T0QXnUJ+VhdfjwYX366afauXOn0VHQSFZW\nlgYNGqSuXbtK4uentbHZbKqsrFRycrIuXryoqKgoff3110bHwl+ys7Pl6+urbdu26ezZs1q4cKEy\nMzONjoW/we+51qmhoUExMTEaOnSohg4danQcNJKQkKBFixYZHeNf8VCUH29v7yYrPaWlpfLy8jIw\nEZo7evSotm3bpp07d8rDw8PoOGgkNzdXFy9e1KFDh1RcXCxXV1f5+vpq2LBhRkeDpC5dumjAgAGy\nWCzq0aOH3N3dVV5ezulVrcS3336r4cOHS5L8/f1VXFwsm83G6nYr5O7urrq6OlmtVpWUlDzy71t4\nGM2bN09PPPGEZs2aZXQUNFJSUqKioiLNmTNHNptNV65cUWRkpNLS0oyO5hAPxWlvAQEBysnJkST9\n+OOP8vHxUbt27QxOhTuqqqq0atUqbdmyRe3btzc6DppZt26dMjMztW/fPk2cOFHR0dEUn1YkICBA\nBQUFstlsqqioUE1NDcWnFenZs6e+++47Sf89RbFdu3YUn1Zq2LBh9v8VcnJy7KUVrUN2drasVqtm\nz55tdBQ04+Pjo5ycHKWnp2vfvn3y8vJ6ZIuPJFlsD8na8Nq1a3X8+HE5Oztr0aJFeuqpp4yOhL9k\nZGQoKSlJvXr1sr8impiYKF9fX6OjoZmkpCR1795dYWFhRkdBIxkZGcrMzJTFYlF0dLSCgoKMjoS/\n1NTUKC4uTmVlZbp9+7beeecdDR482OhYpnfq1CktWLBA5eXlcnZ2VseOHbVz507Fxsaqrq5OXbt2\n1YoVK+Ts7Gx0VFNqaX4aGhrk6uoqd3d3WSwW9enTxzSnWbU2Lc3Pnj171LFjR0nSqFGjHukrjz40\n5QcAAAAA/h8PxWlvAAAAAPD/ovwAAAAAMAXKDwAAAABToPwAAAAAMAXKDwAAAABToPwAAAAAMAXK\nDwBA0n8/xNPf318HDx5ssn3kyJEPZHx/f381NDQ8kLFu376tjRs3aty4cQoPD1dYWJg2bdpkH//G\njRt6+eWXW/xAxaysLEVERCgqKkoTJkzQkiVLdOvWLUlSbm6url+//o+yREVFiU+NAICHA+UHAGDX\nq1cvJSUlqaamxr7NYrE8kLEf1DiStH79el24cEGffPKJ0tPTlZGRocLCQm3cuFGSdO7cObVr105J\nSUlNHldSUqL169dr9+7dSk1N1f79+1VdXa3Dhw9LklJSUlRZWfmPsqSmpj7QYwMAOE4bowMAAFoP\nLy8vDR8+XJs3b1ZMTEyTfQcOHFBeXp5WrVolSYqMjFR0dLScnZ21ZcsW+fj46IcfftAzzzyjJ598\nUkeOHFFlZaW2b98uHx8f2Ww2JScnq6CgQNXV1UpMTFSfPn107tw5JSQkqL6+XvX19Vq0aJH8/f0V\nGRmpfv366cyZM0pLS7MXjKqqKu3bt09HjhyRi4uLJMlqtWrJkiUKDQ3V9OnTFR8fr0uXLuntt9+2\nFyJJunbtmurr61VTU6O2bdtKkv149u7dqxMnTigmJkbLly9XdXW1Vq5cKRcXF1ksFi1cuFB+fn5N\ncqWmpurpp5/WmTNndPv2bS1btky//fabqqurNXbsWE2dOlU///yzFi5cKFdXV/3555+Kjo5WYGCg\nw+cSAHA3Vn4AAHYWi0XTpk1Tbm6ufv311xb3t+T06dOKi4vT/v379fnnn6tTp05KTU1V//79lZOT\nY79f3759lZaWpsmTJ2vTpk2SpLlz52rp0qVKTU3VokWLFBcXZ7+/u7u79uzZ0+R5z58/L19fX7Vv\n375Jhk6dOsnHx0e//PKL4uLi1Ldv3ybF587zjxkzRsHBwZoxY4Y+/PBDFRcXS5IiIiLUpUsXrV69\nWn5+fnrvvfc0f/58paSkaOrUqVq6dOlduZycnOzZUlNT5ePjo5SUFGVkZOjgwYM6d+6cMjIyFBwc\nrJSUFH3wwQeqqKj4X6YCAOAArPwAAJpwcXFRTEyM4uPjtWPHjv/p/Sx+fn72MuLp6akBAwZIknx8\nfHTjxg37/Z5//nlJ0oABA7R7926Vl5erqKhI8+fPtz9PTU2N/es74zTm5uZ2z0w2m01OTvd/XW/B\nggV68803dezYMeXl5SkpKUmrV69WUFCQ/T43btxQeXm5+vfvL0kaPHiw5syZY9/fUq6CggKVlJSo\noKBAklRXV6fff/9doaGhio2N1R9//KHAwECFhYXdNx8AwHEoPwCAuwQGBio9PV2HDx+2r2w0X/W5\nc5EASXJ2dm6yr/HtxkWl8RgWi0VWq1VWq1Wpqakt5rhzWltjPXv2VGlpqSoqKtSpUyf79srKSpWX\nl6tPnz46derUPY/t5s2b8vLy0vjx4zV+/HhlZmYqIyOjSflpfqw2m63JtpZyWa1WzZo1SyEhIXft\n++KLL5Sfn6+srCxlZ2drzZo198wHAHAcTnsDANg1LipxcXFas2aN6urqJEkeHh66fPmyJKmsrEyF\nhYX/ePz8/HxJ0smTJ9W3b195eHioe/fuys3NlSQVFRVp8+bN9x3DarUqMjJSixcvtmerq6tTfHy8\npk6dKldX13s+dt++fYqOjrY/TpIuXryonj17SpKcnJx069YteXh4yMvLS99//70kKS8vT88++2yL\nY975ng0cOFBffvmlJKmhoUErV67U9evXtWfPHl2+fFlBQUGKj4/X6dOn//b7BABwDFZ+AAB2jVc3\nevToodDQUG3dulWSFBAQoF27dik8PFy9e/fWc88997djNNamTRsVFhZq7969qqystF9oICEhQfHx\n8dq+fbvq6+s1b968+44jSbNnz1ZKSoomTpwoNzc31dXVacyYMZo+ffp9j2/SpEkqLS1VRESEPDw8\nVF9fLz8/P8XGxkqSXnjhBc2cOVMJCQlKSEjQihUr5OzsLGdnZ/t7fprnunP7tddeU2FhocLDw9XQ\n0KCgoCB16NBBvXv31pw5c9S+fXs1NDRo7ty5980IAHAci40PJwAAAABgApz2BgAAAMAUKD8AAAAA\nTIHyAwAAAMAUKD8AAAAATIHyAwAAAMAUKD8AAAAATIHyAwAAAMAU/gP06qrioxDMxgAAAABJRU5E\nrkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print 'rsquared', linreg_r2(data['Number Of Stories'], data['log Price'], plot=True)[0]\n", + "plt.xlabel('Number Of Stories');\n", + "plt.ylabel('log Price');\n", + "plt.xlim(0,15);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Number Of Stories` explains about 5.6% of the variation in `log Price`. While better than `Year Built`, it still provides a mostly incomplete understanding. Let's take a look at the final dimension, `Total area`:" + ] + }, + { + "cell_type": "code", + "execution_count": 146, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rsquared 0.168804441783\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print 'rsquared', linreg_r2(data['Total area'], data['log Price'], plot=True)[0]\n", + "plt.xlabel('Total area');\n", + "plt.ylabel('log Price');\n", + "plt.xlim(0,200000);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Total area` was the most insightful dimension, with its model explaining 16.8% of variance. Still, however, this is not a great result as we are still attempting to understand a complex, multidimensional dataset from a single perspective. Let's see if averaging the models, combining information from all 3 dimensions, can produce a more accurate model. \n", + "\n", + "*Note:In the below plot, the blue line is not the model but the line $Y=X$. Points along this line mean the combined model perfectly predicted the observed `log Price`.*" + ] + }, + { + "cell_type": "code", + "execution_count": 147, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rsquared: 0.185624465575\n" + ] + }, + { + "data": { + "image/png": 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w+6gGYLSSEpOWLGnQihV1WrKkgaGWOSxmMDp06JCuv/56mUz+g/ypT31KLpcr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\nHA5167jtfGGBNh1/Z8fz3iYnx6u0tEp//vmXJk8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "combined = (linreg_r2(data['Total area'], data['log Price'],plot=False)[1]\n", + " + linreg_r2(data['Number Of Stories'], data['log Price'],plot=False)[1]\n", + " + linreg_r2(data['Year Built'], data['log Price'],plot=False)[1])/3\n", + "\n", + "plt.scatter(data['log Price'],combined, alpha = 0.3);\n", + "plt.plot(data['log Price'],data['log Price'], label='Y=X **not model**')\n", + "plt.ylim(6.5,7.5);\n", + "plt.xlabel('log Price');\n", + "plt.ylabel('Predicted log Price');\n", + "plt.legend();\n", + "\n", + "print 'rsquared:', np.corrcoef(combined,data['log Price'])[0][1]**2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By taking a simple equally weighted average of all the models we saw $R^2$ increase to 18.6%. While still indicative of a poorly fit model, the result is still interesting considering the $R^2$ values of the individual single-dimension models were 1.9%, 5.6%, and 16.9% respectively. The $R^2$ of the combined model was higher than any of the single models alone.\n", + "\n", + "Simply averaging the model outputs ignores some of the interplay between variables which can be better captured by using a multiple linear regression. Let's run a single multiple linear regression model on the pricing data:" + ] + }, + { + "cell_type": "code", + "execution_count": 181, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rsquared: 0.188016012536\n" + ] + }, + { + "data": { + "image/png": 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+bVS3SCruxBHZMPJ6LcAOMgajG2+8UWvWrNFrr70mh8Ohc889V8uWLStGbQAA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\nuk51daGk30tXc2zx2Kqq3Vq0KKRLLplFgABsxDr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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def linreg_r2(X,Y, plot):\n", + " # Running the linear regression\n", + " Xc = sm.add_constant(X)\n", + " model = regression.linear_model.OLS(Y, Xc).fit()\n", + " params = model.params\n", + " Y_hat = np.dot(Xc,params)\n", + " \n", + " # Plot results\n", + " if plot:\n", + " plt.scatter(X, Y, alpha=0.3) # Plot the raw data\n", + " plt.plot(X, Y_hat, 'r', alpha=0.9); # Add the regression line, colored in red\n", + " return model.rsquared, Y_hat\n", + "\n", + "\n", + "dimensions = [data['Number Of Stories'],data['Total area'],data['Year Built']]\n", + "mlr = linreg_r2(np.column_stack(dimensions), data['log Price'],plot=False)\n", + "\n", + "print 'rsquared:', mlr[0]\n", + "\n", + "plt.plot(data['log Price'], data['log Price'], label='Y=X **not model**');\n", + "plt.scatter(data['log Price'], mlr[1], alpha=0.3);\n", + "plt.xlabel('log Price');\n", + "plt.ylabel('Predicted log Price');\n", + "plt.ylim(6.45, 7.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This model performed slightly better than the aggregated model explaining 18.8% vs. 18.5% of variation in `log Price`. For more information on regression models with more than one explanatory variable, refer to the [Quantopian Lecture on Multiple Linear Regression](https://www.quantopian.com/lectures/multiple-linear-regression).\n", + "\n", + "Despite our best efforts with the data we were given, the best model or combination of models we could generate only explained 18.8% of the variance in `log Price`. What this means is that the dimensions we were given (`Number Of Stories`, `Total area`, and `Year Built`) were not enough to give us a good understanding of what drives multifamily development prices. While dissapointing, this makes perfect sense as none of our models included important dimensions such as:\n", + "\n", + "* Location desireability\n", + "* Lot size\n", + "* Number of family units\n", + "* Occupancy rate\n", + "* ...and probably many more\n", + "\n", + "Furthermore, oftentimes datasets do not have obvious principal dimensions. In this situation you must develop a set of many possible influencers and whittle it down to only the most significant ones through [dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction). " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file From 65d3b11b6d3f9debc3305f5a031e69c0c4ecdd30 Mon Sep 17 00:00:00 2001 From: Christopher Fenaroli Date: Tue, 25 Jul 2017 15:31:06 -0400 Subject: [PATCH 2/4] Model Ensembling Lecture Draft 2. --- .../lectures/Model_Ensembling/notebook.ipynb | 642 + .../lectures/Model_Ensembling/preview.html | 16417 ++++++++++++++++ 2 files changed, 17059 insertions(+) create mode 100644 notebooks/lectures/Model_Ensembling/notebook.ipynb create mode 100644 notebooks/lectures/Model_Ensembling/preview.html diff --git a/notebooks/lectures/Model_Ensembling/notebook.ipynb b/notebooks/lectures/Model_Ensembling/notebook.ipynb new file mode 100644 index 00000000..7fc822d3 --- /dev/null +++ b/notebooks/lectures/Model_Ensembling/notebook.ipynb @@ -0,0 +1,642 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#Model Ensembling\n", + "By Chris Fenaroli, Delaney Granizo-Mackenzie, and Max Margenot \n", + "\n", + "Part of the Quantopian Lecture Series:\n", + "\n", + "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n", + "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n", + "\n", + "Notebook released under the Creative Commons Attribution 4.0 License.\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## What is Model Ensembling?\n", + "\n", + "Model ensembling is the name for a variety of methods which combine information from many *independent* prediction models to obtain results with more predictive power than any of its components alone. The logic which an ensemble uses to combine them into a final prediction can in some techniques be very complicated, but the benefits of ensembling can be taken advantage of with a method as simple as an equally weighted average of independent predictions.\n", + "\n", + "Ensembling plays a vital role in developing accurate predictive models and even employing basic ensembling techniques can in many cases drastically improve predictive performance. " + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib as mpl\n", + "import matplotlib.cm as cm\n", + "import scipy.stats as stats\n", + "import scipy.linalg as linalg\n", + "from statsmodels import regression\n", + "import statsmodels.api as sm" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Why Combine Models?\n", + "\n", + "A common approach to model selection is a \"winner takes all\" process where the best single model is chosen to make predictions. While intuitive and more interpretable than an ensemble, selecting only a single model to base predictions upon has weaknesses as follows:\n", + "\n", + "* Diversifying your prediction through ensembling reduces variance of predictions\n", + "* Should a model begin failing, a large ensemble prevents it from greatly affecting predictions while a single-model approach would be ruined\n", + "* Helps prevent overfitting by not assigning any single approach a significant amount of weight \n", + "\n", + "### Caveats\n", + "\n", + "Important to note is that the benefits of model ensembling will only be seen if the models being combined are at least somewhat independent. Aggregating many very similar models will have a much smaller benefit than aggregating ones with very distinct insights.\n", + "\n", + "Let's define two $I.I.D.$ (independent and identically distributed) standard normal toy models `m_1` and `m_2`, and see what happens to their mean and standard deviation when we average their predictions over 1000 simulations." + ] + }, + { + "cell_type": "code", + "execution_count": 107, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "---- Mean ---- ---- Variance ---- \n", + "Model 1: 0.036 Model 1: 1.02 \n", + "Model 2: 0.045 Model 2: 0.946 \n", + "Combined: 0.041 Combined: 0.486 \n", + "\n", + "Covariance between models: -0.0109611639748\n" + ] + }, + { + "data": { + "image/png": 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55Zd12mmnNdsuHA7LMAw5jhM3O1v9vtPT0xsN/N+xY0ez+2srrsAAAADgoFBe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\ntfnXlUtGpWO8Wy73rY1ZDQvF+RnL6inKd8JQMgyZyaTK588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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Model parameters\n", + "mu = 0\n", + "sigma = 1\n", + "\n", + "# Create two identical models\n", + "m_1 = np.random.normal(mu,sigma,1000)\n", + "m_2 = np.random.normal(mu,sigma,1000)\n", + "\n", + "# Combine them\n", + "m_cm = (m_1 + m_2)/2\n", + "\n", + "# Plot their distribution over 1000 trials\n", + "plt.hist(m_1, bins=50, alpha=0.2);\n", + "plt.hist(m_2, bins=50, alpha=0.2);\n", + "plt.hist(m_cm, bins=50, alpha=0.6);\n", + "plt.legend(['Model 1', 'Model 2', 'Combined Model'])\n", + "plt.title('Histogram of Model Outputs over 1000 Trials')\n", + "\n", + "print \"%-39s %-24s\" % ('---- Mean ----', '---- Variance ----')\n", + "print \"%-15s %-24s %-15s %-15s\" % ('Model 1:', \n", + " np.round(np.mean(m_1),decimals=3), \n", + " 'Model 1:', \n", + " np.round(np.std(m_1)**2,decimals=3))\n", + "print \"%-15s %-24s %-15s %-15s\" % ('Model 2:', \n", + " np.round(np.mean(m_2),decimals=3), \n", + " 'Model 2:', \n", + " np.round(np.std(m_2)**2,decimals=3))\n", + "print \"%-15s %-24s %-15s %-15s\" % ('Combined:', \n", + " np.round(np.mean(m_cm),decimals=3),\n", + " 'Combined:',\n", + " np.round(np.std(m_cm)**2,decimals=3))\n", + "print \"\\nCovariance between models:\", np.cov(m_1, m_2)[1][0]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Benefits of Ensembling: Symbolic Intuition\n", + "\n", + "When the $I.I.D.$ models are aggregated, the mean stays the same while the variance of results decreases. Can this be explained symbolically? \n", + "\n", + "Consider two models with the same mean $m$, the same variance $v$, and zero covariance:\n", + "\n", + "$$ models = \\hat{\\theta_1} \\: , \\: \\hat{\\theta_2}$$\n", + "\n", + "$$E[\\hat{\\theta_1}]=E[\\hat{\\theta_2}]=m \\:\\:\\:\\:\\:\\:\\:\\: Var[\\hat{\\theta_1}] = Var[\\hat{\\theta_2}] = v \\:\\:\\:\\:\\:\\:\\:\\: Cov[\\hat{\\theta_2},\\hat{\\theta_2}] = 0$$\n", + "\n", + "When averaged they form a combined model $\\hat{\\theta_{cm}}$: \n", + "\n", + "$$\\hat{\\theta_{cm}} = \\frac{\\hat{\\theta_1} + \\hat{\\theta_2}}{2}$$ \n", + "\n", + "$$E[\\hat{\\theta_{cm}}] = \\frac{E[\\hat{\\theta_1}]+E[\\hat{\\theta_2}]}{2} = m$$\n", + "\n", + "$$Var[\\hat{\\theta_{cm}}] = \\frac{Var[\\hat{\\theta_{1}}]+Var[\\hat{\\theta_{2}}]+2Cov[\\hat{\\theta_{1}},\\hat{\\theta_{2}}]}{4} = \\frac{v}{2}$$\n", + "\n", + "*Where the combined model keeps the same mean $m$ as its components but sees a reduction in variance.*\n", + "\n", + "### Importance of Model Independence\n", + "\n", + "Should the models being aggregated have a correlation of 1 (equivalent to a covariance of $v$), the variability-reducing effect no longer applies. Instead, the $2Cov[\\hat{\\theta_{1}},\\hat{\\theta_{2}}]$ term becomes equal to $2v$ in turn making variance equal to it's original value $v$. The significance of this is that the magnitude of the variance remains unchanged should the models being combined be perfectly correlated, illustrating the importance of the models being uncorrelated.\n", + "\n", + "### Averaging $n$ Models\n", + "\n", + "Now let's look at a combined model $\\hat{\\theta_{cm}}$ that is the average of $n$ $I.I.D$ models.\n", + "\n", + "$$\\hat{\\theta_{cm}} = \\frac{\\sum_{i=1}^{n}{\\hat{\\theta_i}}}{n}$$\n", + "\n", + "$$Var[\\hat{\\theta_{cm}}] = \\frac{\\sum_{i=1}^{n}{Var[\\hat{\\theta_i}}] + 2\\sum_{1 \\le i" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Number of identical models\n", + "n = 100\n", + "\n", + "# Initizalize n models\n", + "models = np.array([np.random.normal(mu,sigma,1000) for _ in range(n)])\n", + "\n", + "combined_models = [np.mean(models[0:i+1], axis=0) for i in range(n)]\n", + "means = np.mean(combined_models,axis=1)\n", + "stds = np.std(combined_models,axis=1)\n", + "\n", + "plt.plot(means);\n", + "plt.plot(stds);\n", + "plt.plot(range(n), 1/np.linspace(1,n+1,n), linestyle = '--')\n", + "plt.legend(['Model Avg Mean', 'Model Avg STD', 'Perfect U']);\n", + "plt.xlabel('Number of Models Combined');\n", + "plt.title('Mean and STD vs. Number of Models Combined');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As more models are added the mean predicted value is stationary and the prediction variability decreases geometrically. Worth noting, however, is that in this simulation the standard deviation did not decrease at the rate perfectly uncorrelated models would. This is a result of the toy models we used having some level of covariance, purely by random chance.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Benefits of Ensembling: Dimension Intuition\n", + "\n", + "The theory and simulation above demonstrate the benefits of simply averaging uncorrelated models; in both cases, as more models are averaged the mean stays the same but variance decreases. Model combination gets its power from the diversity of uncorrelated models ensuring that different features of the problem are represented. But what are these \"features\" that data apparently has? And how do combinations of diverse models help reveal them?\n", + "\n", + "An interesting analogy is to think of a model as a specific \"view\" of the world, having its own perspective and unique insights into the problem at hand. Data can have many \"dimensions\" and rarely will one model encapture every single one; only by approaching it from many views can we understand its structure.\n", + "\n", + "Consider a 3-dimensional object, such as a cylinder. To fully understand what this object is we require multiple perspectives from distinct viewpoints, as from each viewpoint alone you only see a 2-d projection of the space the cylinder takes up. To illustrate the limitations of attempting to understand a multi-dimensional structure from a single view, imagine looking at a cylinder from a specific viewpoint to the side and trying to decipher what it could be:" + ] + }, + { + "cell_type": "code", + "execution_count": 102, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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AAKCaqLKBVFBQEJtvvnm+xwAAAKqRmvkeYH0qKSnJ9wjVnjWoGqxDfi1atCgi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\nAJAIJAAAgOT/A7BsFUyIEMnLAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.fill_between([-1,0,1], -2, 2, facecolor='blue', alpha = 0.4);\n", + "plt.xlim(-4,4);\n", + "plt.ylim(-3,3);\n", + "plt.xlabel(\"X\", fontsize=20);\n", + "plt.ylabel(\"Z\", fontsize=20);\n", + "plt.title('View of Object from the Side', fontsize=20);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From this perspective alone we have no information on the object's presence in the $Y$ dimension; our only conclusion can be that the 3-d object is constrained in the $X$ and $Z$ dimensions by the rectangle defined by [-1,1] and [-2,2] respectively. \n", + "\n", + "Beyond that, we can not tell if the shape is a prism, cylinder, or any number of possible objects that fit those constraints. The \"variability\" of our understanding is high, and can only be diminished by supplementing our current perspective with an additional \"view.\" \n", + "\n", + "Let's add another view by looking at the same object, this time from above instead of from the side:" + ] + }, + { + "cell_type": "code", + "execution_count": 103, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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miIi9SkkxlZpqKCOjvaKjo+yOCgA4RyFbkAAALZff79f27YXavdunggKpujq5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\nwDBN07QzwKJFi7R48WIZhiHTNGUYhu6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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X = np.linspace(-1,1,50)\n", + "plt.fill_between(X, -np.sqrt(1-X**2), np.sqrt(1-X**2), facecolor='blue', alpha = 0.4);\n", + "plt.xlim(-4,4);\n", + "plt.ylim(-2.5,2.5);\n", + "plt.xlabel(\"X\", fontsize=20);\n", + "plt.ylabel(\"Y\", fontsize=20);\n", + "plt.title('View of Object from Above', fontsize=20);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After adding this second view we can be positive that the shape, if not a cylinder, is restricted to the space of\n", + "a cylinder with a unit circle base an height ranging from [-2,2].\n", + "\n", + "Individually, neither of these perspectives would provide a particularly enlightening idea of the shape being looked at. With the first view, we had no information on the object in the $Y$ dimension, and in the second view we gained no information on the $Z$ dimension. When combined, however, we can make conclusions based on all three dimensions and the size of the set of possible shapes is drastically reduced. \n", + "\n", + "This is the idea behind model ensembling; the aggregation of multiple perspectives yields a more complete view than any of them alone.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Multifamily Real Estate Example\n", + "\n", + "Let's bring this analogy of uncorrelated models providing \"perspectives\" to one involving data. Where the cylinder above was a function of space in the $X$,$Y$, and $Z$ dimenseions, let's consider house pricing data, with possible explanatory dimensions `Number Of Stories`, `Total area`, and `Year Built`. \n", + "\n", + "The data was aggregated by user 'dmikebishop' on [DataWorld](https://data.world/dmikebishop/commercial-real-estate-for-sal). To use exterior data, store it as a CSV in the `data` folder in research and use the `local_csv` function to pull it into a Pandas DataFrame." + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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TU15dcHCwwsPDm72f7OzsFunHmdr6GNv6+CTG2BY0d7HHJXMAAFymT58+ysjI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\nD+mWW25RYmKiZsyYofT0dOXl5WnOnDmOzgt0q62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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Pulling in DataFrame and dropping blank values\n", + "fields = ['Price', 'Number Of Stories', 'Total area', 'Type', 'Year Built']\n", + "data = local_csv('loopnetlistingswithbrokers (3).csv')[fields]\n", + "data = data[data != ' '].dropna()\n", + "\n", + "# Formatting values from strings with thousands separators into integers\n", + "data['Total area'] = data['Total area'].str.replace(' SF', '').str.replace(',','')\n", + "data['Price'] = data['Price'].str.replace(',','').str.replace('$', '')\n", + "data = data[[i.isdigit() for i in data['Price']]]\n", + "for i in [0,1,2,4]:\n", + " data[fields[i]] = data[fields[i]].astype(int)\n", + "\n", + "# Restricting the real estate to only multifamily properties\n", + "data = data[data['Type'] == 'Multifamily']\n", + "\n", + "# Using log price transforms the price distribution to a more normal one\n", + "# Normally distributed independent variables are a linear regression assumption\n", + "data['log Price'] = np.log10(data['Price'])\n", + "\n", + "data.ix[:, data.columns != 'Price'].hist(bins=10);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's begin by attempting to model `log Price` using only `Year Built` as our explanatory variable. We'll also define a linear regression plotting function to make this step simpler as we repeat it for the other data dimensions.\n", + "\n", + "A OLS fitted simple linear regression returns a single set of coefficients that minimizes the sum of squared residuals within the training set. This model is simply an estimate. It will usually have bias (difference betwen model expected value and true value) and variance (sensitivity to small changes in the training set). As we add more models, we should see the aggregate model have a higher $R^2$ as the model leaves less and less variance in `log Price` unexplained." + ] + }, + { + "cell_type": "code", + "execution_count": 106, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rsquared 0.0190269927541\n" + ] + }, + { + "data": { + "image/png": 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XD530/PPSVVcVvaxOKMXwT6CB3UrrlwBAQRh+4AyrLgBqplFh1VlnM420hgaf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\nATOcHlYHwFn8MgAAXMWOEOOFngI4j94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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def linreg_r2(X,Y, plot):\n", + " # Running the linear regression\n", + " Xc = sm.add_constant(X)\n", + " model = regression.linear_model.OLS(Y, Xc).fit()\n", + " params = model.params\n", + " Y_hat = np.dot(Xc,params)\n", + " \n", + " # Plot results\n", + " if plot:\n", + " plt.scatter(X, Y, alpha=0.3) # Plot the raw data\n", + " plt.plot(X, Y_hat, 'r', alpha=0.9); # Add the regression line, colored in red\n", + " return model.rsquared, Y_hat\n", + "\n", + "print 'rsquared', linreg_r2(data['Year Built'], data['log Price'],plot=True)[0]\n", + "plt.xlabel('Year Built');\n", + "plt.ylabel('log Price');" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using only `Year Built` in our model explained only 1.9% of the variation on `log Price`. Using only one dimension to try and understand a multi-dimensional dataset is equivalent to trying to categorize a 3-d object as a cylinder by only approaching it from a single perspective. It cannot be done. In this model alone we ignore many features of the data and it can be improved by adding another dimension or 'view'.\n", + "\n", + "Let's see what `log Price` looks like from the perspective of `Number Of Stories`:" + ] + }, + { + "cell_type": "code", + "execution_count": 145, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rsquared 0.0561128798813\n" + ] + }, + { + "data": { + "image/png": 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SDJk2rUTr1m1WPO5XZWVUixdb/5yKsrJBvflmWLt29WtoKKz5862+1TXOyS9+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\nrkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print 'rsquared', linreg_r2(data['Number Of Stories'], data['log Price'], plot=True)[0]\n", + "plt.xlabel('Number Of Stories');\n", + "plt.ylabel('log Price');\n", + "plt.xlim(0,15);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Number Of Stories` explains about 5.6% of the variation in `log Price`. While better than `Year Built`, it still provides a mostly incomplete understanding. Let's take a look at the final dimension, `Total area`:" + ] + }, + { + "cell_type": "code", + "execution_count": 146, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rsquared 0.168804441783\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print 'rsquared', linreg_r2(data['Total area'], data['log Price'], plot=True)[0]\n", + "plt.xlabel('Total area');\n", + "plt.ylabel('log Price');\n", + "plt.xlim(0,200000);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`Total area` was the most insightful dimension, with its model explaining 16.8% of variance. Still, however, this is not a great result and we are still attempting to understand a complex, multidimensional dataset from a single perspective. Let's see if averaging the models, combining information from all 3 dimensions, can produce a more accurate model. \n", + "\n", + "*Note: In the below plot, the blue line is not the model but the line $Y=X$. Points along this line mean the combined model perfectly predicted the observed `log Price`.*" + ] + }, + { + "cell_type": "code", + "execution_count": 147, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rsquared: 0.185624465575\n" + ] + }, + { + "data": { + "image/png": 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w+6gGYLSSEpOWLGnQihV1WrKkgaGWOSxmMDp06JCuv/56mUz+g/ypT31KLpcr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\nHA5167jtfGGBNh1/Z8fz3iYnx6u0tEp//vmXJk8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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "combined = (linreg_r2(data['Total area'], data['log Price'],plot=False)[1]\n", + " + linreg_r2(data['Number Of Stories'], data['log Price'],plot=False)[1]\n", + " + linreg_r2(data['Year Built'], data['log Price'],plot=False)[1])/3\n", + "\n", + "plt.scatter(data['log Price'],combined, alpha = 0.3);\n", + "plt.plot(data['log Price'],data['log Price'], label='Y=X **not model**')\n", + "plt.ylim(6.5,7.5);\n", + "plt.xlabel('log Price');\n", + "plt.ylabel('Predicted log Price');\n", + "plt.legend();\n", + "\n", + "print 'rsquared:', np.corrcoef(combined,data['log Price'])[0][1]**2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By taking a simple equally weighted average of all the models we saw $R^2$ increase to 18.6%. While still indicative of a poorly fit model, the result is still interesting considering the $R^2$ values of the individual single-dimension models were 1.9%, 5.6%, and 16.9% respectively. The $R^2$ of the combined model was higher than any of the single models alone.\n", + "\n", + "Simply averaging the model outputs ignores some of the interplay between variables which can be better captured by using a multiple linear regression. Let's run a single multiple linear regression model on the pricing data:" + ] + }, + { + "cell_type": "code", + "execution_count": 181, + "metadata": { + "collapsed": false, + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "rsquared: 0.188016012536\n" + ] + }, + { + "data": { + "image/png": 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+bVS3SCruxBHZMPJ6LcAOMgajG2+8UWvWrNFrr70mh8Ohc889V8uWLStGbQAA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\nIzECAAAAEPNIjAAAAADEvP8HkhYyyfgweLkAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "dimensions = [data['Number Of Stories'],data['Total area'],data['Year Built']]\n", + "mlr = linreg_r2(np.column_stack(dimensions), data['log Price'],plot=False)\n", + "\n", + "print 'rsquared:', mlr[0]\n", + "\n", + "plt.plot(data['log Price'], data['log Price'], label='Y=X **not model**');\n", + "plt.scatter(data['log Price'], mlr[1], alpha=0.3);\n", + "plt.xlabel('log Price');\n", + "plt.ylabel('Predicted log Price');\n", + "plt.ylim(6.45, 7.5);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This model performed slightly better than the aggregated model explaining 18.8% vs. 18.5% of variation in `log Price`. For more information on regression models with more than one explanatory variable, refer to the [Quantopian Lecture on Multiple Linear Regression](https://www.quantopian.com/lectures/multiple-linear-regression).\n", + "\n", + "Despite our best efforts with the data we were given, the best model or combination of models we could generate only explained 18.8% of the variance in `log Price`. What this means is that the dimensions we were given (`Number Of Stories`, `Total area`, and `Year Built`) were not enough to give us a good understanding of what drives multifamily development prices. While dissapointing, this makes perfect sense as none of our models included important dimensions such as:\n", + "\n", + "* Location desireability\n", + "* Lot size\n", + "* Number of family units\n", + "* Occupancy rate\n", + "* ...and probably many more\n", + "\n", + "Furthermore, oftentimes datasets do not have obvious principal dimensions. In this situation you must develop a set of many possible influencers and whittle it down to only the most significant ones through [dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction). " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.12" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/notebooks/lectures/Model_Ensembling/preview.html b/notebooks/lectures/Model_Ensembling/preview.html new file mode 100644 index 00000000..40e11fb2 --- /dev/null +++ b/notebooks/lectures/Model_Ensembling/preview.html @@ -0,0 +1,16417 @@ + + + Model Ensembling Lecture + + + + + + + + + + + + + + + + +
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Model Ensembling¶

By Chris Fenaroli, Delaney Granizo-Mackenzie, and Max Margenot

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Part of the Quantopian Lecture Series:

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Notebook released under the Creative Commons Attribution 4.0 License.

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What is Model Ensembling?¶

Model ensembling is the name for a variety of methods which combine information from many independent prediction models to obtain results with more predictive power than any of its components alone. The logic which an ensemble uses to combine them into a final prediction can in some techniques be very complicated, but the benefits of ensembling can be taken advantage of with a method as simple as an equally weighted average of independent predictions.

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Ensembling plays a vital role in developing accurate predictive models and even employing basic ensembling techniques can in many cases drastically improve predictive performance.

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In [99]:
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import pandas as pd
+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib as mpl
+import matplotlib.cm as cm
+import scipy.stats as stats
+import scipy.linalg as linalg
+from statsmodels import regression
+import statsmodels.api as sm
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Why Combine Models?¶

A common approach to model selection is a "winner takes all" process where the best single model is chosen to make predictions. While intuitive and more interpretable than an ensemble, selecting only a single model to base predictions upon has weaknesses as follows:

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  • Diversifying your prediction through ensembling reduces variance of predictions
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  • Should a model begin failing, a large ensemble prevents it from greatly affecting predictions while a single-model approach would be ruined
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  • Helps prevent overfitting by not assigning any single approach a significant amount of weight
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+

Caveats¶

Important to note is that the benefits of model ensembling will only be seen if the models being combined are at least somewhat independent. Aggregating many very similar models will have a much smaller benefit than aggregating ones with very distinct insights.

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Let's define two $I.I.D.$ (independent and identically distributed) standard normal toy models m_1 and m_2, and see what happens to their mean and standard deviation when we average their predictions over 1000 simulations.

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In [107]:
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# Model parameters
+mu = 0
+sigma = 1
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+# Create two identical models
+m_1 = np.random.normal(mu,sigma,1000)
+m_2 = np.random.normal(mu,sigma,1000)
+
+# Combine them
+m_cm = (m_1 + m_2)/2
+
+# Plot their distribution over 1000 trials
+plt.hist(m_1, bins=50, alpha=0.2);
+plt.hist(m_2, bins=50, alpha=0.2);
+plt.hist(m_cm, bins=50, alpha=0.6);
+plt.legend(['Model 1', 'Model 2', 'Combined Model'])
+plt.title('Histogram of Model Outputs over 1000 Trials')
+
+print "%-39s %-24s" % ('---- Mean ----', '---- Variance ----')
+print "%-15s %-24s %-15s %-15s" % ('Model 1:', 
+                                   np.round(np.mean(m_1),decimals=3), 
+                                   'Model 1:', 
+                                   np.round(np.std(m_1)**2,decimals=3))
+print "%-15s %-24s %-15s %-15s" % ('Model 2:', 
+                                   np.round(np.mean(m_2),decimals=3), 
+                                   'Model 2:', 
+                                   np.round(np.std(m_2)**2,decimals=3))
+print "%-15s %-24s %-15s %-15s" % ('Combined:', 
+                                   np.round(np.mean(m_cm),decimals=3),
+                                   'Combined:',
+                                   np.round(np.std(m_cm)**2,decimals=3))
+print "\nCovariance between models:", np.cov(m_1, m_2)[1][0]
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---- Mean ----                          ---- Variance ----      
+Model 1:        0.036                    Model 1:        1.02           
+Model 2:        0.045                    Model 2:        0.946          
+Combined:       0.041                    Combined:       0.486          
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+Covariance between models: -0.0109611639748
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Benefits of Ensembling: Symbolic Intuition¶

When the $I.I.D.$ models are aggregated, the mean stays the same while the variance of results decreases. Can this be explained symbolically?

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Consider two models with the same mean $m$, the same variance $v$, and zero covariance:

+$$ models = \hat{\theta_1} \: , \: \hat{\theta_2}$$$$E[\hat{\theta_1}]=E[\hat{\theta_2}]=m \:\:\:\:\:\:\:\: Var[\hat{\theta_1}] = Var[\hat{\theta_2}] = v \:\:\:\:\:\:\:\: Cov[\hat{\theta_2},\hat{\theta_2}] = 0$$

When averaged they form a combined model $\hat{\theta_{cm}}$:

+$$\hat{\theta_{cm}} = \frac{\hat{\theta_1} + \hat{\theta_2}}{2}$$

+$$E[\hat{\theta_{cm}}] = \frac{E[\hat{\theta_1}]+E[\hat{\theta_2}]}{2} = m$$$$Var[\hat{\theta_{cm}}] = \frac{Var[\hat{\theta_{1}}]+Var[\hat{\theta_{2}}]+2Cov[\hat{\theta_{1}},\hat{\theta_{2}}]}{4} = \frac{v}{2}$$

Where the combined model keeps the same mean $m$ as its components but sees a reduction in variance.

+

Importance of Model Independence¶

Should the models being aggregated have a correlation of 1 (equivalent to a covariance of $v$), the variability-reducing effect no longer applies. Instead, the $2Cov[\hat{\theta_{1}},\hat{\theta_{2}}]$ term becomes equal to $2v$ in turn making variance equal to it's original value $v$. The significance of this is that the magnitude of the variance remains unchanged should the models being combined be perfectly correlated, illustrating the importance of the models being uncorrelated.

+

Averaging $n$ Models¶

Now let's look at a combined model $\hat{\theta_{cm}}$ that is the average of $n$ $I.I.D$ models.

+$$\hat{\theta_{cm}} = \frac{\sum_{i=1}^{n}{\hat{\theta_i}}}{n}$$$$Var[\hat{\theta_{cm}}] = \frac{\sum_{i=1}^{n}{Var[\hat{\theta_i}}] + 2\sum_{1 \le i<j \le n}^{n}{Cov[\hat{\theta_i},\hat{\theta_j}]}}{n^2} = \frac{nv}{n^2} = \frac{v}{n}$$

This shows how if the models are perfectly uncorrelated, the ensemble's variance will decrease geometrically. Let's go back to our simulation and increase the number of models being combined:

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In [101]:
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# Number of identical models
+n = 100
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+# Initizalize n models
+models = np.array([np.random.normal(mu,sigma,1000) for _ in range(n)])
+
+combined_models = [np.mean(models[0:i+1], axis=0) for i in range(n)]
+means = np.mean(combined_models,axis=1)
+stds = np.std(combined_models,axis=1)
+
+plt.plot(means);
+plt.plot(stds);
+plt.plot(range(n), 1/np.linspace(1,n+1,n), linestyle = '--')
+plt.legend(['Model Avg Mean', 'Model Avg STD', 'Perfect U']);
+plt.xlabel('Number of Models Combined');
+plt.title('Mean and STD vs. Number of Models Combined');
+
+ +
+
+
+ +
+
+ + +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+

As more models are added the mean predicted value is stationary and the prediction variability decreases geometrically. Worth noting, however, is that in this simulation the standard deviation did not decrease at the rate perfectly uncorrelated models would. This is a result of the toy models we used having some level of covariance, purely by random chance.

+ +
+
+
+
+
+
+
+

Benefits of Ensembling: Dimension Intuition¶

The theory and simulation above demonstrate the benefits of simply averaging uncorrelated models; in both cases, as more models are averaged the mean stays the same but variance decreases. Model combination gets its power from the diversity of uncorrelated models ensuring that different features of the problem are represented. But what are these "features" that data apparently has? And how do combinations of diverse models help reveal them?

+

An interesting analogy is to think of a model as a specific "view" of the world, having its own perspective and unique insights into the problem at hand. Data can have many "dimensions" and rarely will one model encapture every single one; only by approaching it from many views can we understand its structure.

+

Consider a 3-dimensional object, such as a cylinder. To fully understand what this object is we require multiple perspectives from distinct viewpoints, as from each viewpoint alone you only see a 2-d projection of the space the cylinder takes up. To illustrate the limitations of attempting to understand a multi-dimensional structure from a single view, imagine looking at a cylinder from a specific viewpoint to the side and trying to decipher what it could be:

+ +
+
+
+
+
+
In [102]:
+
+
+
plt.fill_between([-1,0,1], -2, 2, facecolor='blue', alpha = 0.4);
+plt.xlim(-4,4);
+plt.ylim(-3,3);
+plt.xlabel("X", fontsize=20);
+plt.ylabel("Z", fontsize=20);
+plt.title('View of Object from the Side', fontsize=20);
+
+ +
+
+
+ +
+
+ + +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+

From this perspective alone we have no information on the object's presence in the $Y$ dimension; our only conclusion can be that the 3-d object is constrained in the $X$ and $Z$ dimensions by the rectangle defined by [-1,1] and [-2,2] respectively.

+

Beyond that, we can not tell if the shape is a prism, cylinder, or any number of possible objects that fit those constraints. The "variability" of our understanding is high, and can only be diminished by supplementing our current perspective with an additional "view."

+

Let's add another view by looking at the same object, this time from above instead of from the side:

+ +
+
+
+
+
+
In [103]:
+
+
+
X = np.linspace(-1,1,50)
+plt.fill_between(X, -np.sqrt(1-X**2), np.sqrt(1-X**2), facecolor='blue', alpha = 0.4);
+plt.xlim(-4,4);
+plt.ylim(-2.5,2.5);
+plt.xlabel("X", fontsize=20);
+plt.ylabel("Y", fontsize=20);
+plt.title('View of Object from Above', fontsize=20);
+
+ +
+
+
+ +
+
+ + +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+

After adding this second view we can be positive that the shape, if not a cylinder, is restricted to the space of +a cylinder with a unit circle base an height ranging from [-2,2].

+

Individually, neither of these perspectives would provide a particularly enlightening idea of the shape being looked at. With the first view, we had no information on the object in the $Y$ dimension, and in the second view we gained no information on the $Z$ dimension. When combined, however, we can make conclusions based on all three dimensions and the size of the set of possible shapes is drastically reduced.

+

This is the idea behind model ensembling; the aggregation of multiple perspectives yields a more complete view than any of them alone.

+ +
+
+
+
+
+
+
+

Multifamily Real Estate Example¶

Let's bring this analogy of uncorrelated models providing "perspectives" to one involving data. Where the cylinder above was a function of space in the $X$,$Y$, and $Z$ dimenseions, let's consider house pricing data, with possible explanatory dimensions Number Of Stories, Total area, and Year Built.

+

The data was aggregated by user 'dmikebishop' on DataWorld. To use exterior data, store it as a CSV in the data folder in research and use the local_csv function to pull it into a Pandas DataFrame.

+ +
+
+
+
+
+
In [105]:
+
+
+
# Pulling in DataFrame and dropping blank values
+fields = ['Price', 'Number Of Stories', 'Total area', 'Type', 'Year Built']
+data = local_csv('loopnetlistingswithbrokers (3).csv')[fields]
+data = data[data != ' '].dropna()
+
+# Formatting values from strings with thousands separators into integers
+data['Total area'] = data['Total area'].str.replace(' SF', '').str.replace(',','')
+data['Price'] = data['Price'].str.replace(',','').str.replace('$', '')
+data = data[[i.isdigit() for i in data['Price']]]
+for i in [0,1,2,4]:
+    data[fields[i]] = data[fields[i]].astype(int)
+
+# Restricting the real estate to only multifamily properties
+data = data[data['Type'] == 'Multifamily']
+
+# Using log price transforms the price distribution to a more normal one
+# Normally distributed independent variables are a linear regression assumption
+data['log Price'] = np.log10(data['Price'])
+
+data.ix[:, data.columns != 'Price'].hist(bins=10);
+
+ +
+
+
+ +
+
+ + +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+

Let's begin by attempting to model log Price using only Year Built as our explanatory variable. We'll also define a linear regression plotting function to make this step simpler as we repeat it for the other data dimensions.

+

A OLS fitted simple linear regression returns a single set of coefficients that minimizes the sum of squared residuals within the training set. This model is simply an estimate. It will usually have bias (difference betwen model expected value and true value) and variance (sensitivity to small changes in the training set). As we add more models, we should see the aggregate model have a higher $R^2$ as the model leaves less and less variance in log Price unexplained.

+ +
+
+
+
+
+
In [106]:
+
+
+
def linreg_r2(X,Y, plot):
+    # Running the linear regression
+    Xc = sm.add_constant(X)
+    model = regression.linear_model.OLS(Y, Xc).fit()
+    params = model.params
+    Y_hat = np.dot(Xc,params)
+    
+    # Plot results
+    if plot:
+        plt.scatter(X, Y, alpha=0.3) # Plot the raw data
+        plt.plot(X, Y_hat, 'r', alpha=0.9);  # Add the regression line, colored in red
+    return model.rsquared, Y_hat
+
+print 'rsquared', linreg_r2(data['Year Built'], data['log Price'],plot=True)[0]
+plt.xlabel('Year Built');
+plt.ylabel('log Price');
+
+ +
+
+
+ +
+
+ + +
+ +
+ + +
+
rsquared 0.0190269927541
+
+
+
+ +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+

Using only Year Built in our model explained only 1.9% of the variation on log Price. Using only one dimension to try and understand a multi-dimensional dataset is equivalent to trying to categorize a 3-d object as a cylinder by only approaching it from a single perspective. It cannot be done. In this model alone we ignore many features of the data and it can be improved by adding another dimension or 'view'.

+

Let's see what log Price looks like from the perspective of Number Of Stories:

+ +
+
+
+
+
+
In [145]:
+
+
+
print 'rsquared', linreg_r2(data['Number Of Stories'], data['log Price'], plot=True)[0]
+plt.xlabel('Number Of Stories');
+plt.ylabel('log Price');
+plt.xlim(0,15);
+
+ +
+
+
+ +
+
+ + +
+ +
+ + +
+
rsquared 0.0561128798813
+
+
+
+ +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+

Number Of Stories explains about 5.6% of the variation in log Price. While better than Year Built, it still provides a mostly incomplete understanding. Let's take a look at the final dimension, Total area:

+ +
+
+
+
+
+
In [146]:
+
+
+
print 'rsquared', linreg_r2(data['Total area'], data['log Price'], plot=True)[0]
+plt.xlabel('Total area');
+plt.ylabel('log Price');
+plt.xlim(0,200000);
+
+ +
+
+
+ +
+
+ + +
+ +
+ + +
+
rsquared 0.168804441783
+
+
+
+ +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+

Total area was the most insightful dimension, with its model explaining 16.8% of variance. Still, however, this is not a great result and we are still attempting to understand a complex, multidimensional dataset from a single perspective. Let's see if averaging the models, combining information from all 3 dimensions, can produce a more accurate model.

+

Note: In the below plot, the blue line is not the model but the line $Y=X$. Points along this line mean the combined model perfectly predicted the observed log Price.

+ +
+
+
+
+
+
In [147]:
+
+
+
combined = (linreg_r2(data['Total area'], data['log Price'],plot=False)[1]
+            + linreg_r2(data['Number Of Stories'], data['log Price'],plot=False)[1]
+            + linreg_r2(data['Year Built'], data['log Price'],plot=False)[1])/3
+
+plt.scatter(data['log Price'],combined, alpha = 0.3);
+plt.plot(data['log Price'],data['log Price'], label='Y=X **not model**')
+plt.ylim(6.5,7.5);
+plt.xlabel('log Price');
+plt.ylabel('Predicted log Price');
+plt.legend();
+
+print 'rsquared:', np.corrcoef(combined,data['log Price'])[0][1]**2
+
+ +
+
+
+ +
+
+ + +
+ +
+ + +
+
rsquared: 0.185624465575
+
+
+
+ +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+

By taking a simple equally weighted average of all the models we saw $R^2$ increase to 18.6%. While still indicative of a poorly fit model, the result is still interesting considering the $R^2$ values of the individual single-dimension models were 1.9%, 5.6%, and 16.9% respectively. The $R^2$ of the combined model was higher than any of the single models alone.

+

Simply averaging the model outputs ignores some of the interplay between variables which can be better captured by using a multiple linear regression. Let's run a single multiple linear regression model on the pricing data:

+ +
+
+
+
+
+
In [181]:
+
+
+
dimensions = [data['Number Of Stories'],data['Total area'],data['Year Built']]
+mlr = linreg_r2(np.column_stack(dimensions), data['log Price'],plot=False)
+
+print 'rsquared:', mlr[0]
+
+plt.plot(data['log Price'], data['log Price'], label='Y=X **not model**');
+plt.scatter(data['log Price'], mlr[1], alpha=0.3);
+plt.xlabel('log Price');
+plt.ylabel('Predicted log Price');
+plt.ylim(6.45, 7.5);
+
+ +
+
+
+ +
+
+ + +
+ +
+ + +
+
rsquared: 0.188016012536
+
+
+
+ +
+ +
+ + + + +
+ +
+ +
+ +
+
+ +
+
+
+
+
+

This model performed slightly better than the aggregated model explaining 18.8% vs. 18.5% of variation in log Price. For more information on regression models with more than one explanatory variable, refer to the Quantopian Lecture on Multiple Linear Regression.

+

Despite our best efforts with the data we were given, the best model or combination of models we could generate only explained 18.8% of the variance in log Price. What this means is that the dimensions we were given (Number Of Stories, Total area, and Year Built) were not enough to give us a good understanding of what drives multifamily development prices. While dissapointing, this makes perfect sense as none of our models included important dimensions such as:

+
    +
  • Location desireability
    • +
  • Lot size
    • +
  • Number of family units
    • +
  • Occupancy rate
    • +
  • ...and probably many more
    • +
+

Furthermore, oftentimes datasets do not have obvious principal dimensions. In this situation you must develop a set of many possible influencers and whittle it down to only the most significant ones through dimensionality reduction.

+ +
+
+
+
+
+
+
+

This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. ("Quantopian"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.

+ +
+
+
+
+
+ From 016139bb893692d36af2dd02fe87645bddbac6ad Mon Sep 17 00:00:00 2001 From: Christopher Fenaroli Date: Tue, 1 Aug 2017 16:13:36 -0400 Subject: [PATCH 3/4] Updated model ensembling lecture. --- .../lectures/Model_Ensembling/notebook.ipynb | 349 +- .../lectures/Model_Ensembling/preview.html | 6501 ++++++++--------- 2 files changed, 3006 insertions(+), 3844 deletions(-) diff --git a/notebooks/lectures/Model_Ensembling/notebook.ipynb b/notebooks/lectures/Model_Ensembling/notebook.ipynb index 7fc822d3..0f3ede1f 100644 --- a/notebooks/lectures/Model_Ensembling/notebook.ipynb +++ b/notebooks/lectures/Model_Ensembling/notebook.ipynb @@ -23,14 +23,14 @@ "source": [ "## What is Model Ensembling?\n", "\n", - "Model ensembling is the name for a variety of methods which combine information from many *independent* prediction models to obtain results with more predictive power than any of its components alone. The logic which an ensemble uses to combine them into a final prediction can in some techniques be very complicated, but the benefits of ensembling can be taken advantage of with a method as simple as an equally weighted average of independent predictions.\n", + "Model ensembling is the name for a variety of methods which combine information from many *independent* prediction models to obtain results with more predictive power than any of its components alone. An model ensemble takes these component forecasts and uses some logic to combine them into a final prediction.\n", "\n", - "Ensembling plays a vital role in developing accurate predictive models and even employing basic ensembling techniques can in many cases drastically improve predictive performance. " + "Ensembling plays a vital role in developing accurate predictive models and even employing basic ensembling techniques can in many cases drastically improve predictive performance." ] }, { "cell_type": "code", - "execution_count": 99, + "execution_count": 36, "metadata": { "collapsed": false }, @@ -61,14 +61,14 @@ "\n", "### Caveats\n", "\n", - "Important to note is that the benefits of model ensembling will only be seen if the models being combined are at least somewhat independent. Aggregating many very similar models will have a much smaller benefit than aggregating ones with very distinct insights.\n", + "Important to note is that the benefits of model ensembling will only be seen if the models being combined are at least somewhat independent. Aggregating many very similar models will have a much smaller benefit than aggregating ones with distinct insights.\n", "\n", - "Let's define two $I.I.D.$ (independent and identically distributed) standard normal toy models `m_1` and `m_2`, and see what happens to their mean and standard deviation when we average their predictions over 1000 simulations." + "Let's define two $I.I.D.$ (independent and identically distributed) standard normal toy models `m_1` and `m_2`, and see what happens to their mean and standard deviation when we average their predictions over 1000 trials." ] }, { "cell_type": "code", - "execution_count": 107, + "execution_count": 37, "metadata": { "collapsed": false }, @@ -78,18 +78,18 @@ "output_type": "stream", "text": [ "---- Mean ---- ---- Variance ---- \n", - "Model 1: 0.036 Model 1: 1.02 \n", - "Model 2: 0.045 Model 2: 0.946 \n", - "Combined: 0.041 Combined: 0.486 \n", + "Model 1: -0.029 Model 1: 1.014 \n", + "Model 2: 0.015 Model 2: 1.038 \n", + "Combined: -0.007 Combined: 0.514 \n", "\n", - "Covariance between models: -0.0109611639748\n" + "Covariance between models: 0.00281306569105\n" ] }, { "data": { - "image/png": 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55Zd12mmnNdsuHA7LMAw5jhM3O1v9vtPT0xsN/N+xY0ez+2srrsAAAADgoFBe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\ntfnXlUtGpWO8Wy73rY1ZDQvF+RnL6inKd8JQMgyZyaTK588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rMvB/+/btLR5vf3EFBgAAAIeE0qoq7amoaJf/Squq2mzvtNNO086dO/W3v/1N\nUt0X+bvvvlsrVqzQscceq//85z+Kx+Oqra3VRx99pOOOOy6l8/jwww/luq5KSkoUiUSUk5Mj13Vb\n3P7444/XO++8I8uy5LqufvOb38hxHA0aNEgfffSRJCVuT2us/rijR4/WwoULk24fk6QhQ4boP//5\njyRpzZo1GjZsWNJx33//fTmOI6luRrO///3vkqTly5cnZiZrrfb9wRUYAAAAeF6vXr00/Nqr2+14\ng746Zmt8Pp8effRR3XzzzVq4cKFCoZBOO+00XXPNNZKkKVOm6PLLL5fruvrOd76jPn36NNm/8Z99\nPp8GDRqk6dOna+vWrbr++uubbNtYnz59NG3aNF1++eUKBoM6++yzZRiGpk2bpp/97Gd6/fXXNWTI\nkBbPQZImTJiggoICDR48OOmqyS9/+Uvdeuut8vv9ys7O1u233y7TNPXcc89p6tSpOuaYYxJTTc+a\nNUtz5szRww8/rHA4rHvuuUeVlZXtPguZz23vSNSMtWvXasSIER3dDNpAP3QN9EPnow9SZ1mWNpVs\nSfk5MLZlaVDuESk9yJJ+6Broh85HH+wfy7IkiQfnelRL/ZfKzwO3kAEAAADwDG4hAwB0Oa7ryrbt\n/drXNM12v10BANB1EGAAAF2Obdv6dONuGSFjn/Zzoo6OHZzHLSUAcAgjwAAAuiQjZKQ89gbA4Wl/\nr9Si89m2LdM092tfxsAAAADAc0zT3O8vwM355JNP2u1YaNuB9B9XYAAAAOA5Pp+v3W8X5fZTb+AK\nDAAAAADPIMAAAAAA8AwCDAAAAADPIMAAAAAA8AwCDAAAAADPSGkWspdeekmPPvqogsGgpk+frmOO\nOUY33nijXNdVr169dOeddyoUCnV0rQAAAAAOc21egSkrK9Mf/vAHPfPMM3rwwQf15ptvasGCBZo6\ndaqWLFmigQMHaunSpQejVgAAAACHuTYDzNtvv63TTjtNaWlp6tmzp+bOnas1a9Zo9OjRkqTRo0fr\n7bff7vBCAQAAAKDNW8i2b9+umpoa/eQnP1FlZaWuvvpqWZaVuGWsR48eKioq6vBCAQAAAKDNAOO6\nbuI2su3bt2vatGlyXTdpfSrWrl27/1Wi3dAPXQP90Pnog9TYtq1Cq1iGaaS0vWM7Kg0XyzTNlLZv\nqR9s29bOUkeGkdpxEu07tsqLjJTbRx1+HjoffdA10A/e0GaA6dmzp0488UT5/X4NGDBAGRkZCgaD\nchxHhmG1g0otAAAgAElEQVSosLBQeXl5bTY0YsSIdikY+2/t2rX0QxdAP3Q++iB1lmVpU8kWmeFw\nStvblqVBuUconML2rfWDZVna8GVZyu02bP/IATkptY86/Dx0Pvqga6AfuoZUQmSbY2BOO+00vfPO\nO3JdV6WlpYpEIho5cqRWrlwpSSooKNCoUaMOvFoAAAAAaEObV2Dy8/M1fvx4TZkyRT6fT3PmzNHX\nvvY1zZgxQ3/5y1/Ut29fTZ48+WDUCgAAAOAwl9JzYKZMmaIpU6YkLXvsscc6pCAAAAAAaEmbt5AB\nAAAAQFdBgAEAAADgGQQYAAAAAJ5BgAEAAADgGQQYAAAAAJ5BgAEAAADgGQQYAAAAAJ6R0nNgAADo\nKK7ryrbtpGWWZcm2rVb3M0xTPp+vybEsq/X9mmM2cywAQNdEgAEAdCrbtvXZrv/JMEJ7lzlR7YxU\nKlRrNrtPbTSqI3KOkBkOJy13HFufba5WZkZmyu07UUfHDs5TuNGxAABdEwEGANDpDCOUHEb8fhmm\nI8NoPsC0JtT4WACAQwpjYAAAAAB4BgEGAAAAgGcQYAAAAAB4BmNgAKCLaG42rlQcajNoxeNx7Sna\no9LiKoVCRrPbpGVkdHgd9AcAdE0EGADoImzb1qcbd8to4Ut7cw7FGbRK9hRrxxPPKhQw5Pc3vVGg\nvDoi58JzNSCrf4fW0dzsaG1xnKiO6X3UIdUfANDVEGAAoAsxQgYzaEnKyUiXGQwr4A80u37fn/Sy\nf5rMjgYA6HSMgQEAAADgGQQYAAAAAJ5BgAEAAADgGQQYAAAAAJ5BgAEAAADgGQQYAAAAAJ5BgAEA\nAADgGQQYAAAAAJ5BgAEAAADgGQQYAAAAAJ5BgAEAAADgGQQYAAAAAJ5BgAEAAADgGQQYAAAAAJ5B\ngAEAAADgGQQYAAAAAJ4R7OwCAACHj3g8rqKiIklScXGxCgsLZVmW9pTtkWmadcv3FMvnui0fw3VV\nVlqqPelFiX3qVVaUS36fHMtWbo+e8vv5PR0AHGoIMACAg6aoqEjv3/cHdc/MVG1xsTa9/6FitTFF\nnCrZgYAkafvu3crLzFI4lNbsMSoiEem1N1XT81M5X+1TLxp1JJ/0pR2VrrhSPXvldfg5AQAOLgIM\nAOCg6p6ZqZ7Z2ZJtq2d2tmK1MZm2T4GvwkhpVVWbx+iWlqYeWVkKBJL/GXMcW/JJoaDdIbUDADof\n19YBAAAAeAYBBgAAAIBnEGAAAAAAeAYBBgAAAIBnMIgfAA4TDacwbkmvXr1anHrYdSUn6rS6v+1E\nZVlWk+Wmacrn86VeLAAALSDAAMBhouEUxs0prarS8GuvVn5+frPrnaijTdtLFAqGWmzDsW3Fq8pk\nmuGk/Y4dnKdwONzifgAApIoAAwCHkcQUxvspFAzJMMwW17uuZJphmYQVAEAHYQwMAAAAAM8gwAAA\nAADwDAIMAAAAAM9gDAwAHI5cKRaLJS2K1cZkWVbSLGKWZcl2opLfL8d25Mo92JUCAJCEAAMAh6FY\nLKayypqkKZMrI44276hQlbN3kL5tW9oZqZRhOopEqhUyDJlGZ1QMAEAdAgwAHKb8fr8Cgb3/DAQC\nAZmm2WQGsVCtKcMwFXVafwYMAAAHA2NgAAAAAHgGAQYAAACAZxBgAAAAAHgGAQYAAACAZxBgAAAA\nAHgGAQYAAACAZxBgAAAAAHhGm8+BWbNmja677jodffTRcl1XxxxzjH74wx/qxhtvlOu66tWrl+68\n806FQqGDUS8AAACAw1hKD7I8+eSTtWDBgsTrmTNnaurUqRo3bpzmz5+vpUuX6tJLL+2wIgEAAABA\nSvEWMtd1k16vWbNGo0ePliSNHj1ab7/9dvtXBgAAAACNpHQFZsOGDfrpT3+q8vJyXX311bIsK3HL\nWI8ePVRUVNShRQIAmue6rizLSmlby7IUq43V/ReLNVkfd+MqKd6TtMy2bZVGimUYhiLV1ZJfSgun\ny+8/dIZQtvQeWpYl24lKrZyrETLk87V9rLaYpilfwwMBAFrkcxtfXmmksLBQ77//viZOnKgvv/xS\n06ZNUyQS0TvvvCNJ2rp1q2666SY9/fTTLR5j7dq17Vs1AByCbNvWzlJHhmGmvE9VVaVqa2uVnp7e\n5rZlpSXK+vc/1T0jU7W1tfL5/UnjFzcVFSrqRNUrJyexLB6LyXYd+f1+xWprVVFTo9i4MerWvXuz\nbUQdR7nB3KRzcBxbfbobMk1TxcXFqn39TeVmZibWx2Jx1cQs+QN1QWFj4W6FA37lZOY0G5Q2FxUp\n7PdrQG5v+QOB5Paj0br3xbEVOe0sde+e2+b70tJ76DiOSmMlChlGs/vFamPKzw3LCO1dX1VZpdpY\nrdLT2u6PerW1UfXL7C3TTL3fAeBQNmLEiFbXt3kFJj8/XxMnTpQkDRgwQD179tTHH38sx3FkGIYK\nCwuVl5d3wIWg461du5Z+6ALoh87XVfvAsixt+LJMZjic8j4V5WWS36fsrG5tbrunaLcqP/uvemRl\ny3FsyScZob1fmotrapQeDKpvr71/p8ditaqORhQIBBSNOiqprlZgwEDl9uzZbBu2batfRt+kc7At\nS0cOyFE4HFZhYaE2vf+hemZna09RkXr26qVYbUyVdqUCX4WRbjU1Mv0BZWZmKeAPNGkjIxKR6fMp\nJydHgUDyP2P15xWwbPU/6mj17NX2v08tvYe2ZWl79Y4Wg4Xj2OqfnyWzQcCpKCuX/H5lZ2e12W7D\ndgblHqHwPvR7e+qqPw+HE/qga6AfuoZULny0eQ/Ayy+/rIULF0qSiouLVVxcrIsuukgrV66UJBUU\nFGjUqFEHWCoAAAAAtK3NKzBjxozRDTfcoMsuu0yu6+rWW2/V0KFDddNNN+kvf/mL+vbtq8mTJx+M\nWgEAAAAc5toMMBkZGfrjH//YZPljjz3WIQUBAAAAQEtSmoUMAID91XBmruSZ0OKJGdFi8bjqp/OK\nxeOKyyep1TlmAACHKQIMAKBDOY6tzzZXKzMjU3v2VKgm4sgI2IrYMVVU24rFYorURuUPxCVJETum\nmGLKznQVOHRmawYAtBMCDACgw4WMkMxwWKZpygkEFAgE5f/q/5LkjwcSM44F/P7UnrIMADgs8W8E\nAAAAAM8gwAAAAADwDAIMAAAAAM8gwAAAAADwDAbxA0A7c11Xtm3v836WZcll6mAAAFpFgAGAdmbb\ntj7duFtGyNin/SqrKmSYpsLhtA6qDAAA7yPAAEAHMEKGzHB4n/axbauDqgEA4NDBGBgAAAAAnkGA\nAQAAAOAZBBgAAAAAnkGAAQAAAOAZBBgAAAAAnkGAAQAAAOAZBBgAAAAAnkGAAQAAAOAZBBgAAAAA\nnhHs7AIAAIcO13Vl21bSMtu2Jb9kh0zZtq1YLKZYrFbxr/4fi8UkuZ1T8EHmupITdZKW2U5UlmW1\nsMdepmnK5/N1VGkA4BkEGABAu4k6jrZGtio9IzOxLFJTKfl9qvRVqzRSrFBtjcLRgGzXVnU0otpo\nVP6AX4FAJxZ+kDhRR5u2lygUDO1dZtuKV5XJNMOt7nfs4DyFwy1vAwCHCwIMAKBdhUIhmaaZeF0b\ndSS/T6ZpyjCMr8JKQH5/3f/jsVgnVnvwhYIhGcbe98d1JdMMyyScAEBKGAMDAAAAwDMIMAAAAAA8\ngwADAAAAwDMIMAAAAAA8g0H8AOBBruvKse2kKYrbYllWYgrjWCwm+aSYvzaxPhaPKRb3KxZrsKwL\nT3Eca2bwf+K8YjHZti27wfTEBtMQA8AhgQADAB7k2La2lG2RY1uJKYrbsmPPVmVYFQqHA6qtjUo+\nKaq9YaWm1pJPUVVHI4llXXWK43jcVZVTpWCD6YglJc4rUmurPLJLdnW0bnk0qiNyjmCmLwA4BBBg\nAMCjgqGQJDcxRXFbAsGQfPVTF8djks+nQINkEgj4FfAHkpZ15SmO66dhbmjvefnlM4yU3hcAgLcw\nBgYAAACAZxBgAAAAAHgGAQYAAACAZzAGBgCQsrjrqrKkpMX1VZVVysnNOYgVeZ/rurJtq9VtbNuS\n1WBGNZMZ1QAcxggwAICUVUQi0orX5O/evdn10bJylV8wSdndCDGpijqOtka2Kj0js5VtbPnLqmQa\nITlOVMf0PkphZlQDcJgiwAAA9km3tHTlZmY1uy7qRNX6tQQ0JxQKtTpjms8nmWFTpmEcxKoAoGti\nDAwAAAAAzyDAAAAAAPAMAgwAAAAAzyDAAAAAAPAMBvEDQCvqpri192kfy7Lkyu2gigAAOLwRYACg\nFbZt69ONu2WEUp/9qbKqQoZpKhxO68DKAAA4PBFgAKANRsiQuQ/P3GjroYQAAGD/MQYGAAAAgGcQ\nYAAAAAB4BgEGAAAAgGcQYAAAAAB4BgEGAAAAgGcQYAAAAAB4BgEGAAAAgGcQYAAAAAB4BgEGAAAA\ngGcEO7sAADjcua4rx7Zl27bkl+yQ2WSbeDyukpLixGvHtlRaW6ra2tq6fSKWcnJz5fd37u+l4q6r\n8tJSZWRmJpZFqqsTNZaVlKi724kFAgA8jwADAJ3MsW1tKdsix7Ykv0+Vvuom25QWFyuy7CV1S8+Q\nJMWiUQUCfgUkyedTpe1I35ms3J49D27xjVREIgq8+Zb8eb0Sy8xoVPL55A8GVVVUpMysbCkrqxOr\nBAB4GQEGALqAYCgkyZX8Pplm0yswhmEonJWl3My6L/5Rx5F8X630+RQKWoofvHJblZ2enqhTkqJR\n56saQyqrbhrOAADYF4yBAQAAAOAZKQUY27Z1zjnn6IUXXtCuXbs0depUXXHFFfq///s/RaPRjq4R\nAAAAACSlGGDuv/9+5eTkSJIWLFigqVOnasmSJRo4cKCWLl3aoQUCAAAAQL02A8zGjRu1adMmnXnm\nmXJdV++++65Gjx4tSRo9erTefvvtDi8SAAAAAKQUBvHfeeedmjNnjp5//nlJUk1NjUKhkCSpR48e\nKioq6tgKAQA4QK7ryratZte1NH11TU1EpXv2yGhmUgWpbnKCvr0y2r1WAEDrWg0wL7zwgk466ST1\n7du32fWum/pk/mvXrt23ytAh6IeugX7ofKn2gW3b2lnqyDCa/xLbnKqqSklSZmZqUwU7jq2S2hJF\na+vGFKanN/1SXF5aqp5VVQp99fdubbR27yxkkqpsW3u+3Kryr9puzq7t29S3ulqVwWDd82MkBYN7\n/xmorq6WGwiq0jQSy+rbCX61T011tYK1saRtGqqJRKRQUJWVFXuP0aCtxm1UVlYktVFfR9TnU5Vh\nJNXXsE5DUpXZdH19W43fj0hVlT6Lfaq0tPQmx4tE6mZGa/y+F+7cqZx/v6fuLUz5XFZdrTXnnam8\n/PzEsqrKKskvZWZkNruPE3W0pyKqUGjv+xepqpJ8UnoL+0h1YamqNCQjZMixHZWGi5udrW5/8XdS\n56MPugb6wRtaDTBvvfWWtm3bptdee02FhYUKhUJKT0+X4zgyDEOFhYXKy8tLqaERI0a0S8HYf2vX\nrqUfugD6ofPtSx9YlqUNX5bJDIdTPn5FeZnk9yk7q1tK29uWpe3VO1QbdSS/TxnpTb/IlmRmyf/R\np8pqYRplNxRS+oCBrT4HJuD6lPbZBmVlZSdNbVwvIxJReiCorKzsxLL6dkIhQ9Goo7RIRBlmOGmb\nhtLSy5UeCiUfo0FbDduorKyoq6VBG/V1GJIys7KS6mtYZ8iVMjMzk4JAw7Yavx+VFRXy+VT3DJpG\nqqsqm33fwyFTaf/brPzuuc2fa0W5eh19tPr12/tLvoqycsnvV3Z286HHdhxtK6xMCsSt1VbPcWz1\nz8+SaRiyLUuDco9QeB8+k63h76TORx90DfRD15BKiGw1wMyfPz/x54ULF6p///56//33tXLlSl1w\nwQUqKCjQqFGjDrxSAAAAAEjBPj8HZvr06XrhhRd0xRVXqKKiQpMnT+6IugAAAACgiTYH8de75ppr\nEn9+7LHHOqQYAAAAAGhNygEGANB1xV1XZSUlrW5TXlqqtH2YfAUAgK6IAAMAh4CKSESxFa/J3717\ni9tEd+yUk93yQHEAALyAAAMAh4huaenKbWXq5qK0soNYDQAAHWOfB/EDAAAAQGchwAAAAADwDAIM\nAAAAAM8gwAAAAADwDAIMAAAAAM8gwAAAAADwDAIMAAAAAM8gwAAAAADwDAIMAAAAAM8gwAAAAADw\njGBnFwAAgCe5rqK2I9txEovsaFQ++ZKWNeTYjly5B6k8V7Ztt7mdbduyLCtpmWma8vl8HVUaABwQ\nAgwAAPshHo9r2+4KxUJZiWVVFZXy+XzKsJrfJxKpVsgwZBodX59t2/p0424ZodYb21nqaMOXZYnX\nTtTRsYPzFA6HO7pEANgvBBgAAPZTIBiQYZiJ1yHDlM+npGUNRVu4MtNRjJAhs40gYhhmm9sAQFfC\nGBgAAAAAnkGAAQAAAOAZBBgAAAAAnsEYGABoRd1MTi2MyG6Bbdsyws2PgWhOPB5XaXGxaqNRyS/Z\nkabtlZWUqPvBmbwKKYq7rspLS5WelpFYVlVZJZ+vbrYxScrJzZXfz+8KAaA9EWAAoBW2bWtr+Val\nZ2SmvE9FRan6+funvH1JSbEiy15SVjgs+XzyB5v+1VxVVKTMrGwpK6uZI6AzVEQiCrz+N/l79Uos\nS3Oikk/yh0Iqr45I35ms3J49O7FKADj0EGAAoA2hUEimmfoVlWBo3/9q7ZaeoZz0NMnnUygYarK+\nrLp6n4+Jjpednq7czL2hMuo4kk8KfTV1cbyzCgOAQxjXtQEAAAB4BgEGAAAAgGcQYAAAAAB4BgEG\nAAAAgGcwiB/AYaFuOmRbUt3MYpaV2tTIlmXJ1b7NX1zflp1iG45tSfvYBg5MPB5XWUmJJClSXd3s\n9NXlpaVKc+kXAOhqCDAADgu2bevTjbtlhAztLHW04cuylPbbU1yk2njtPrUVdRztsLfLCae2346K\n7cqMM1/VwVRWUqLKZ5epW0a6zGi02emrozt2ysnO7qQKAQAtIcAAOGwYIUNmOCzDMGWGwynvI3vf\n2woGgylPvRxoZtpkdLxuGXVTIEejTrPTVxelpRZyAQAHF2NgAAAAAHgGAQYAAACAZxBgAAAAAHgG\nAQYAAACAZxBgAAAAAHgGAQYAAACAZxBgAAAAAHgGAQYAAACAZxBgAAAAAHgGAQYAAACAZxBgAAAA\nAHgGAQYAAACAZxBgAAAAAHgGAQYAAACAZxBgAAAAAHgGAQYAAACAZwQ7uwAAANpb3HVVVlKSeF1V\nWSWfT3JsR5JUVlKi7m5nVbdXPB5XaXFJUm2N5eTmynXdxHrbicqyrDaPbVmWXHWBkwSAdkaAAQAc\ncioiEcVWvCZ/9+6SpDQnKvkkfygkSaoqKlJmVraUldWZZaqspETRl5crOyM9UVtD5dUR6TuTZYZN\nbdlpKS0tTY5tK15VJtMMt3rsyqoKGaapcDito8oHgE5BgAEAHJK6paUrN7MuoEQdR/JJoZAhSSqr\nru7M0pJkp6crNzMzUVtj8a/+HwwFZRimXFcyzbDMcOsBxrbbvkoDAF7EGBgAAAAAnkGAAQAAAOAZ\nBBgAAAAAnsEYGAAAOkDjmdAkKVJdLfklO1I3PqWspERZzBQGAPuEAAMAQAdoPBOaJJnRqOTzyR+s\n++e3qqhIZlp6Z5UIAJ5EgAEAoIM0nAlNkqJRR/L5FArWTZlcVl0tLsAAwL5pM8BYlqVf/OIXKi4u\nluM4+slPfqKhQ4fqxhtvlOu66tWrl+68806Fmpm/HgAAAADaU5sBZtWqVRo2bJh+8IMfaMeOHbry\nyis1fPhwXXHFFRo/frzmz5+vpUuX6tJLLz0Y9QIAAAA4jLU5C9mkSZP0gx/8QJK0Y8cO9enTR+++\n+67GjBkjSRo9erTefvvtjq0SAAAAALQPY2AuvfRS7d69Ww888ICuuuqqxC1jPXr0UFFRUYcVCAAA\nAAD1Ug4wzzzzjNavX6+f//znct29Iw4b/rk1a9eu3ffq0O7oh66Bfjj4bNvWzlJHhmFKkj5d/2lK\n+5WUFKssXqqy8oqU29qzu1A+v1+RGjul7Xdt36a+1dUyvnodDDb9q7m6ulpuIKhKs26r2mit5Gt5\nfXNqIhEpFFRlZYVqa2ubtNXcMerbCQaDqq2tVU11tYK1sRbbadhG4hgN2mrcRmVlRVIb9XVEfT5V\nGUaL74Uhqcpsur6+rZber4Zt1K9v7r1o6Vyarg8ln2uDdpp9Pxu11dq5SFJVdbX2fLlVoa+OkZ6e\noajjqDJYkfgst6SqqlKSlNlgEoGWNPx5cBxb5UWGTLP146N98e9C10A/eEObAebjjz9Wjx491KdP\nHw0dOlTxeFwZGRlyHEeGYaiwsFB5eXltNjRixIh2KRj7b+3atfRDF0A/dA7LsrThyzKZ4bA+Xf+p\njh16bEr7Fe0uVKFdqO7de6TcVrphSAGf8vP7prR9wPUp7bMNyszMTJqhqqGMSETpgaCysrIlSVHH\n2RtgfD5lOE7S+uakpZcrPRRSVlZ2k9mwmmujYTuhkKFo1FFaJKIMM9xiOw3bSByjQVsN26isrKir\npUEb9XUYkjKzslp8L0KulJmZmdincVuN34/m2qhf39x70dK5JK0vL1dG43Nt0E6z72ejtlo7F0mK\n+nxKHzBQZtiU/D5lpGfKtm31y+grMxxutq56FeVlkt+n7KxurW7X+OfBtiwdOSBH4TaOj/bDvwtd\nA/3QNaQSItscA/Pee+/p8ccflyTt2bNHkUhEI0eO1MqVKyVJBQUFGjVq1AGWCgAAAABta/MKzGWX\nXaZZs2bp8ssvl23buuWWW3T88cdrxowZ+stf/qK+fftq8uTJB6NWAAAAAIe5NgOMaZq65557mix/\n7LHHOqQgAAAAAGhJm7eQAQAAAEBXkfIsZADgda7ryrYsOY4t27JS2se27ZRnW2xJPB5XWUlJi+vL\nS0uVdoBtAK1xXVeO3fyseI1/HmzbkvXVa9M05fP5mt2vveqyW6irNR1dF4CujQAD4LDhOLZ21RSq\npLZE26t3pLTPnspCBc0D+6uyrKRElc8uU7eM9GbXR3fslJPd8uxhwIFybFtbyrYoGGo6q1vjn4eo\nY8tfViWfpGN6H9Whs5HZtq3Pdv1PhtG0rpY4TrTD6wLQtRFgABxWgqGQQkbqz7gIBgPt0m63jHTl\ntvA8jqK0snZpA2hNMBRq9nPf+OfB51PdtM3x+EGpyzBCbU4JDQANMQYGAAAAgGcQYAAAAAB4BgEG\nAAAAgGcwBgZAp2k4A9G+zkZUPwsRsxEBHcN13cRsZKni5xHAwUCAAdBpbNvWpxt3ywgZsm1LW8u3\nKtTMLEmNRWuj+v/65h6UWZKAw5VjO/oiskmZLcye12R7ZgcDcJAQYAB0KiNkJGYgSs/ITGl2MMex\nD+osScDhKhRihjAAXQ9jYAAAAAB4BgEGAAAAgGcQYAAAAAB4BgEGAAAAgGcQYAAAAAB4BgEGAAAA\ngGcQYAAAAAB4BgEGAAAAgGcQYAAAAAB4BgEGAAAAgGcEO7sAANhXruvKsR25rivLslLax7IsuXI7\nuDIAANDRCDAAPKc2GtWWnZYCfr/iVWUyzXCb+1RWVdQFGN9BKBAAAHQYAgwATwqGggoGQjLNsMxw\n2wHGti3ZUfsgVAYAADoSY2AAAAAAeAYBBgAAAIBnEGAAAAAAeAZjYADgAMXjcZWVlCRel5WWSn6f\nQgGj7nVJibozARraieu6su29s+/F43GVlBQ32a6qskLyS5UZFcrIyJDcjvsQuq5kO9GUZwWsZ1lW\nR5YF4BBFgAGAA1RWUqLKZ5epW0a6JKlbJCL5JH9a3euqoiJlZmVLWVmdWSYOEVHH0dbIVqVnZEqS\nSouLFVn2krqlZyRtF4tGJZ+023HkG3e2evXOT2nCi/3hRB1t3lGieFVmSrMC1qusqlC4e1ThtI6p\nC8ChiQADAO2gW0a6cjPrAkqN3y/5pLS0ui+UZdXVnVkaDkGhUEimaUqSDMNQOCsr8fmrF406ks8n\nw7JUEQx1fE3B1GcFrFd3JcnpuKIAHJIYAwMAAADAMwgwAAAAADyDAAMAAADAMwgwAAAAADyDQfwA\nAHRRcddVWUmJDNOU/JIdsVRVWSWfT3LsusHv7T1Nt+u6cmxHdjQqn3yynbYH2Tu2I1fMhwzg4CDA\nAADQRVVEIoqteE1mZqbk88kfDCrNqZse2R+qm1msvafpro1GtWWnpVg0Kp/Pp4wUHu0SiVTL5YEu\nAA4SAgwAAF1Yt7R05X4VYP7/9u4tRpLyPv/4UzVdVdOH2dmZPXptcGwsx5aDLYsQhWxswDGJZEdR\nNsqShZgcFDkXkSIRKbEWsEjuEMuFRYIcg7QkUYwzCIgdnIAWkP8mRrbxZi1h7CxEwHoX2ONsT08f\nauqt6un6X8x0b09P9WFmZ6a3p7+fG5auw/urqj79uud92kk5isJQsiTHWfyh1HWI6U45KdmWLcuS\nXNfrun4Uhgoj4pABbAzmwAAAAAAYGDQwAAAAAAYGDQwAAACAgcEcGAAAcNniOJYxPcz4bxIEgUYc\nIxN2n2dTZ8KIwABgyNHAAACAyxaFoU7NnlImm+t5m+mL56QZWzt2Wj1vU6mU9Qtb36d0Or2aMgFs\nAjQwAABgTTiOI8/r/duUVGpEGrF6SjqrC41ZTWkANhHmwAAAAAAYGDQwAAAAAAYGDQwAAACAgUED\nAwAAAGBg0MAAAAAAGBg0MAAAAAAGBg0MAAAAgIFBAwMAAABgYNDAAAAAABgYNDAAAAAABkaq3wUA\n2HziOJYxput6QRDImECSFv4bx41ltVpNhXw+cTu/UpFsacROadLe2lNNxhiZyEhe3H1lAFesOI4V\nBIGCIFjxtp7nybKsdagKwEaigQGw5owxev3sG3Jdp/N6YaQzfklO1ZNfLstxHXmjo5KkQj6v0hPf\n1Hg2s2w7L4oky1KxXNFPP3eL9lx1ddea/LmSfH9O41vHV3dQAK4I1SjS/528qG2llW0XRqE++sGd\nGt9koIQAACAASURBVF18jgEwuGhgAKwLt6kZacu25XqhXNdTmPCNzXg2o8nc2LLboyiULEuqxQpS\njjzP61pPNQoVRmHP9QO4cjluqvvzC4BNq6cG5tChQ/rxj3+s+fl5/fmf/7muvfZa/c3f/I3iONaO\nHTt06NAhOU7nT1oBAAAA4HJ1bWBefvllvfHGG5qamlKhUNC+ffv0q7/6q/rCF76g3/qt39JXvvIV\nPfXUUzpw4MBG1AsAAABgiHVNIbv++uv14IMPSpK2bNki3/d19OhRfeYzn5Ek3Xzzzfr+97+/vlUC\nAAAAgHr4Bsa2baXTaUnSk08+qZtuukkvvfRS40/Gtm3bpgsXLqxvlQCQoBbHmp2ZUTaXa7vO1slJ\n2TaJ8QAAbBY9T+J/4YUX9NRTT+nw4cP6zd/8zcbtcdxbJOmxY8dWXh3WHNfhyrDZr4MxRueCi3I9\nt+N6YRRquhjJcVz55bJkSZnsQjMyOzOj7eWynITnmGq1Kkk6Nz2t6n8+K3/btsT9F31fp37jRo1P\nTMj3K/LLZWWyWWWyOZ34+YmejmX6/DlZti1/rn0sdGutwdycZFmqVuclSZVKRfFISqU252PO9yUn\npfLi8lRq+VNz6z6qUVWy2i/vNE6pVGycw+axkvZRHyeVSqlarWquUlGqOt/1WEql4qV9NI3VOkap\nVFwyRr2OyLJUdt2258KVVPaWL6+P1e58NY9RX550Ltody/LlztJjbRon8Xy2jNXpWJrr9Ebsxnad\njiXpXJSN0bvvvq2SX2o8vlo1Px58v7Lwj1q85DHZSevjq1e9PL5azRZmNGuXND2dHLPeThgazV5w\newr96IfN/rowKLgOg6GnBuZ73/ueHnnkER0+fFi5XE7ZbFZhGMp1XZ07d047d+7suo/rrrvusovF\n5Tl27BjX4QowDNchCAKdyJ/smhJkwlDvnCvJdT2VikVZlpQb2yJJyufGZL96XGMdUsjS5YoyjqOr\ndu9O3H++XFLtqqs1uX27KuWSyuWSstmcLly8qA/8wgd6OpaM60ojlnbt2tN2ndZaUyMjkiWl01lJ\nUtb3lRlJaWzx2FqlM7PKOI5yuZxkWXJSy0NRWvcRheGlBsaylA3DjmM0jzM2tqVxDpvHSqqzPo7j\nuIqiUGnfV9Yb7XosS/bRNFbzGKVScaGWpjHqdbiScmNjbc+FE0u5XK6xTetYrecjaYz68qRz0e5Y\nliyfnVW29Vibxkk8ny1jdTqW5jqb7xudjiXpXMSOo/e+9ypNbp9sPL6anfj5iSWPh0q5JNmWatXa\nksdkJ82Pr17Wr+vl8dVq5uKYdmV3a8f2XT1vI0kmCHTNVVuvyBjlYXhdGARchytDL01k17+rKJfL\neuCBB/S1r31NY2MLL8433HCDjhw5Ikk6cuSIPvWpT11mqQAAAADQXddvYJ555hkVCgXdeeediuNY\nlmXp/vvv1z333KPHH39ce/bs0b59+zaiVgAAAABDrmsDc+utt+rWW29ddvujjz66LgUBAAAAQDtE\n8wAAAAAYGD2nkAHAoKnFsQr5haQiv1JRpVJWGISanZlRvikcgKhlAAAGBw0MgE2r6Puaf/Y52RMT\n8qJIqSjSiONouzGyXz0uSZqt+NL+fZrcvr3P1QIAgF7QwADY1MbTGU3mxhRFoapRpJTjKEillsQz\n1/pYHwAAWBn+ZgIAAADAwKCBAQAAADAwaGAAAAAADAzmwABDJo5jGWNWvJ3nebIsax0qAoD1E8ex\nQmNkTKAgCHrejuc84MpFAwMMGWOMXj/7hlzX6XmbMIz0i7s/pNHR0XWsDADWXmiMThZOKo5rsgtl\neT089/GcB1zZaGCAIeS6jjxemAEMiZTjyLIkb9ST57r9LgfAZWIODAAAAICBQQMDAAAAYGDQwAAA\nAAAYGMyBAQbAapPDJJJ0AHRXq9VUyOclSX6lItlSrRrLsqTQhJKkrZOTsu3+f+5Zfz40PSaKGRNI\ncSzxPAhsGjQwwAAwxuj4W+flOiubfBpGoT76wZ0k6QDoqJDPq/TENzWezciLooU3+7VYsiTbcTRb\n8aX9+zS5fXu/S1UUhjpt3lU4Wu1pfb9cluM6cj1vnSsDsFFoYIAB4TouyWEA1s14NqPJ3JiiKFzS\nwDiLH5zU+lxfs1QqJa/HhiRc5bfXAK5c/f8uGAAAAAB6RAMDAAAAYGDQwAAAAAAYGDQwAAAAAAYG\nk/gBoINarabibFHOSPsEuEI+r4l4A4sCVqAWx5qdmVkSidxsdmZGcRhxHwYwMGhgAKCD4uys9Px3\nZE9ua7tO+cIF5ca2SGNjG1gZ0Jui7yv1nRc1OrFVtuMsW769XFZ+bo77MICBQQMDAF2Mp9OazLV/\nY1eoVDawGmDltmQymszlGpHIzZw4VpUfeQQwQJgDAwAAAGBg0MAAAAAAGBg0MAAAAAAGBnNgAKyJ\nOI5ljJEkBUEgE0aS3fkzktCEikX0EQAA6B0NDIA1YYzR8bfOy3VcGRPojF+S6y2PbG3m+xU5riuv\nfUIxAADAEjQwANaM67jyRkclSU7Vk+t6HdePws4NDgAAQCvmwAAAAAAYGDQwAAAAAAYGDQwAAACA\ngUEDAwAAAGBgMIkf2MTiOFYQBEtu6xZxHMcLscaWZTVuM2G0bD+tgiAgEhkAAKw7GhhgEwtDo9d/\nXlEum2vc1i3i2Pcrsixb6XT60n6MUa1ckOeNth2rVC7K9TyNjqbbrgMAAHC5aGCATc5xnUa0ceO2\nDhHHURhKtrVkeRxLnje6bD/NjOn8DQ0AAMBaYA4MAAAAgIFBAwMAAABgYNDAAAAAABgYzIEBBlgc\nxwqNabvcGCPZknG8ptuChUktKxyn2xyX5rFWMwYAAEAvaGCAARYao5OFk0o5TuJyf64k2ZZKVuXS\nbeVy4sT+TqIw1Cn/lDJNaWadxlrNGAAAAL2ggQEGXMpx5HnJiWLVaCFRrHl5p29sOnE6jNM61mrH\nAAAA6IY5MAAAAAAGBg0MAAAAgIFBAwMAAABgYDAHBsBQq8WxCvl82+XFQkFbSFQD1l2tVuv4WGxe\nzx4Z2YCKAFypaGAADLWi72v+2edkT0wkr/D22wq3jG1sUcAQKuTzKj3xTY1nM23Xma34Cj59g7Zu\nn9zAygBcaWhgAAy98XRGk7nkJmUsTRQ0sFHGs+0fi3Wdf5EKwDBgDgwAAACAgUEDAwAAAGBg0MAA\nAAAAGBg0MAAAAAAGBpP4AfRFrVbTzMW8ZEvGD1QulWVZUmhCSQuJRBOkFwMYQHEcyxjT8/rGGAVB\nIM/zZFnWOlYGbA40MAD6opDPyzz9X9qSzcpOpZQOI8mSbMeRJJUvXFBubIs0RoQxgMFijNHxt87L\nddye1j8zE+r4W+f10Q/u1OgoyYdANzQwAPpmSyajyVxOTspRFIaSJTmLL/iFSqXP1QHA6rmOK6/H\nZsR1vZ6bHQA9zoF57bXXdMstt+ixxx6TJJ09e1Z33HGHvvCFL+iv/uqvFEXRuhYJAAAAAFIPDczc\n3Jzuv/9+7d27t3Hbgw8+qDvuuENf//rXdfXVV+upp55a1yIBAAAAQOqhgfE8Tw8//LC2b9/euO1H\nP/qRbr75ZknSzTffrO9///vrVyEAAAAALOo6B8a2bbnu0r/LnJubk7M40Xbbtm26cOHC+lQHAACu\neLVaTYX8jMIgbCQJJtk6OSnb3py/4NCcPBYEgYwJetrO9bz1LAvYlC57En8c95ZzeuzYscsdCmuA\n63BlWOl1MMbozEwo1136QheGRvlqXo6bPPnT9xcmwmcy2Uu3lcuSJWWyuTXbpnW7XtafnZnRRKUi\nV1IqlVI1qkrWwr8lqVKpKB5JqeQtP7ZqtSpJmvN9yUmpVComjtG8j2q1qmoUKeU4SqUubdNpnIXj\n8iXHbTtG0j6CuTnJslStzvc0Rv04yovL6+eg0xj189VueadxSqVi4xw2j5W0j+brUq1WNVepKFWd\n73oszeereazWMUqlYuK1jyxLZddtey5cSWVv+fL6WO3OV9L9K+lctDuW5cudpcfaNE7i+WwZq9Ox\nNNfpjdiN7Xp9rDSfi05jtDsfitUYp1ypaPrtU5otlxK3P3v6XY3+v5c0OjYmv80YRd/Xqd+4UeMT\nE43bps+fk2Xb8ueMZmdmtL1cltPhfUW5UtG7p99Vac6XP9dbTHH9+chxXZVnnJ4my4cm1MzoRXkr\naC6MMXq3fFaplKOwGupiMWqEkrRTrVa1c3SnXNfTa//3mmYvuCsaE2uP90mDYVUNTDabVRiGcl1X\n586d086dO7tuc911161mKKyhY8eOcR2uAKu5DkEQ6M23C8sSbUwQ6N3K6bYveJVySbItZTOXGolS\nsSjL0kJE8Rpt07pdL+vnc2Oaz/5EubGxxBSyrO8rM5LSWMI+oiiULEvpckUZx0lcp3UfURQ2Gpgg\nCBrbdBpHkjKZjNIdxkjaR2pkRLKkdDrb0xjpzKwyjqNcLidZlpyU03WM+vmSJFmWsmHYcYzmcern\no3WspDqbr0sUhUr7vrLeaNdjWbKPprGaxyiVigu1JFx7V2rcN5LOhRNLuVxu2RvE+lit56PT/Svp\nXLQ7liXLZ2eVbT3WpnESz2fLWJ2OpbnO5vtGr4+V5nPRaYxSqahsNrvsfKgWX7r2lqXMVVdrsunP\nyZs5lq3Utm3aMTHR9k17vlxSrWUfGdeVRizt2rVH+dyY7FePayzXPjo9siy9d897tXX7pHbt2tN2\nvSXHt/h85Hqe3rdrTF6bD3yamSDQBybfv6JI4yAINJE/KW90VCYM9c650rIPnZaNY4zem92jt35+\nQh/58Ed0zVVbiVHuI94nXRl6aSJX9T3uDTfcoCNHjkiSjhw5ok996lOr2Q0AAAAArEjXb2BeeeUV\nffnLX1Y+n9fIyIimpqZ0+PBhHTx4UI8//rj27Nmjffv2bUStAAAAAIZc1wbmE5/4hL797W8vu/3R\nRx9dl4IAAAAAoJ3LnsQPIFlzIk0zY4yCYHk6TT0Qw7KsZcvaJdoYE0g9BmkAwKCrxbGKhYJkW3JG\nkueytEs6i+O4Y0JaMxNGCoKg4/NyqyAIZMJIsm2FJlQsnpuB9UIDA6wTY4xeP/uGXHfpxOBzwUWd\nyJ9ctn6pVJZl28plM8v3FUY645fkVJdOCPXLZTmus2xyPwBsRkXfV/qlH2p867js9PLnytmKL+3f\nlxg2UI0inTwTKJ1Odx0nNEa1ckFhFMqybOU6JCrWGRPojF+S64Xy/Yoc11WHUEAAl4EGBlhHbkJz\n4XpuYsNhAiPZdnIzYttyvYQY5YRveABgMxtLpzWRyzVS/lrVOmybclJdk8GkhS+2PW/xudi2ev6Q\nyKl6cl1vISkOwLrZnL8mBQAAAGBTooEBAAAAMDBoYAAAAAAMDBoYAAAAAAODSfxAD9pFIneyEMG5\nTgUBwAaqxbEK+Xzb5bMzM5okNviyxHGcGLHfjed5PcU8A5sJDQzQg3aRyJ2USmW5nqfRNBHHAAZb\n0fc1/+xzsicmEpebM2cU9hBPjPbC0Oj1n1d6imxubBOF+ugHd2qUKH0MGRoYoEdJkcidmICIYwCb\nx3g6o8ncWOKyC+nCBlezOfG7XkBvmAMDAAAAYGDQwAAAAAAYGDQwAAAAAAYGc2AwdPqdKBYrlgnD\nZbebKJIlK3FZaELFa5TwU6vVVCwUFJrl40iSX6lItpQezci2+YwDwNpISjIrzMxItiVnxFUhn9cE\nQWYAekADg6HT70SxKIp04t28nNTS8cvFkizLUjYhRdP3K3JcV5572cNrdqag6D+f0dj4eOJyL4pU\nnJtT4cB+TW7ffvkDAoCSk8zGfV+yJDudUfnCBeXGtkhjyUEBAFBHA4Oh1O9EMSflyHW9pbe5nixL\ny26XpCjhW5nLsSXTPk0oikKJ3xQAsA5ak8zmbFuypHQ6q0Kl0sfKAAwS/j4EAAAAwMCggQEAAAAw\nMGhgAAAAAAwMGhgAAAAAA4NJ/NgQq4kuliTP82RtwITyOJbCqP1E+aSI43gxV7ldfe1ikaNw7SKR\nAQAAhg0NDDaEMUbH3zov1+k9BziMQn30gzs1uoK0sNUKozAx2rguKeLY9yuyLFvpdLrnbSTp3IxR\nblt1TSKRAQAAhg0NDDaM67grii7eaEnRxo1lCRHHURhKtrWibSRpJDWydkUDAAAMGebAAAAAABgY\nNDAAAAAABgYNDAAAAICBwRwYAMvU4lilfL7x/+VSWZYlheZSotrWyUnZNp+BANh8FpIzg4X0TFsy\nTvJcx2bGBAuRlutcV9iU6GlMoCAIOmyRnJjZSzJoUgroRiWDAt3QwABYpuj70rPPyZ6YkCSlw0iy\nJNtZSGmbrfjS/n2a3L69n2UCwLqIwlCn/FMLDYltqWRVum7jl8tyXGddw2pCY3SycFKpxefiKDSy\nC2V5bnKCpiSVSmVZtq1cNtO4zYSRfn66ffJmFEW6evxqed6lY9nIZFCgGxoYAInG0xlN5sYkLSau\nWZLTFINd61dhALABHMdZ+LbBtuR53b+BCVfxW2erkXKcRj2WJXmjnjy3fS6/CYxk20sbK9tWNptr\nm6JpjJHnjV7RyaEYbvz9BwAAAICBQQMDAAAAYGDQwAAAAAAYGMyBwbppTjkJgmAhoaUH7gpTTnpJ\nU2kWBMF6B8VserU4VqEppUyS/EplIa3HD1QulRXHNQVzRradfC0L+bzGuA4AAGCFaGCwbowxev3s\nG3JdRyaMdMYvyal2nghZjSK9f+v7VzRxsHmcXpRKZbmep9E0kxNXq+j7mm9KKZMkL4oky5KdSikd\nRnr74rTC0VHtaFqnWfnCBY1mMonLAAAA2qGBwbpy65GSti3XC9smnqzZOD0wwcYkxWx2zSllkhRF\noWRZclKOojBUwa9ofDS9ZJ1mhUr3WFIAAIBWzIEBAAAAMDBoYAAAAAAMDBoYAAAAAAODBgYAAADA\nwGASP1ZkJZHFQRDIhJFk2wpNqFjrn5kbx1IYhR3XMVEkS5ZMeGm9japvI9RqtUbEcXO0cd3szIzS\n5EgD2ISSIt7LpbIsSwvx/IvPh1snJ2Xb6/cZbq1W0+xMYclzb6utk5OLr6mBwtAsvLbaknHah90Y\nE2gjfgegXlfr2EGQfDzxYk0r+QkESfJW+LMJQB0NDFbEGKPjb52X67g9rBvojF+S64Xy/Yoc15XX\nfbPLEkahTrybl5NqH6lcLpZkWZayTc/DG1XfRijk8yo98U2NZzNLoo3rotNnFG7Z0scKAWB9JEW8\np8NIqr9HtiyVTCjt36fJ7dvXrY7ZmYLMt59Rrs1z7WzFl/b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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -97,7 +97,6 @@ } ], "source": [ - "# Model parameters\n", "mu = 0\n", "sigma = 1\n", "\n", @@ -174,16 +173,16 @@ }, { "cell_type": "code", - "execution_count": 101, + "execution_count": 296, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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W1KlTtWjRIrVq1UqZmZnFjh02bJh+/fVXjRgxQnXq1JHFYtHUqVOLrc5W2kjR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DwSOPPKIVK1aUOn/dunWaM2eOfHx81KNHDyUnJ1uH9i1ZskQ9evSo1Pd9qe+++05ZWVkq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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -214,6 +213,7 @@ "metadata": {}, "source": [ "As more models are added the mean predicted value is stationary and the prediction variability decreases geometrically. Worth noting, however, is that in this simulation the standard deviation did not decrease at the rate perfectly uncorrelated models would. This is a result of the toy models we used having some level of covariance, purely by random chance.\n", + "\n", "\n" ] }, @@ -232,7 +232,7 @@ }, { "cell_type": "code", - "execution_count": 102, + "execution_count": 39, "metadata": { "collapsed": false }, @@ -241,7 +241,7 @@ "data": { "image/png": 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AAKCaqLKBVFBQEJtvvnm+xwAAAKqRmvkeYH0qKSnJ9wjVnjWoGqxDfi1atCgi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\nAJAIJAAAgOT/A7BsFUyIEMnLAAAAAElFTkSuQmCC\n", "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -270,7 +270,7 @@ }, { "cell_type": "code", - "execution_count": 103, + "execution_count": 40, "metadata": { "collapsed": false, "scrolled": false @@ -280,7 +280,7 @@ "data": { "image/png": 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miIi9SkkxlZpqKCOjvaKjo+yOCgA4RyFbkAAALZff79f27YXavdunggKpujq5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\nTcXFMbwOQMtEQQKAIKIgoS2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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -306,34 +306,42 @@ "\n", "Individually, neither of these perspectives would provide a particularly enlightening idea of the shape being looked at. With the first view, we had no information on the object in the $Y$ dimension, and in the second view we gained no information on the $Z$ dimension. When combined, however, we can make conclusions based on all three dimensions and the size of the set of possible shapes is drastically reduced. \n", "\n", - "This is the idea behind model ensembling; the aggregation of multiple perspectives yields a more complete view than any of them alone.\n", - "\n" + "This is the idea behind model ensembling; the aggregation of multiple perspectives yields a more complete view than any of them alone.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Multifamily Real Estate Example\n", + "## Example: Predicting Consumer Staples Sector ETF (XLP)\n", + "\n", + "Let's bring this analogy of uncorrelated models providing \"perspectives\" to one involving data. Where the cylinder above was a function of space in the $X$,$Y$, and $Z$ dimensions, let's consider an ETF that tracks the consumer staples sector (XLP), with the following possible explanatory dimensions:\n", + "\n", + "* US unemployment rate\n", + "* US inflation rate\n", + "* price of gold\n", + "* USD vs. EUR exchange rate\n", "\n", - "Let's bring this analogy of uncorrelated models providing \"perspectives\" to one involving data. Where the cylinder above was a function of space in the $X$,$Y$, and $Z$ dimenseions, let's consider house pricing data, with possible explanatory dimensions `Number Of Stories`, `Total area`, and `Year Built`. \n", + "The first step will be to import these macro indicators, which are all available as free [Quantopian Data Feeds](quantopian.com/data), and standardize them keeping in mind that:\n", "\n", - "The data was aggregated by user 'dmikebishop' on [DataWorld](https://data.world/dmikebishop/commercial-real-estate-for-sal). To use exterior data, store it as a CSV in the `data` folder in research and use the `local_csv` function to pull it into a Pandas DataFrame." + "* The specific inflation and unemployment datasets we are using have one month intervals, so time index intervals cannot be anything smaller than monthly\n", + "* The unemployment data is released at the start of the month after the relevant month and inflation rate data is released ~3 weeks after so we must shift both back a month from the asof_date to prevent look-ahead bias\n", + "* Gold prices must be shifted back one day from asof_date to prevent look-ahead bias\n", + "* Equity pricing data only goes back to 2002, so we can only consider data from 2002 on" ] }, { "cell_type": "code", - "execution_count": 105, + "execution_count": 295, "metadata": { - "collapsed": false, - "scrolled": false + "collapsed": false }, "outputs": [ { "data": { - "image/png": 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TU15dcHCwwsPDm72f7OzsFunHmdr6GNv6+CTG2BY0d7HHJXMAAFymT58+ysjI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\n6/bbb7c97rQ+MJygubnZWLBggfH8888bGzduNAzDMO69917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CpnUNHDjQwWndR15enkP2R3BwsPTBCbuv1xtER0erd+/eZseQ5LjPh7tifzTX1kKPa24A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\npCvIy8tz621w9/wS2+AK3D2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97v5dhn0dPnxYTz31lGbMmKFp06bpxIkTWrRokQzDUHh4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\npM8++0xhYWHVvy/r0qWLSktLlZeXp6tXr+rAgQP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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -341,56 +349,75 @@ } ], "source": [ - "# Pulling in DataFrame and dropping blank values\n", - "fields = ['Price', 'Number Of Stories', 'Total area', 'Type', 'Year Built']\n", - "data = local_csv('loopnetlistingswithbrokers (3).csv')[fields]\n", - "data = data[data != ' '].dropna()\n", - "\n", - "# Formatting values from strings with thousands separators into integers\n", - "data['Total area'] = data['Total area'].str.replace(' SF', '').str.replace(',','')\n", - "data['Price'] = data['Price'].str.replace(',','').str.replace('$', '')\n", - "data = data[[i.isdigit() for i in data['Price']]]\n", - "for i in [0,1,2,4]:\n", - " data[fields[i]] = data[fields[i]].astype(int)\n", - "\n", - "# Restricting the real estate to only multifamily properties\n", - "data = data[data['Type'] == 'Multifamily']\n", - "\n", - "# Using log price transforms the price distribution to a more normal one\n", - "# Normally distributed independent variables are a linear regression assumption\n", - "data['log Price'] = np.log10(data['Price'])\n", - "\n", - "data.ix[:, data.columns != 'Price'].hist(bins=10);" + "from quantopian.interactive.data.quandl import fred_unrate as unemployment_bz\n", + "from quantopian.interactive.data.quandl import rateinf_inflation_usa as inflation_bz\n", + "from quantopian.interactive.data.quandl import bundesbank_bbk01_wt5511 as gold_bz\n", + "from quantopian.interactive.data.quandl import currfx_usdeur as fx_bz\n", + "\n", + "import blaze as bz\n", + "from odo import odo\n", + "\n", + "# Start date dictated by sector ETF XLP\n", + "start = '2002-01-01'\n", + "end = '2017-01-01'\n", + "\n", + "# Sample period will be 2010-2014\n", + "s = '2010-01-01'\n", + "e = '2015-01-01'\n", + "\n", + "index = pd.date_range(start=start, end = end, freq= 'MS')\n", + "\n", + "# Migrating Blaze expressions into Pandas DataFrames and setting index\n", + "unemployment = odo(unemployment_bz, pd.DataFrame).set_index(['asof_date'])\n", + "inflation = odo(inflation_bz, pd.DataFrame)\n", + "inflation = inflation.set_index(inflation['asof_date'] + pd.Timedelta('1 days'))\n", + "gold = odo(gold_bz[gold_bz.asof_date >= start], pd.DataFrame).set_index(['asof_date'])\n", + "fx = odo(fx_bz, pd.DataFrame).set_index(['asof_date'])\n", + "xlp = get_pricing('XLP', start_date=start, end_date=end, fields = 'price')\n", + "\n", + "data = pd.DataFrame(columns = ['unemployment','cpi','gold','fx','xlp'],\n", + " index = index[1:])\n", + "\n", + "# Adjusting data along points mentioned above and putting into a Pandas DataFrame\n", + "data['unemployment'] = unemployment.shift().loc[index].ffill()['value'][1:]\n", + "data['gold'] = gold['value'].sort_index().asof(index).ffill()[1:]\n", + "data['fx'] = fx['rate'].sort_index().asof(index).ffill()[1:]\n", + "data['xlp'] = xlp.asof(index).ffill()[1:]\n", + "\n", + "# Finding first order differences; \n", + "# differences are more likely to be stationary and normally distributed\n", + "data = data.pct_change()[1:]\n", + "\n", + "# Inflation is already a first order difference of the consumer price index\n", + "# therefore we will leave it alone\n", + "data['cpi'] = inflation.shift().loc[index].ffill()['value'][1:]\n", + "\n", + "# Plot histograms for each variable\n", + "data.hist(bins=10);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Let's begin by attempting to model `log Price` using only `Year Built` as our explanatory variable. We'll also define a linear regression plotting function to make this step simpler as we repeat it for the other data dimensions.\n", + "A OLS fitted simple linear regression returns a single set of coefficients that minimizes the sum of squared residuals within the training set. This model is simply an estimate. It will usually have bias (difference betwen model expected value and true value) and variance (sensitivity to small changes in the training set). As we add more models, we should see the aggregate model have a higher $R^2$ as the model leaves less and less unexplained variance.\n", "\n", - "A OLS fitted simple linear regression returns a single set of coefficients that minimizes the sum of squared residuals within the training set. This model is simply an estimate. It will usually have bias (difference betwen model expected value and true value) and variance (sensitivity to small changes in the training set). As we add more models, we should see the aggregate model have a higher $R^2$ as the model leaves less and less variance in `log Price` unexplained." + "Let's begin by attempting to model `xlp` returns using four different models, each a simple linear regresion with exactly one explanatory variable. We'll also define a linear regression plotting function to make this step simpler." ] }, { "cell_type": "code", - "execution_count": 106, + "execution_count": 292, "metadata": { - "collapsed": false + "collapsed": false, + "scrolled": false }, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "rsquared 0.0190269927541\n" - ] - }, { "data": { - "image/png": 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XD530/PPSVVcVvaxOKMXwT6CB3UrrlwBAQRh+4AyrLgBqplFh1VlnM420hgaf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\nRERERCTEP1Yty/2VF4YbAAAAAElFTkSuQmCC\n", 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m/nKBNxNWfZ3UajCY0Nn5K+rrWxATY4FCkczL4hmR1EEhCMIzkZC2NRxwtg4V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\nsXdvLaqr+4+jVGaguXkvJk2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SCQB9OH06ARpNO4B2GAw6fPbZUbz7bg1SUtrxwAMjUVtb\n45VWu9NYT/prPaZWq4ZaLbPN32pv/xHnz9dzplnHj7ejqSkOPRfX7jKZjDh+vGtQX2CgXhqNJkgk\nMdzo6LRpwLRpMN69FHv3Oh6rzt2xensR3daG6JYWRGs0iG5pgbilBYaL70Xt7b7eDjZY6GfavyUm\nBj0KBXpGjGD/VSjQo1TCfPE94uJ4+ZvgCo8OVXZ2Nh577DFcfvnlEAqFtr/ffvvtfp1w5syZ2Lx5\nM37729+ivLwcqampiL04uU+lUkGn06GhoQFKpRIHDx7Eyy+/jLa2Npf7eIKvCzuW+DLpMgx4sm/r\n1lIwzFVISmKjVCZTMVSqNIwYoby4lkIHZs6UorDwOq+jjN5UFdTrjdiw4WvIZNnQapugVI6wVSIa\nP77Vp0pnpaWlqKlJs5uj5Nv+A+nu3g+L5d8AiGCx9KK7uwT5+b/z+3gAkJurxYULKpuNycnxXj8X\nsbgEv/xiwIgRckilvVi0KBlA/29i4DOsrg7vvIlI/02EE58WCg8DwRZRrnUKCK1W8eHZOWt/Q/md\nP3BABpWq34GSybTIz892s0d4fpPOdAOAk7+ZefFcB2Jt9/X6RiQmpqG6ugzTpsU72G+xiJCWxr7/\n3/89hJ6eGyAUjkRbmwX/+tdubNlyk1fncqex7j6zf645ObkoKuqvPpiT81uIxVKvNcvTyCdrRyw6\nOtjqt0lJEkybJh3UF7DXy9ras3j//UpMmjQBFRVNUCoLkJQUzYmOeltd2ek1WsTQxlRizRte9rtM\nJuDCBbaQR2Mjm9Ju/behwb/5ZO3t7KuqatBHOr0ece7aQ5mMHQlTqWyjYka5Al8eM+K8RYXEUaKg\njlwHqlMeHarm5maIxWIcP+64BoC/QjV9+nTk5uZiyZIlEAqFePrpp7Fjxw7Ex8dj/vz5WL9+PR59\n9FEAwKJFi5Ceno709PRB+xChx75hOnq0EZmZWYiOlkAgEGDChDFIS2PnYN1yixmFhbP9+tJ7yrn+\n05++QWlpLtLSZMjK+s2gSkS+wHXlm76+RADHAMQB0F18Hxjz5snx5ZelMBhiIJWaMG+e85ETK/bp\nEQADs7kFbPKA6WL6kcDptjRvgohkuNYpgLQq1PAh7dAbXOlGUVEZ1GoGNTXnIZGMQW2tGjk5uWFJ\nW3Sno87a/XvuScWaNcW2daz++tdLsXcve40WSztSU9lEtaioKDQ1yVyedyDuNNZb/bWfjrBxI5sJ\nYm+7JzylFg5cx2nePDkKC/McjqHXG1Fc3Ij2djFiY83QaC5AKr0Mo0ePQF0dA42mDdOmpXplUzBS\nW+2vUa2WoajIy5TFmBggPZ19+YNe7+iIqdX9zlhjo+/rkmm1rCNm54xpWw240l3FX3uefdan4iRc\n49GheuGFFzg/qVWErGRn90ehZsyY4bTM7MB9iNBj/6M1GhNRVlaF6dOngGEYpKWBk9ENTznXdXUZ\n6O1Vor1dhurqZsya5ViJyBe4rnzT02MEcA2sGdA9PaUBH3PZsjyIxdXQaACFQjCooR+IfafEZJIh\nK2sMpk1jK5F1dVUC0Drdls8dGILwRDB0CiCtCiWRUtrZlW6sWDEZW7eWwmwugMkkgFot975jyzHu\ndNTa7gOwtfu7dtVDpSrA6NGsFuzd2799RcVZVFWxhQwsFgtSUz2n8Ftxp7H+6K8/muUpcDhwHSdn\nbN9eDaNxCkymVJhMQEPDWUyZws6fjYvrgU7H3h9vbApGkY2wBUdjY4EJE9iXFwzKpOjqcnTABo6Q\n6fWeK/7as349Px2qRx55BK+99hrmzJnjdIHEgwcPBtMugofY/2jz8hQ4c+Y0ZLJKTsXPXcOg0YgR\nF2dGayvboOp0UX45AcGa/CyXJ6C5uQZADAAT5PKEgI/pq+jYd0rS089BqVwAwHlDHykdGIJwBenU\n0GEolHbmy6i/Ozus7X5nZxPGj291WGPK2fYbNlyNJ57YbRu92rDhattnoS4kYq9Z8fHd6OkRYOPG\nSrfn5iJwqNGIkZenQHl5M/R6IWJjtcjJYbNFcnIy0dx8ADKZd5kywfiORGxwNCGBfU2a5HKT3a6W\nj2EYNrXQ3hG79toQGj8Ylw7VX/7yFwDAJ598EjJjCH5j/6MViYQoKFBgxQr/Roe8OcfAhkGhMCMn\nJxPt7UcRHa1Eevo5FBbOdXM05wRrzZWMjD5otb3o7Y2CSNSLjIy+gI/pq2DZd0oMhnQUFVU47Gtf\n3GEodGCI4Q3pFMEn+NKxdWeHtd0vKTHb5gm5214uT8KWLc6j/qFev8xes7badbTdnZuLwCF7f4SY\nNi0VDMOgt1eKrKx+bV23bq7XjqSzex2oY2p/jSpVJQoLr/O8U4Tg8vkJBP0FpHJzw2vkRVw6VIqL\n5XftJ4kSw5tQjGi4O8fixWOwZs0BWCy9SE9nI2X+RMOCFUWcO/cSNDSUobMzFomJesybd0nAx/RX\nsI3jD2gAACAASURBVCKlBDFBBALpFMEnwtmxtW/zExJMGD36GDo7ZV5ptb/aHs4ROW/PzUXgcPA6\nnWmYOdO/Yzq710VFgTmm9tdYUqL1qPV8W8PTHZEU+PU4h4oYugQy+hEs3J3js8/OoKVlNHp6jGhp\nkeCzz87ggQdm+HyOYEURm5o6kZ5+C3Q6HeLi4nDhwu6Aj+mvYIU6ckgQBDHc8bVjyyUD2/zx48u8\nnl/sj7YPXAw4JyczpCNyoRwNDHSdTnfHArzXea4cGb6t4TlUoCWThzHWH4VWm42amjwUFVWH2yS3\nfPNNGzo6JqOn5xJ0dEzG/v1+lPQEGyEaP74MMlklxo8v42ykbcKEMZDLWxAd3QK5vAUTJowJ+JgK\nhdm2OKgvosGXXH6CIAgi+IS6zbcuBhwXlwydbiSamw+EdB5usHQ8HHir81z12QL9rlD/wjkeR6jM\nZjM+/fRTNDY24vHHH8eJEycwadIkxMSEdwFQInAi7UfR1xeFCxd00Ol6odXqMGKEf/GAYI20paUB\nU6cqoVQ2Ii1NibS05oCP6W8qhrvoHaUDEkMN0iliuBPq+VsajRhicbStiqxMNiGkOhKojnOpg1zO\ngXKn81z12QL9rvBlriDf8OhQPfPMM4iPj8exY8cAAOXl5di6dSteffXVoBtHBJdI+1HIZHowjBZA\nHxhGCJlMH26THGDneBWjsrIXFosIq1Zd7XknD/grGu4aaBquJ4YapFPEcCfUVVsD6T/wIajHpQ4G\neixvdZ6rPlug3xWqEOwcjw7VuXPnsG3bNixbtgwAcNddd+HLL78MumFE8Im0H8XEiePQ0dGCCxcM\nGDlSiokTx4XbJAe4muPFBc4aaL3eiF271CgpSYJQWIbcXHZh5mCPTPJBPIPFUL62SIJ0ihju+Bp8\nMxhM2Lq1NKijKq7aR66cmUDaXy4zdEKV7cNVn00qleC3v82y3buiomqf7l0kFYoIJR4dKpGI3cT6\nZdHr9TAajcG1iggJkfajGDVKgKlT8y6m1KVh1KiycJvkwK5d53DokBgmUzxiYhrQ12cOm0PljO3b\nq6FW50MoFKGtbQTKy8sxdWpe0Ecmh/KI2FC+tkiCdIrgA/YdfK1WjZycXN4GWPbt04BhrgrqqIqr\n9tGVA2K9f8ePt6O0tNRjJz+QKrhsQQ054uIsyMmRB6SDocr24bLPRtrFPR4noSxcuBC/+93vcP78\neTz33HO4+eabsXjx4lDYRhAOWCehxsae4uUk1J9+0sBguAkWy7UwGG7CTz9pwm2SA1YRy81NgVze\ngr6+9pDcx0ibq+cLQ/naIgnSKYIP2BcNUKvzeV3oqaMjNuhtl6v20VURBuv90+tzvCq6EEgVXKXy\nWsTFXYBO147m5r0B6WAkFsgg7eIejyNUS5cuxZQpU3DkyBGIxWK88soryMvLC4VtBAFg4LA+cMcd\nsU7XgAh3+pVQqIRQ2AuLhUFUlABCoTJk5/YGhcKMykoG0dEiTJ2qxPjxzSGJSEXaXD1fGMrXFkmQ\nThF8IJI6qUlJejBMcNsuV+2jq9Q1jUaM3t4+VFV1o7ZWjIoKDRYv7sCuXfVOdd3f9pctqCHFtGms\n/slkgoD6CpGW7QOQdgUDjw7V0aNHAQBTp04FABgMBhw7dgxjx461LapIEMFk4NB0be0uzJzpeTvr\nEHaoHK3MTB1OnTKht5eBSCRAZqaO83MEQmFhFmprv4ZMpg3ZnDm93giz2YSKir0AojF/fgIKC/mx\nqjkXRNo8xKEK6RTBByKpkzprVjy2bStGU5MMqalan4soeaOrrtpHVw6IQmHGoUMadHWlIT4+HkZj\nCtas+R4qVYHT1LRgVMEdLpB2cY9Hh2rz5s04duwYxo0bBwCoq6vDJZdcArVajX//93/H3XffHWwb\niWGOfdSvt7cPR4/2YOPGSlsjwDCsM/X55+0QCpuRm5uC6GiRLToYqlzhoqLrceed/4v6einGjDHg\nn/+8nvNzBIJUKsHixSrk53u32CMXWOdtXXIJK1zR0WW8nVPgD5EYmRyKkE4RfMC+k6pSVaKw8Lpw\nm+SSw4e7oVItxujRbNu8c2cZVqxI8np/d7o6MKvk4YfTvWr3CwuzUFz8LcTiJCQnS5GbOxEnT3Zg\n9Gjno35cV8ENd5ZLKCHt4h6PDtW4ceOwbt06ZGZmAgDOnDmDjz/+GB988AGWLl1KQkUElYGTR3t7\ne2EyKaDVZtsacQCoqcmDUFh2sdhCC6ZOVdqiTgPTMBoaEFB1I1eoVCPx7bdLUVJSgvz8/ICPNxSI\npBQYInIhnSL4gH0ntaREy+vOeEdHLJKSgrO4q79BTKlUgoKCNHz3nRxKZSrKyjRoamrEL7+cRF7e\nRIhEMZyMJrlyJsJVqGE4OXJDGY9FKSorK20iBQCZmZmoqqqCRCJBVJR/C6sShLcMnjz6f8jIGAOg\nvxHvL7aQBbm8HH19jhNDB06APXeunpPVxgnPeLsCPEEEAukUQfiGdQ4V4F/b7K5tDySQVliYBZWq\nBGfOHALQjGuuuRGAEmfOfBv0gg/hCgDaFzOhPknk4nGESqFQ4JFHHsGMGTMgEAhQVlYGsViMvXv3\nIiUlJRQ2EsOYgZNHT59uhEgUA8CxEe/uZhAdLcHUqXkYP94xqjRweD8mZjTMZu4bTV9Lvg4HKE+b\nCAWkUwThiKdRjwULFKiuDs7iroHMUbKmpstkMmi1bHr69OkyyGSdWLEiuOnq4ZpbRZkcQwOPDtVL\nL72EnTt3oqqqChaLBTk5OXjqqaeg0+kw01llAGLIEc7h6IEN3Pz5CVCrSwYVVnDXaR84vL91aylq\narhvNPtLvqagpiaN1nUA5WkToYF0iiAc8ZS+JpHEBNQ2u2vbuQikhcO58WR3sIKmVCRjaODRoZJK\npbjhhhtw9dX9FWDa29sxZsyYoBpG8IdwLgA3uIHLxalTGFRYwRd7gjVqEu4oE+VhE8MV0imCcCSc\nesRFIG3x4jFYs8b/KoT+4MnuYAVNKZNjaODRoXruuefw+eefQy6XA4Bt3YL9+/cH3TiCH0R6wxyK\nYwJAQoIWhw5dQFOTEU1NF7BokZbzc7jD2tj39vbh0CENiou/RUFBGjlWxJCHdIogHIn0UY9du+qh\nUhX4XYXQGYEGHYPVF/LUJ6FgaWTg0aH66aef8OOPPyImJiYU9hA8JNIb5lBhMhnx668laG0Vw2Qy\nw2QKrPH3FWtjX17eio6OVMTEpKOmZqJfUTRqwIlIgnSKIBzh26iHr5rijfPi6zEDzbax9oWA0BZZ\nCmeWEOE9Hssfpaenk0gNcwoLszB+fBlkssqgV9mJZA4f1iEh4QaMGHElEhJuwKFDoV3Y11p1Sa8X\nAgBiY81+R9Go6hARSZBOEYQj1lGPxx/PxooVk8MeEPNVU7ypEOvrMQMdYbL2hWJjT4W0LxTu6QSE\nd3gcoRo5ciTuvvtu5OfnQygU2v6+atWqoBpG8AcajvaWaA/vg4s1IllRoYHRmILc3Il+R9H42oDT\nd41wBukUQfAbXzXFmxE2+2P29vahuFgDjabSpTbYZ9uYzQZUVJzFxo3wWkusfaGSEjPy80M3QkRZ\nQpGBxxGqpKQkXHXVVRCLxRAKhbYXQVih0QyW+fMTkJTUhOjoFiQlNWH+/ISQnt/a2G/dehVuuUWA\n5OQ6v6NofF0/ir5rhDNIpwiC3/iqKd6MsNkfs6yMDSS60wb7bJvm5gNQKhdEhJZQllBk4HGEauXK\nlYP+9uKLLwbFGCIy4etoRqhZujQX0dHVOH68CdOmpaKwMDcsdnBRdINv+fdW6LtGOIN0iiD4TTA0\nxf6YEkkdMjNnA3CtDfbauHEjoNVGu92eL9DyI5GBR4fqu+++wyuvvIKOjg4AgNlsRlJSEtasWRN0\n44jIgIajWcKVDhAM+NqA03eNcAbpFEHwm2BX7N261YyaGnYepTfaQFpCcI3HlL/XXnsN69atQ0pK\nCt5++23cdtttWL16dShsIyIEGo4mQgV91whnkE4RxPDGV20gLSG4xuMIlUwmw7Rp0xAdHY2srCw8\n8sgjuPfeezF79uxQ2EdEAHwdzSDCD9dFJOi7RjiDdIoghgZ6vRG7dqlx4IDMJ83wVRtISwiu8ehQ\nmc1mHDlyBAkJCdixYwcmTJiAhoaGUNhGEG6him/8h9bPIEIB6RRBDA22b6+GWp0PlUoVsZpBfZPh\niUeH6m9/+xs0Gg2eeOIJ2///8Ic/hMI2gnALddb5DxWRIEIB6RRBDA2GgmZQ32R44tGhysjIQEZG\nBgDgvffeC7pBQ5WBEYusLFO4TYp4+NbwWp/x8ePtKC0tpagUaOIvERpIpwiCPwQyQqNQmFFZyb8l\nO3wh3H0TGiELDx4dql27duGdd96BVqu11fsHgIMHDwbTriHHwIhFbe0uzJwZbqsiG7511q3PWK9P\nQU1NGkWlwN/y68TQgnSKIPhDICM0hYVZqK39GjKZNmI1I9x9ExohCw8eHarNmzfj73//O0aOHBkK\ne4YsAyMWHR2xYbYo8uFbZz3cUSk+QhN/iVBAOkUQ/CEQLZRKJVi8WIX8/OxgmRd0wt03ob5IePDo\nUP1/9u49Lqo6/x/4a7gPoCKOoKIiKmGItzBJ3E1t1dSy2pTGXDHt5q7lWunXNLPavvWwTGst12+5\nmZTWilr2E4vUvKZ5xVTQRdEIFRQYuSjMwDBwfn9MMzAww1yYmXMGXs/Hg4fOzDkz7zMDn/e8z+dy\nevbsifj4eKe9oE6nw6JFi1BQUABvb28sW7YM3bt3N9lm+/bt+OKLL+Dt7Y2kpCRMmTIF27Ztw6pV\nq9CzZ08AwIgRIzB79mynxeVqjc9YhISoxQ7J40nty7rhMwY8d6gCkSdiniKSDrF7aMQm9neTtv7+\ni8ViQXXkyBEAQJ8+fbBy5UokJCTA29vb+Pjw4cMdesEdO3agQ4cOWLFiBQ4fPoyVK1figw8+MD6u\n0WiwZs0afP311/Dx8cGUKVMwbtw4AMDEiROxcOFCh15XbI3PWERHK8QOyeXa2jhew2dcXl6IqKib\noveYEbV2zFNE0uPKHpq29r3CEWL3kLVVFguqNWvWmNw+ffq08f8ymczhRHXkyBE88sgjAIDExES8\n8sorJo+fOXMGAwcORFBQEADgrrvuwqlTpwDAZGy8p2l8xiIjI0PEaNxDrHG8YjW4hs84I0OL+Hjp\n9JwRtVbMU0TisZRrXdlDw/lB1ondQ9ZWWSyoNmzYYPx/RUUFgoODAQDFxcXo3Lmzwy+oUqkQGhoK\nQJ/wvLy8oNPp4OPj0+RxAAgNDUVxcTF8fHxw4sQJPPPMM9DpdFi4cCHuvPNOh+Mg1xNrHK/YhRxX\n+SNyD+YpIvHYm2udcbKT84NIqqzOofryyy9x+PBh45nAl156Cffffz+mT59u9cm3bNmCrVu3Gn/5\nBUHA2bNnTbapq6tr9jkMZ/sGDx6M0NBQjBw5EqdPn8bChQuRlpZmNQYp9wRJOTag5fFVVOQjPz/Y\nOI43IuICMjIqXB7b6dOlUKs7GW+XlxciI8P1Y4jT0vKRnx8PmawTDh8W8NtvuzBpUoTLX9deUv69\nk3JsgLTjk3JsrsY85TpSjg2QdnxSjg1oeXz25tr6HCnDhQvN50hLsbnye4U9pPzZMjZxWC2otm/f\nji+//NJ4+7PPPsP06dNtSlRJSUlISkoyuW/x4sVQqVSIiYmBTqfTB+FTH0ZYWBiKi4uNtwsLCzFk\nyBBERUUhKioKgD5plZaWQhAEYxK0xJkTlZ0pIyNDsrEBzokvNrY/UlMbno0a55QeG2uxZWZmIje3\nq7HBjYq66ZYhePv2BSMiIgIFBQWIiIhAcHCF5FYqkvLvnZRjA6Qdn5RjA1yfRJmnXMMTfq+kGp+U\nYwOcE5+9udaQIw0s5cjmYnPV9wp7SPmzZWyOa2me8rK2QW1trUki8fKyukuzRowYgR9++AEAsHfv\nXiQkJJg8PmjQIGRlZaGiogKVlZX45ZdfEB8fj08//RRbtmwBAFy6dAmhoaFWkxSJyzCOd8GCGMyc\nOcBtjZ5SGY2oqCz4+WUiPz8dBQUCUlIyodFUufR1FQqt8Uw1V9Yhch/mKSL3M+Ta4OALiIrKsrr4\nQXM5Uq2uQkpKJlasuIC0tHyL+Vqs7xVE1ljtobrvvvswdepUxMfHo66uDkePHjWuZuSIiRMn4vDh\nw5g2bRr8/f3xzjvvAADWrl2LhIQEDBo0CPPnz8eTTz4JLy8vzJ07F8HBwZg0aRIWLFiA7du3o66u\nDm+//bbDMVDrZmhwU1IyUV09AVqtDLm5rp9LxVX+iMTBPEXkfvYuftDc6nMN52Pl5wcjNTWHCyuQ\nR7FaUM2ZMwfDhg3D2bNnIZPJ8Prrr2Pw4MEOv6CXlxeWLVvW5P5nn33W+P9x48Y1SYbh4eEmE5CJ\nrHH35FWu8mcdl7wlV2CeIpK+5gowLjbhOsy77mG1oAKAoUOHYujQoa6OhcipeHE76eGSt+QqzFNE\nnov52nWYd92jZQPNiSTM3vHd5Ho8C0lERI01zNcRERnM107EvOseNvVQEXkiXtxOengWkoiIGmuY\nrzMyKjgkzYmYd93Dag/VokWLmtz31FNPuSQYIk9mWKVow4ZSt6wq6InYa0iuwDxFZB+Nptq4qh7z\nVevGvOseFnuotm/fjk2bNiEnJwd/+ctfjPfX1NRApVK5JTgiT2IYp6xWd0JubleOUzaDvYbkTMxT\nRI758UcVBGE459W0Acy77mGxoHrooYeQkJCABQsWYO7cucb7vby80LdvX7cER+RJOE6ZyL2Yp4gc\nU1YWiJAQ5isiZ2l2yF94eDg+/vhjqFQqDBs2DMOGDUNOTg58fX3dFR+Rx+CFfYncj3mKyH4hIWrm\nKyInsmkOVcOhExqNBgsXLnRpUESeyDBOOTDwPMcpE7kR8xSRfcaOVXBeDZETWV3lr6ysDDNmzDDe\nfvLJJ7Fv3z6XBkXkiXhhXyJxME8R2ScgwJ/zaoicyGoPVU1NDS5fvmy8nZWVhZqaGpcGRUREZCvm\nKSIiEpPVHqrFixdjzpw5uH37Nurq6tCxY0csX77cHbERERFZxTxFRERislpQDRo0CDt37kRpaSlk\nMhlCQkLcERcRUauhVldh8+YcqFR+UCi0UCqjeeFKJ2KeIqni3z5R22CxoKqoqMCaNWvw66+/4u67\n78YTTzwBHx+r9RcRETViuEYZr/niXMxTJHX82ydqGyzOoXrjjTcAAEqlEpcuXcLq1avdFRMRUbPU\n6iqkpGRixYoLSEnJhEZTJelYeI0y12CeIilSq6uQlpaPFSsuID39OnS6agD82yfrpJTbyD4WT+Xl\n5+djxYoVAIB7770XM2fOdFdMRETNktJZX1tiUSi0uH1bgEwm4zVfnIh5iqRo8+Yc5OfHIyIiAlVV\nHZCVdRFDhgzk3z5ZJaXcRvax2EPVcNiEt7e3W4IhIrKFlHp8bInFcI0yXvPFuZinSIoatglxcQoE\nBNzk3z7ZREq5jexjsYfK8IFauk1tAyfUkhRJqcfHllgM1ygj52KeIilSKLS4cEEAAPj4eGPCBAVm\nzoyBWl2F1FTmU7JMSrmN7GOxoPrll18watQo4+2bN29i1KhREAT9B71//343hEdiY/czSZFSGY3U\n1CyTLyaMpe1hniIpUiqj8dtvuxAcXGHSJjCfkjXMJ57LYkH1ww8/uDMOkih2P5MUSanHR0qxtDXM\nUyRFcnkAJk2KQHx8jMn9zKdkDfOJ57JYUEVERLgzDpIodj8TkVQxT5EnYT4lar0sLkpBBHAyPRER\nkTMwnxK1XrwCIjWL3c9EREQtx3xK1Hqxh4qIiIiIiMhBLKiIiIiIiIgcxIKKiIiIiIjIQSyoiIiI\niIiIHMSCioiIiIiIyEEsqIiIiIiIiBzEgoqIiIiIiMhBLKiIiIiIiIgcxIKKiIiIiIjIQSyoiIiI\niIiIHOTj7hfU6XRYtGgRCgoK4O3tjWXLlqF79+4m25SXl+Oll15CcHAwVq1aZfN+RGJSq6uweXMO\nTp8uRWZmJpTKaMjlAWKHRUR2Yp6itsiQw1QqPygUWuYwIju4vYdqx44d6NChA7766iv89a9/xcqV\nK5ts849//AP33HOP3fsRiWnz5hzk5sZBrY5Fbm4cUlNzxA6JiBzAPEVtkSGHVVTEMIcR2cntBdWR\nI0cwZswYAEBiYiJOnTrVZJu3334bgwYNsns/IjGpVH6QyWQAAJlMBpXKT+SIiMgRzFPUFjGHETnO\n7QWVSqVCaGgoAP0frJeXF3Q6nck2crncof2IxKRQaCEIAgBAEAQoFFqRIyIiRzBPUVvEHEbkOJfO\nodqyZQu2bt1qPOMhCALOnj1rsk1dXZ1Dz23rfhkZGQ49vztIOTZA2vFJMbbo6Gr89lsaAgMDIZOd\nRHS0QpJxSjEmAynHBkg7PinHJmXMU82TcmyAtOOTcmxA0/gMOaysLBAhIWpRc5invXdSwtjE4dKC\nKikpCUlJSSb3LV68GCqVCjExMcYzdz4+1sMICwtzaL/4+HgHIne9jIwMycYGSDs+Kcc2YoQhvjFi\nh2KWlN87KccGSDs+KccGSDuJMk9Z5gm/V1KNT8qxAZbjGzFChGAa8dT3TgoYm+NamqfcPuRvxIgR\n+OGHHwAAe/fuRUJCgtntBEEwdj3bsx8REVFLME8REZE93L5s+sSJE3H48GFMmzYN/v7+eOeddwAA\na9euRUJCAgYMGICHH34YGo0G5eXlmDRpEl5++WWL+xERETkT8xQREdnD7QWVl5cXli1b1uT+Z599\n1vj/tLQ0s/ua24+IiMiZmKeIiMgebh/yR0RERERE1FqwoCIiIiIiInIQCyoiIiIiIiIHsaAiIiIi\nIiJyEAsqIiIiIiIiB7GgIiIiIiIicpDbl00nImqt1OoqbN6cA5XKDwqFFkplNOTyALHDIiIicqvG\n+TA6ulrskFyKPVRERE6yeXMOcnPjUFERg9zcOKSm5ogdEhERkds1zoe7d6vEDsmlWFARETmJSuUH\nmUwGAJDJZFCp/ESOiIiIyP0a58OyskCRI3ItFlRERE6iUGghCAIAQBAEKBRakSMiIiJyv8b5MCRE\nLXJErsU5VERETqJURiM1NctkDhUREVFb0zgfRkcrxA7JpVhQERE5iVwegJkzB4gdBhERkaga58OM\njAwRo3E9DvkjIiIiIiJyEAsqIiIiIiIiB7GgIiIiIiIichALKiIiIiIiIgexoCIiIiIiInIQCyoi\nIiIiIiIHsaAiIiIiIiJyEAsqIiIiIiIiB7GgIiIiIiIichALKiIiIiIiIgexoCIiIiIiInIQCyoi\nIiIiIiIHsaAiIiIiIiJyEAsqIiIiIiIiB7GgIiIiIiIichALKiIiIiIiIgexoCIiIiIiInIQCyoi\nIiIiIiIHsaAiIiIiIiJykI+7X1Cn02HRokUoKCiAt7c3li1bhu7du5tsU15ejpdeegnBwcFYtWoV\nAGDbtm1YtWoVevbsCQAYMWIEZs+e7e7wiYiolWOeIiIie7i9oNqxYwc6dOiAFStW4PDhw1i5ciU+\n+OADk23+8Y9/4J577kFWVpbJ/RMnTsTChQvdGS4REbUxzFNERGQPtw/5O3LkCMaMGQMASExMxKlT\np5ps8/bbb2PQoEHuDo2IiIh5ioiI7OL2gkqlUiE0NBQAIJPJ4OXlBZ1OZ7KNXC43u+/x48fxzDPP\nYNasWfjvf//r8liJiKjtYZ4iIiJ7uHTI35YtW7B161bIZDIAgCAIOHv2rMk2dXV1Nj3X4MGDERoa\nipEjR+L06dNYuHAh0tLSrO6XkZFhf+BuIuXYAGnHJ+XYAGnHx9gcJ+X4pByblDFPNU/KsQHSjk/K\nsQHSjk/KsQHSjo+xicOlBVVSUhKSkpJM7lu8eDFUKhViYmKMZ/x8fKyHERUVhaioKAD6pFVaWgpB\nEIxJ0Jz4+PgWRE9ERK0d8xQREbWU24f8jRgxAj/88AMAYO/evUhISDC7nSAIEATBePvTTz/Fli1b\nAACXLl1CaGhos0mKiIjIEcxTRERkD5nQMBu4QV1dHZYsWYK8vDz4+/vjnXfeQXh4ONauXYuEhAQM\nGDAADz/8MDQaDcrLy9GlSxe8/PLLiI6OxoIFC4zPsWjRIgwYMMCdoRMRURvAPEVERPZwe0FFRERE\nRETUWrh9yB8REREREVFrwYKKiIiIiIjIQSyoiIiIiIiIHOTRBZVOp8OCBQswbdo0JCcn49q1a022\n2b59O6ZMmQKlUomtW7cCAIqKivD0009jxowZSE5Oxvnz5yUVHwCsW7cOjzzyCJKSkpCVlSWp2AD9\nhS+HDRuGEydOOD22lsRXW1uLRYsWYdq0aZg6dSpOnTrl1LiWLVuGqVOn4vHHH0dmZqbJYz///DOS\nkpIwdepUrFmzxqZ9nM2R+JYvX46pU6ciKSkJu3fvllRsAFBdXY2xY8fi22+/lVRs27dvx8MPP4zJ\nkyfjwIEDLovNkfjUajXmzp2LGTNm4PHHH8ehQ4dEiU2r1eLll1/GlClTbN6nrSkpKcEzzzyDGTNm\nYNq0aU2ugSUmV7enLXXs2DEkJia6/O/PXlL//c7OzsbYsWPx5Zdfih1KE+7KR/aqqqrCCy+8gOTk\nZCiVSuzfv1/skJpwR650xPHjxzF8+HDjd+633npL7JCacEo+FzzYtm3bhDfffFMQBEE4dOiQ8MIL\nL5g8rlarhfvvv1+oqKgQqqqqhAcffFAoLy8X3nnnHSE1NVUQBEE4deqU8NRTT0kqvpycHGHy5MlC\nXV2dcP78eeGjjz6STGwGCxcuFB599FHh+PHjTo+tJfF9/fXXwuuvvy4IgiDk5OQIU6ZMcVpMx48f\nF2bPni0IgiBcunRJUCqVJo9PnDhRuHHjhlBXVydMmzZNuHTpktV9nMmR+I4ePSo888wzgiAIQmlp\nqTBq1CjJxGbw/vvvC1OmTBG2bdsmmdhKS0uFcePGCWq1WiguLhaWLl3qktjsje8vf/mLcOnSPDth\nbwAAIABJREFUJWHjxo3C+++/LwiCIBQWFgrjx48XJbb//d//FTZu3ChMnjzZ5n3amvXr1ws7duwQ\nBEH/3jz55JMiR1TPle1pS+Xl5QnPPfecMHfuXGH//v1ih2Mk9d9vtVotzJw5U3j99deFjRs3ih2O\nCXflI0d89913wqeffioIgiDk5+cL48aNEzmiplydKx117Ngx4e9//7vYYVjkrHzu0T1UR44cwZgx\nYwAAiYmJTc6enTlzBgMHDkRQUBD8/f1x1113ISMjAwqFAmVlZQCA8vJyhIaGSiq+ffv2YcKECZDJ\nZLjzzjvx/PPPSyI2wzZHjx5Fu3btcMcddzg9rpbG99BDD2Hx4sUAgNDQUJSXl7skpj59+uDWrVuo\nrKwEAFy9ehUhISEIDw+HTCbDyJEjceTIkWb3cTZ74zt69CjuvvturFq1CgDQvn17aDQak+vqiBkb\nAFy+fBm5ubkYOXKk02NqSWw///wzRowYAblcDoVCgTfffFMS8d177704evQoOnXqhNLSUgDua+PM\n/X7Pnz8fo0aNsmuftmbmzJl44IEHAAAFBQXo0qWLyBHVc2V72lJdunTB6tWrERQUJHYoJqT+++3v\n749PPvkECoVC7FCacFc+csTEiRPx1FNPAdD/nXbt2lXkiEz9+uuvLs+VLSGVz9EcZ+Vzjy6oVCqV\n8YuCTCaDl5eX8ar2jR8H9AlBpVIhOTkZ6enpmDBhAl5//XXMmzdPMvEVFxcjPz8fBQUFePrppzFr\n1ixkZ2dLJraamhr83//9H1544QWnx+SM+Hx8fODv7w8A+Pzzz/Hggw+6JCYA6NixI1QqVbPxNLeP\ns9kbX1FREby8vCCXywEAW7ZswciRI11yIVJHYgOA9957D4sWLXJ6PC2NLT8/HxqNBn/7298wffp0\nHDlyRFLxjR8/Hjdu3MC4ceMwY8YMl72H1n6/Db9b9uzTFqlUKkyZMgWffPKJy9tWe7iyPW0pPz8/\nsUMwS+q/315eXpJ979yVj1pi6tSpWLhwIV555RWxQzGxfPlyl+fKlrh8+TLmzJmDv/zlL/j555/F\nDseEs/K5j5PjcpktW7Zg69atxj8uQRCajDWvq6tr9jkMFfK6deswfvx4zJ49GwcOHMC7776LDz/8\nUBLxyWQyCIKAuro6fPrpp8jIyMCrr77aZA6TGLEBwNq1a/H4448jODjY5P6WcGZ8Bl9++SXOnz+P\njz/+uMXx2fqatjzmzrM09sT3448/4ptvvsG6detcHZbZ1zf32Lfffou7774b3bp1s7qPu2MTBAFl\nZWVYs2YNrl27hhkzZmDfvn2SiW/79u3o0qUL1q5di+zsbCxduhRbtmwRNTZn7uOpGrZ1hvZ+7ty5\nGDFiBLZu3YqDBw9i0aJFbvs7tDU2d7SnjsYmdW3p99tZ3J2P7LFp0yZkZ2djwYIF2L59u9jhABAv\nV9oqMjISzz//PCZMmICrV69ixowZ2L17N3x8pFGCOCufS+NobJCUlISkpCST+xYvXgyVSoWYmBhj\n70XDDygsLAzFxcXG24WFhRgyZAh27dqFF198EQAwfPhwvPHGG5KKr3PnzujduzcAID4+HgUFBZKJ\nbdu2bfjpp5+wfv16XLlyBZmZmVi1ahX69OkjifgAffLdv38/1qxZA29vb4fjaiwsLMzkTGNRURE6\nd+5sMZ6wsDD4+vpa3MfZHIkPAH766SesXbsW69atMxbKUojt4MGDuHr1Knbt2oUbN27A398fXbp0\nwfDhw0WPLTAwEEOGDIFMJkOPHj0QFBSEkpISlwytcyS+U6dO4Y9//CMAoF+/frhx44bxi6i7YnPm\nPq2Fubbu+PHjKC8vR4cOHXDvvfdi4cKFkokNcF17ag9LsUlRW/79dgZ35CNHZGVloVOnTujatSv6\n9euH2tpal7X59jpw4ACuXbvm8lzpqPDwcEyYMAEA0KNHDygUChQWFiIiIkLkyPQUCoVT8rlHD/kb\nMWIEfvjhBwDA3r17kZCQYPL4oEGDkJWVhYqKClRWVuKXX35BfHw8IiMjcfr0aQDA2bNnERkZKan4\n/vjHP+Knn34CoO8mdcWYekdj++qrr7Bp0yakpqZi1KhReP3111tUTDk7vqtXryI1NRWrV6+Gr6+v\n02PauXMnAODcuXMIDw9HYGAgACAiIgKVlZUoKCiATqfD/v378Yc//KHZfZzNkfgqKirw3nvv4eOP\nP0a7du1cEpejsb3//vvYsmULUlNTkZSUhDlz5rgkQTgSW2JiIo4dOwZBEFBaWgq1Wu2yxOpIfA3b\nuPz8fAQGBrpk6Iwtv9+CIJicMXXn34Qn2L17t3FVrgsXLhjPMkuBK9tTZ5LSGXn+fjvOXfnIESdP\nnsT69esB6Id1ajQaSRRTAPDBBx+4JVc6Ki0tDatXrwYA3Lx5EyUlJQgPDxc5qnojRoxwSj6XCVJq\niexUV1eHJUuWIC8vD/7+/njnnXcQHh6OtWvXIiEhAYMGDcKuXbvw6aefwsvLC8nJyXjggQdQXFyM\nJUuWQKPRQCaT4dVXX3XJAguOxgcAH330EQ4fPgxA31szaNAgycRmsHjxYjz66KO4++67nRpbS+L7\n4IMP8P3336Nr167GM/KfffaZ07qW33//fRw/fhze3t547bXXcP78ebRr1w5jxozByZMnsWLFCgDA\n+PHjMXPmTLP7xMTEOCUWZ8S3efNmrF69Gr169TK+X8uXL3dJEe/Ie2ewevVqdO/eHY888ojT43I0\nts2bN2PLli2QyWSYM2dOk8UXxIxPrVbjlVdewc2bN1FbW4sXXngBw4YNc3tss2bNwo0bN3D9+nX0\n6NEDM2fOxOTJk7Fy5UqcOHHCLX8TUldaWopFixZBrVZDq9ViyZIlGDhwoNhhAYDL29OW2L17Nz78\n8EMUFRUhKCgIHTt2xNdffy12WADc2+bb68yZM3j11VdRUlICb29vdOjQARs3bkSHDh3EDs2t+che\n1dXVeOWVV3Djxg1UV1dj7ty5klwAwtW50hGVlZWYP38+ysvLIQgCnnvuOeMICqlwRj736IKKiIiI\niIhITB495I+IiIiIiEhMLKiIiIiIiIgcxIKKiIiIiIjIQSyoiIiIiIiIHMSCioiIiIiIyEEsqIiI\niIiIiBzEgoqIiIiIiMhBLKiIiIiIiIgcxIKKiIiIiIjIQSyoiIiIiIiIHMSCioiIiIiIyEEsqIg8\nQL9+/VBYWNjk/u3btyM5OVmEiIiIqK1asGABRo8ejcOHD4sdCpEk+IgdABFZJ5PJHHqMiIjI2b7/\n/nvs3LkTPXr0EDsUIklgDxWRCD7++GMkJiYiKSkJX331Fe677z5otVq89tprGD9+PB544AG8++67\nEAQBAEz+ffPNNzF69GgolUpcuHBBzMMgIqI2Jjk5GYIgYObMmUhMTDSOnkhLS8PUqVNFjo5IHCyo\niNzs0qVLWLduHdLS0vDll18iPT0dMpkMKSkpKCoqQnp6Or755hucPHkSO3bsMNn34MGD+Pnnn5Ge\nno4NGzbgxIkTIh0FERG1RRs2bAAA/Oc//8Hs2bOxfPlyaDQa/POf/8Rbb70lcnRE4mBBReRmJ06c\nQEJCAjp16gQ/Pz9MnjwZgiDg4MGDeOyxxyCTyeDv749JkyY1GZ9+8uRJjBo1CgEBAfDz88OECRNE\nOgoiImqrBEGAIAhITk5GXl4eXnzxRTz44IPo27ev2KERiYIFFZGb3bp1Cx06dDDeDg8PBwCUlJSg\nffv2xvvbt2+PmzdvmuxbXl6O4OBgk22IiIjE4OXlBaVSiQMHDiApKUnscIhEw4KKyM2Cg4OhVquN\nt4uLiwEAnTp1QllZmfH+srIyKBQKk33bt2+PiooK4+2SkhIXR0tERGSeRqPBp59+iuTkZLz33nti\nh0MkGhZURG42YMAAHDt2DGVlZdBqtfj2228hk8kwevRobN26FXV1dVCr1di+fTtGjRplsu/gwYNx\n6NAhVFVVQaPRYOfOneIcBBERtXkffvgh7r//fixevBhXrlzB/v37xQ6JSBRcNp3IzQYOHIhHHnkE\njzzyCLp164aJEyciJSUF06dPx5UrV/DAAw/Ay8sLEyZMwP333w+gfmn0++67DwcPHsT48ePRuXNn\njBo1CsePHxfzcIiIqI2RyWS4evUqdu3ahR07dkAmk2HJkiVYuHAhEhISIJfLxQ6RyK1kgmE9Zjda\ntmwZzpw5A5lMhldeeQUDBgwwPqbVarF06VJcvnwZW7dutWkfIk924MABrFq1Ct98843YoRBRA8xV\nRERkC7cP+Ttx4gTy8vKwadMmvPXWW3j77bdNHl++fDkGDhxo1z5EnqSkpAQJCQkoKCiAIAhIT0/H\n4MGDxQ6LiBpgriIiIlu5vaA6cuQIxowZAwDo06cPbt26hcrKSuPj8+fPbzJvxNo+RJ4kNDQUL730\nEmbOnInx48ejvLwczz//vNhhEVEDzFVERGQrt8+hUqlUiIuLM97u2LEjVCoVgoKCAMDsuFtr+xB5\nGqVSCaVSKXYYRGQBcxUREdlK9EUpHJnCZes+GRkZdj83ERE5X3x8vNghtIirchXzFBGRNLQkT7m9\noAoLC4NKpTLeLioqQufOnZ2+j4EnJfGMjAzG62KeFrOnxQt4XsyM1/U8sWhwZ67ytM/TUZ74u+so\nHmvr1ZaOt60da0u4fQ7ViBEjjNfOOXfuHMLDwxEYGGiyjSAIJmf2bNmHiIjIWZiriIjIVm7voRoy\nZAj69++PqVOnwtvbG6+99hq2bduGdu3aYcyYMZg1axZu3LiB69evY9KkSZg5cyYmT56M2NhYk32I\niIhchbmKiIhsJcocqpdeesnkdkxMjPH/69evN7vP/PnzXRoTEXkmQRBQXV3doueoqqpyUjTuIeV4\n/f39jRei9nTMVUTkLM7IVWKQcr5xlCvylNuH/BEROVN1dXWLklT//v2dGI3rSTneln4WREStlSe2\nj1LON45y1ecg+ip/REQt5e/vj4CAALHDICIisoi5qvViDxUREREREZGDWFARERERERE5iAUVERER\nERGRg1hQERE52ffff4+kpCRMnToVH3zwgUPPsX37dkyZMgVKpRJbt25t8viNGzeQnJyM6dOn48UX\nX0RNTU2z+x07dgyJiYk4cOAAAKCurg7JycmYMWMGkpOTcf/992Pt2rUmr/H4449j9erVJsc1ZMgQ\nXLp0yaFjIiIi6RAzV23atAlTpkzBtGnTsGvXLgD6i6E//fTTxrx0/vx5APp89d5772H48OFmY2iY\nq1QqFZ5++mkkJydj3rx50Gg0Dh2XvVhQERE5kUajwYoVK/D5559j06ZNOHLkCC5fvmz3c6xZswaf\nf/45vvjiC3z++ee4deuWyTarVq1CcnIyNm7ciJ49e+Lrr7+2uN+VK1ewYcMGDB061Li/l5cXNmzY\ngC+++AIbNmxAZGQkHn74YePjmzdvhk6nM94+duwYjh49ijvvvNPBd4aIiKRCzFxVUlKC9evX4z//\n+Q9SUlLw2WefQavVYv369Rg3bhy++OILvPTSS3j//fcBAP/+97/Rq1cvszE0zlWffPIJxowZgw0b\nNmD06NH44osv7HtjHMRV/oiodVm1CvjxR+c+55gxwLx5Fh/etm0bfvrpJxQVFWHlypXYvn07AgMD\nAQAhISEoKysz2X7evHkoLS0FoL82iZ+fH9atW2d8/MyZMxg4cCCCgoIAAHfddRdOnTqFUaNGGbc5\nfvw43nzzTQDA6NGj8dlnn6FXr15m90tMTMTq1auxePFis/EfOXIEvXr1Qnh4OACgtLQU3333HZRK\nJW7cuAEAGDhwIBISEpCcnGzz20ZERBa04VwVGxuL3r17w9fXFwBwxx134PTp01AoFMYYysvLERoa\nCgCYMWMG5HK5scAyMJer8vLy8Oc//xkAkJiYiPnz52P27Nl2vImOYUFFROQEBQUF2LRpk8l9Fy5c\nQEFBAQYPHmxy/6pVq5p9LpVKZUwkABAaGori4mKTbaqqqozJqFOnTigqKsLNmzfN7ufn59fs633+\n+edYsmSJ8faKFSswf/58k7OVcrm82ecgIiLpEztXFRcXo1evXrh48SLKysrg6+uLM2fOYPjw4UhO\nToZSqcS2bdugVqvx1VdfAbCcf8zlqujoaOzfvx+xsbH4+eefUVJSYuUdcQ4WVETUusyb1+wZOlcZ\nMGCAye3ffvsNCxYswMqVK+Ht7d2i5xYEwaHHre0HAIWFhaiqqkKPHj0AACdPnkRAQAAGDhxo9/AP\nIiKyURvOVe3bt8f8+fPx17/+Fd27d0ePHj0gCALWrVuH8ePHY/bs2Thw4ADeffddfPjhh2afy1Ku\nmj17Nl577TU88cQTGD58uE150BlYUBEROYHhDBygn4Q7d+5cvPfee4iJiWmyrbVhFGFhYSZn+QoL\nCzFkyBCT5wgMDIRWq4Wfnx8KCwsRHh5u036NHTx4EPfcc4/x9p49e/DLL79g6tSpuHnzJmpqatCz\nZ0889NBDNr4TREQkVWLnqrCwMADAxIkTMXHiRADAk08+ie7du2Pbtm148cUXAQDDhw/HG2+8YfE4\nmstV//znPwEAp06dQkZGhj1vj8NYUBEROdmSJUvw+uuvo1+/fmYftzaMYtCgQVi6dCkqKiogk8nw\nyy+/mAzJA/TJZufOnZg0aRJ27tyJP/7xjxg4cCBeffXVZvdrfLYuMzMT9913n/H2yy+/bPz/tm3b\nkJ+f36SYctcZPyIich2xclVtbS1mzZqFTz/9FEVFRbhy5Qri4uIQGRmJ06dPIzY2FmfPnkVkZKTJ\nczXMPZZy1ZYtWwAASUlJ+PbbbzF69Gi73hNHsaAiInKi3377DadOncKHH34IQRAgk8kwa9Ysuxp1\nf39/zJ8/H08++SS8vLwwd+5cBAcHIzs7Gz/++COef/55zJ07Fy+//DJSU1PRrVs3/PnPf4a3t7fZ\n/Xbv3o0PP/wQRUVFOHbsGD766CN8/fXXAIDi4mKTMfCWbNy4Eampqbh27Rqef/559OnTB2vWrHH4\nfSIiIvGInavGjx+PqVOnoq6uDm+//Ta8vLwwe/ZsLFmyBOnp6ZDJZFi6dCkAffF0/vx5VFRUYNKk\nSZg4cSL+9re/mY3pT3/6E/7+979jy5Yt6NmzJ5RKpVPeL2tkQis+1ZiRkYH4+Hixw7AZ43U9T4vZ\n0+IF3B9zVVUVACAgIMBtr0nmWfosPPH32F3a0nvDY22d2tKxAo4fL3OVNLgqT/E6VERERERERA5i\nQUVEREREROQgFlREREREREQO4qIUROTxqqurxQ6BoP8c/P39xQ6DyCnU6ips3pwDlcoPCoUWSmU0\n5HLOfyHHMVeJz1V5igUVEXm0ljaM586dQ//+/R3a95tvLuLatWjIZDIIgoDu3XPw6KN3tCgea1oS\nr6v5+/uzoKJWY/PmHOTmxkEmk+H2bQGpqVmYOXOA9R2JzPDEtlHK+cZRrspTLKiIRMQzoC0nk8la\nvGqSo/sXFPhDrZab3HbHCk5cJYrI9VQqP8hkMgD6dkal8hM5IvGZy1lkG2fkKjF4Ysxi4BwqIhEZ\nzoBWVMQgNzcOqak5YodEdlAotMYLDQqCAIVCK3JEROQs/PtuijmLyDz2UBGJqLkzoGp1FdLS8rFv\nXzB7ryRKqYxGamoWz9YStUJS/PsWe1SD+ZzFQpOIBRWRiBQKLW7fFoxzcBqeAd28OQf5+fGIiIjg\n+H2JkssD+JkQtVJS/PsWe15XczmLqC3jkD8iESmV0YiKykJw8AVERWWZnAHl+H0iImpI7LzQXM4i\nasvYQ0XkJpaGalg6u6hQaHHhAsfvExGRnlg9RKb5C3juuUgOQSdqgD1URG5i72RepTIaEREZPBNI\nREQAxOsh4mIURM1jDxWRm9g7VEMuD8CkSRGIj49xR3hERCRxYs3rEnuoIZHUsYeKyE24BC8REXki\n5i+i5rGHishNpLgELyD+MrzO1JqOhagt4t+wNLkyf/Ezp9aABRW1GlJvlF0xVMMZxyz2MrzO1JqO\nhagtEutvWOr5wx6uOBZXDjVku02tAYf8UavRFifNOuOYW9PY+NZ0LERtkVh/w60pf3jasbDdptZA\nlB6qZcuW4cyZM5DJZHjllVcwYED9mYiff/4ZH3zwAby9vXHvvfdizpw5OH78OObNm4fo6GgIgoCY\nmBi8+uqrYoROEtYWG2VnHHNrulBjazoWEh9zlfuJ9TfcmvKHpx0L221qDdxeUJ04cQJ5eXnYtGkT\nLl++jCVLlmDTpk3Gx99++2189tlnCAsLw/Tp03H//fcDAIYNG4ZVq1a5O1zyIO5ulKUwRMQZxyzV\nuV2OaE3HQuJirhKHWH/DzmhLG+aEiop8xMb2F2XYoKcVKGy3qTVwe0F15MgRjBkzBgDQp08f3Lp1\nC5WVlQgKCsLVq1cREhKC8PBwAMDIkSNx9OhR49k+oua4u1GWwrhvZxyzWMvwukJrOBYpFOrEXCUW\nsf6GndGWNswJ+fnBSE3NkcyxSLldaQ3tNpHbCyqVSoW4uDjj7Y4dO0KlUiEoKAgqlQqhoaHGx0JD\nQ3H16lVER0fj8uXLmDNnDsrLy/Hcc88hMTHR3aGTxLm7UW5uWIU9yaslia4tJiIpfzFwBikU6sRc\n1da0tC1Vq6uQnq5CaelNBAbWIjS0zuxQO3e0X+aOJSUls0XtSmtvd4laSvRV/po7m2d4rFevXnj+\n+ecxYcIEXL16FTNmzMDu3bvh42M9/IyMDKfF6g6M1/WcFXNFRT7y84ONwyoiIi4gI6MCAJCWlo/8\n/HjIZDJcuCDgt992YdKkCLPPY23bQ4d+Rnp6AY4cqUJRERAWJsPw4f6YOLEbAgL8nXIszmbve6zR\nVOPHH1UoKwtESIgaY8cqLB6bPe+tq+J1pdOnS6FWdzLeLi8vREaG6ZAdKcXbVrgyV7Wlz7O1Hmta\nWj5u3OiA27f1RVRpaSl69rxozAkNt8vLG4zcXA00mkB8+20q/ud/ol3SljdsV8+fL0f37iHw8fEG\nYL5daU7DdjcrS4Nvv01Fr14Rxvbals/VnnZe6lrr77E5belYW8LtBVVYWBhUKpXxdlFRETp37mx8\nrLi42PhYYWEhwsLCEBYWhgkTJgAAevToAYVCgcLCQkREWP8SFR8f7+QjcJ2MjIw2H6+rz4I5M+bY\n2P5ITW0Y6zhjrPv2BZv8fgYHVyA+Psbs8zS3bUZGBi5daoesrDuQnx+Gqqpw1NRUICsrF9HRMkn2\nXDjyHqekZEIQhiMkRF+c5uRYPntqz3vrqnhdKTMzE7m5XY2FelTUTcTH178XUovXFp6YkN2Zqzzt\n83SUJ/7u2mrfvmD84Q+ROHcuB2q1H4DTePnlR5rkr337glFa6g9B6AG5XIbKyhrk5NSYtHfOyoMN\n21W5/Cxu3vTFkCFdzLYrthyf4ff49OlMVFZOREhIZwiCgN270/DGGw/ZFY+1dl7KWvPvcWNt7Vhb\nwu3Lpo8YMQI7d+4EAJw7dw7h4eEIDAwEAERERKCyshIFBQXQ6XTYv38//vCHPyAtLQ2rV68GANy8\neRMlJSXGsevUunjScq+GYRULFsRg5swBJgnPnqvKW9tWpfKDRuMPnc4HMpkMOp03NBp/m1duUqur\nkJKSiRUrLiAlJRMaTZW9h+py9qxKZc9764mUymhERWUhOPgCoqKyOEFbJMxVZA+FQgsfH38MHjwA\nw4ffgcTEQLNFkEKhRWWll/GESVBQTZP2zll5sGG7Ghd3BwICzjrcrjRsdysrfREUVAdA316XlQXa\nHY8tqw96Qu4iMnB7D9WQIUPQv39/TJ06Fd7e3njttdewbds2tGvXDmPGjMHrr7+Ol156CQDw4IMP\nIjIyEgqFAvPnz8fjjz8OQRDwxhtv2DTcjzyPpy33aok9E5ytbatQaCGXC/Dx0UGnE+DjUwu5vBoK\nhcymWKQ8J8dwJvbECRWqqqoRF3cHfHz8my2SWvuKUG1xXpwUMVeRPRq3S9HRCovbHTq0F3l5vREU\nVIPY2L5QKC6ZbOOsPNhwtT8fH39MmNAVjz0Wic2bc/Cvf+XZ1fvV8PgiI39FWNhYAPqTWiEharvj\nseVkmJRzF1FjorT0hiRkEBNTP1xn6NChJkvTAkBQUBA+/vhjt8RG7tdweEN29mWEhfWEn5/co3sf\n7PlSbG1bpTIaWm0WfH0zcPVqDXr08MO4cWFQKuMs7tOQpeTs7OGVhuc7fboUmZmZNj2fIWH27VuL\nrCwVLl06iAkTujZbJLHgIHdhrmqdXDG0vHG7ZGn4kFwegI8+uq/BcPFLZk+iOWPZc3Mnn1JTHStS\nGh6fRhOJ1NRsq8WjLfEYmPtMWlJYchENcjeeOiPRNTwLFRbWG0VFu9GvXx+X9T60pKEVo5GWywPw\n7LND8eyzju1vKTk7++yf4fnU6k7Ize1q0/MZEqavrw+GDOmC4OByzJzp+HwoIiJrxO75sOUkmjN6\n4c29jjN6vywVj9byY+P9DEP66k+mjoWfn6/xM1Eo4HBhKfZnTG0PCyoSXcMG3s/PF/369cGCBa77\nUt2ShtYTG2lLydnZwysdeT5PuwAlEXk+qQ8td2UvvCvbXHvzY8Pt8/IEqFQlGDw43PiZPPdcpMOF\npdQ/Y2p9WFCR6Nz9pbolDa27GmlHhs9ZYik5O/t9NzwfAGi1NcjOvowVK9BsT15rnw9FRNIjlRM5\nYox4cGWbq1L5QaerNq50mJ19vdljaphPg4JqUFmpXyfN8Jm0pLCUymdMbQcLKhKdu79Ut6ShdVcj\nvWFDFr7/3g8FBcE4cKAMaWk/YtKkSKcmXGe/74bnKy8vRFGRFmFho1FRIW/2TGUzl/aRLI7NJ/Js\nUjmRs3lzDi5e7Ivz5y+hstIXhw7txUcf3efS9sRckeKMNk2trkJ29mUcOVIAna4TOnfuCbm8A1JT\ncywWRQ3zaWxsXxQV7UNwsH64/6RJPYzDAR2JSSqfMbUdLKhIdO5eZKAlDa07Gmm1ugqbSYnPAAAg\nAElEQVTr1l2GSvUgbt26Dbm8M7TaPYiLi3PqEENnv++G58vI0GLfvmBUVMgBNN+T54lDKD0xZiKq\nJ5WFbVQqP5w/fwmlpYZhb52aLUBcxRlt2ubNOb+v/HcN1dUKXL16CP7+A5GeroJSWWXTCIWlS+uL\nyZSUzBbFJJXPmNoOFlTU5rSkoXVHI715cw4qK8NQWxuI6upaCIIOHTr4etQ4cFt78jxxnLsnxkzk\nUWbPBgyr5N1/PzBzJhDd+noY9Nek8m1wTao6UdoTZ7RpKpUf/Px8ER0diP/+V4aamh7Q6cJQVVVo\nsUhsLp+ynSVPw4KKSGJUKj9ERbVHTk4hfHxuQybzQ69e7T1qHLi5njxzw0o8cZy7J8ZM5FGKi+v/\nv3On/sdg8GBg1iwgMRGQ2XYtPqmqvyZVJwQF1SE2NhQKRZHTnt/WoXzOaNMMz9G/fydcvPgbfHyu\noGPHGvTvfwdUqjyHn4/tLHkKFlREEqNQaDFwYCx8fC6hXbtbCAzMRWLiQHTrZv/V7cVi7syjuSEc\nnjjO3RNjJvIo33wD3LoFbN0KrF8PaDT1j50+DcybV3+7Sxd9gTVpEuDnWb0YTa9JVeTU9sTWoXzO\naNMaPkdi4mWEhY1u0fUk2c6Sp2FBRWSBWIsPGC6+GBrqh4qKm3j55SlmX9fTFkcwN4TDE8e5e2LM\nRB6nfXvgySf1PwCg0wG7dukLrNzc+u1u3ACWLdP/GMyaBTz+OBAa6t6YHdDS9qS5PGDrsLmWxKBW\nVyEtLR/79gVDoQCeey4SQGSDItGxYojtLHkaFlRE0CeFjRvPYc+eWwBq8Kc/hUImk+HatbvcvvhA\nw0SSkVFhsUiS0uIIDZN6RUU+YmP7N4mbQziIyGE+PsDEifofQL9E6C+/6AusI0dMt12/Xv9jMGEC\n8MQTQN++7ovXTZrLAy1tcy0Vaw3vz86+jNrawYiM7Gny+q2tGLIlx1HbxoKKCPqk9N13ESgruwsA\n8N13mQgIuIk775TupFhbzz7a2pNlT49X42212mrk58dDJpMhPz/Y7CRkDuEgIqeRyYC77tL/GFy5\nAmzYAGzbZrpterr+x2DIEP1CF61gHpa5PGBon69fB/Ly0nD7tj98fGSIiAiFRmN+xT1zLBVrjS/I\nW1OjQWSke/KkWCMzGh6zpRxHbRsLKrJbSy8668oG0dHnVqn8oNH4GBOTRuOPgIAaCILzelTMxSYI\naPa+5s6ENTz7qNVqLF5I19aeLHt6vBpvm52922rxySEcRORSPXsCS5bofwD9PKwtW4CUFNN5WL/8\nov8x6NpVX2B52Dwsw7WfcnO1KC29ig4dItCnTz42brxtPMFVWtoZtbX5qK4WsGrVTaxb9wOefroH\npk+33sNi6aRd4wvyXr8eCADN5kln5X1HRmY099q2xsVVB8kaFlRkN0ODplZ3Qm5uV5uHmhkarvT0\n66iqGoi4OAVu3/Z26lA1R4fB6a/KrkN1tf5Ks3J5Nf70p1D4+TmvR8VcbABM7tuw4RSOHy9EXl5v\nBAVpERLS3+KZsIY9PtnZlxEWNhYVFb5NjtvWRGBPwmi8LeDr1OKTiKjF2rcHnnpK/wNYnod1/brp\nPCyZTF9gSXweluHaT6dO/YbS0nsBnEZY2Fjs2bPPeIJLo/FBQcEt1NR0QlXVOGg0auzYcRu+vtZ7\nWAwn7XS6amRlXURAwE2kpGjRvn21yQV5gc0IDtY1myedNUTdkcKmude2NS5Hhk962jxnahkWVGQ3\nR8/UGBqu0lI/VFeH49y5IgweHO7UMz2OxqZURqOm5hx+/PG/MMyhSk6Oc2rjZym2hvft2XMLJSV3\no6amM0pLBZSW/oS4uHCzz9ewx2fFCqC0tBanT2dDrfZDdvZ1Y+NtLhHYsoR5u3a3LV6pvvG2Y8a0\nh6+vvriLiLgApXKcze8Lkw4RuYW5eVinTul7sBrOwxKEpvOwAODtt/XXxZIIw7WfOnZsD7UaqKgI\nxPnzJfDx8TKe4JLLdRAELWpq/CEIddBoqvDf/1YjIMDyBXcNDCft0tOvAxiIvn1jkZvrje7dTyEq\nqv5k4wMPRGPEiBirsZrLf/a2//VFXi2yslQICMhDSkrz+zX3vcDW7wwNT2DamuOkNM+ZXI8FFdnN\n0KABzXfxN2ZouAIDtaiuBtRqb6f3Zjg6CVcuD8Azz8TjmWfsf01DQigoAH799Sp69+6Obt1kTRp4\nc7FptVr89NMNaDQ+kMt18PXVICioDqWl+u00Gn+bjkGh0OKnny6irEzfWFdVdTD2bJmbu5Sa2rSh\nb7xdTY3MYjJo+pz1w0eaW0jDHCYdIhKFTAbEx+t/DCzNwwJMhxMCQLduwLffAl5ero/VDENOKS29\nBbW6M+RyX5SUdEbv3mpjwfPggxU4dEiDkydVuHmzE/z8QiGT1aCqqhNSU3Pw2GPRFgsaw0k7/fDz\nLsbXLS8PxoIF9QVUhuEizA00LpQa9mo1zM0bNmTh++/9oNEAcrkArTYLzz471OIx1xd5KgCd0Lfv\nvcjN9W82bzT3vcDW7wy2LhbVEIcJti0sqMhuhgatvLwQUVE3bR4KV3/hv2hkZekXfYiKUjh1cQIx\nFj4wFAQZGddx8WJnHDlyFn37dmmSGMzFtmFDFoAiAP4AqhEUpEVERCjOny9CZaUXQkKyoVQqrcag\nVEYjPf0I/P1vIjCwFv37K6BSlQMwP3fJliXMV6y4YDEZOHM+FJMOEUlG43lY164Bjz0GaM180S4o\nAIYNM71v506gUyfXx4n6nBIergKQg5CQ7mjf/hzuuKOXSfs8fXp/bNiQhX/9ax9qaxXo1as94uL6\nQ6XKs+mEliMnKhs/b+NeLcPF3tetuwiV6i74+mrRuXM09uz5Cc8+a/l564u8C6ioqC/qmssbzX0v\ncOV3Bq5s27bYVFBdvHgRly5dgkwmQ0xMDHr37u3quEjCDA1aRoYW8fG2f6lu2HD9+c8yKJXDnT60\nS4yFDwwFQW6uBtXVvaHTRaKs7A7s2bPbmBgsDWu4dasdhgypTwp+fkC3btkIDdVvFx1t2/A3uTwA\nEyYokJvbyabG25aGXqHQoqSkBufPl6Cy0guRkZeh0US2+DOzdOay8Th9Dv0jezBPkUt07w78/HP9\n7aoqYNo0fU+WOb8PCeynVgOBgcCaNU2LLieRywPw2GPROHToKnS63ggKqkFsbF9063apyXbPPjsU\nfn7+xiLH0O6rVH7Q6apx7lxOk+HiBvYUHYb2/euvS+HtXYT+/TvB19enSa8WoL/Ye0XFPaitjUJt\nLVBcnImICN8mz2XLsPPm8l1z3wtc+Z2BK9u2LVYLqnfffRd79uxBXFwcBEHAypUr8eCDD+KFF15w\nR3zUikhxlbeWLBXeeI4SoB+37utraNjrE4PhbJ1OV4ufflIhPf0gJkzoig4dTJNCt24yk/fI3FAK\nS+xpvG3ZVqmMxty5u1FZqU/UYWGjnbJUrKUzl43H6XPoH9mKeYrcJiAA+Oab+tuCAPz1r4CltnrO\nHNPbTz7Z9L4WMCxMoVKVoLxci0OHvka7doOQktJ0BV5Lw78bDhevrAzG3Ll70a9fH5M8N3PmAGMO\n/Ne/8izmS0P77u2dhZKSzjh3rhiDBoWZLXhUKj/06ROAixcrodN5wcenGmPGtG/yXLYNO5desSLF\n7zzkOlYLqmPHjuG7776Dr6/+y6FWq8XUqVOZqMgqT1hswN6lwi9e7GfssTl0aC8++ui+34funUJg\n4G8oLT0LmawdgoPzTBKDoRfr3LmbKCsLh79/JHJz70BEREaTYRCOsqfxtiVByuUB6NevD7p3t21Y\nha0aD/EznLlsPE6fQ//IVsxTJBqZDPjkE9P7vvoKeOst89t/9pn+xyAiQj9fy8F5WIaFKQYPDsfp\n05morLwf1dWdkZurXzXWz8/PJL+Yuz5gw+HitbUy5OX1RvfuMQ6tiGdo3/v3j8a5c+dQW1uKqKgi\ns7lNodBiwIDO8PbW59Ru3fIB9MCKFRegUGhRUCDYPOxcra7CJ5+cxN69JQB8MWZMe5uWhidyFqsF\nlUKhgI9P/Wa+vr7o3r27S4Oi1kGKiw1oNNUmK9ddvw6b5++oVH44f74EpaVhv1/QsLexx8bPzw9j\nxz5kLLa6dj2B6dPvM+5r6MVSq70BAIGBWshkMty61a7JMAh3svYZWRv2Z65otsbSUA2ONydHMU+R\npEybhuyYGMQbFrs4fx6YMcP8tvn5TYcEpqYCffrY9FIN283KSl8EBdUBqF81tl+/Uc3mYEEA2rXT\noKREv9BUZaUX2revMT6HpRXxdLpapKerfp/LVH+9REM8vr4BGDQoDlFRlvO+vpepfoh7TU0PXLt2\nlzHe/Px0REQMaJITzOWdzZtz8P33figrGwsA2LGj0Kal4YmcxWpB1bFjR0yePBn33HMPBEHAiRMn\n0LNnT6xatQoAMG/ePJcHSZ5JiosN/PijCoIwvFGDHWfTl3iFQovKSi/jtkFBNSYXOjScJQSA4OA+\nZodaZGerUFXVCf373yGJosHaZ2Rt2J+5gmyAlfxlaaiGJwzhIGliniJJi40FTp6sv11RAYwaZXn7\nxgsR3XcfsHy5hU3r283IyF8RFqYvKARBAFBjNQfrhwyOhkp1CZWVvtDpTiI2drLxOSytiJeVpV9l\nr6IiBvn5wc2uKmuJtYWQ+vTpga5dmz6XubyjUulXCjTsr9H4SOI7B7UdVguqHj16oEePHsbbo5pr\nBIgakGKPQ1lZIEJC6hts/RLnts87OnRo7+8X3dVP/lUo9JN/rR2rIXEolVVITc2BSpXX7OsZzsCd\nPl36+zwqAbdutXP60Elb4m5u2J/5gqz5z9nS0ESONydHMU+RRwkONi2wBAG4+27L2+/dCwxttJT4\n7/s3bDc1mkikpmYb81lERCjy85vPwfqTgXIMHqx/Dn//GnTteqnZFfEKCoDr1zMRHByH06cz0bFj\nkDEvtKQdb5yPunZFk2F9KSmZvy94kYX+/aPh6xtgjFUuF1BdLfweh04S3zmo7bBYUNXV6buN51iY\nPOkl0nUXyHNIscchJERtvOChuUUgmiOXB+Cjj+77vSDyg0JxyabeFUfmkhnma50+7Yddu7zh738d\nEycOxu3bji/WYC4OWz4jS0WXWl2F7OzLyMsLRVBQHWJjQ80mMHfOpfOEeXvkPMxT5CrObEusPpdM\nZlpgAU0LqMYaP370aJNiRqOpsrl9b7jKateuCjz3XCQEAQ3yXf0crJSUTHTteh/KysJRWgqUlh7E\nyJGh9r4tTVjLR/ULXhT9vuDFOcTG9kV29mX06dMDISG/wtf3Kry9AzFmTHtMmtTH4sXpiZzNYkEV\nGxtrPPPckOHL6H//+1+XBkaeT4o9DmPHKpCT43iR50jviiNzyQzztW7d6orqai2qqnQ4d+4mBg8O\nd3gYg6U4rMViKck1HipSVJSBpUvvw/nz51p8/I6S4rw9ch3mKXIVZ7YlDj1X4wLrgw+AL7+0vP09\n95je/vhjyIcOtbl9N7fKKgCzcatUfoiLU+DcuaLf5wWroFQmNH88NrD2naF+wYtOOHeuGLW1pSgq\n2oewsLGorvZFr16mc7ZSUjKZD8htLBZU2dnZFncynBUk8jQBAf7NNqiu6OFwZC5Zw/laPj46AFqo\n1d5mh200jLl9+wpYGh7o6Jw2S0mu8VCR4GCZ2ffKnXPppDhvj1yHeYpcxZltiVOe68UX9T8GublA\nUpLl7f/6V9PbUVHAli1NNqu/UK75VVbNxa3v1fJG//6dkJWlgkZTgy++yIKXl37VVlf1BtUveOGD\nQYPCEBVVBJUqHBUVvk1iNByDre87RzdQS1kdDzFv3jyUl5cbb//222+YNm2aS4MicgbDeOsVKy4g\nJSUTGk2V1X0MZxIrKmKQmxuH1NScFsehUGh/nyDcdJKvJUplNCIjT8DH5zyio/PRt281OnbMRFRU\nlsVhEBUVMfjuuwh8952f2fgdicMZx+Xs13VGTNS6ME+RszmzLXFJuxQVpe/FMvycONH89rm5+mGC\nDX+sxGgpbqUyGlFRWcjO3oMrVzJQWtoDH39ciG+/7eTU3NmY4XWDgy8Yc2Fz760977srcj+1LVYX\npRg5ciSmT5+OF154AQUFBdi8eTMWLVrkjtiIWsSRFehc0cNhachcc2fEDPO13n13F4KDY35/fIDV\nHiCNxgeAPwBAp6tGevp14/M/9FAPbN/uvDltts6RM1yna8+eWwBqEBERCo2myiVn/1o6b49nKT0T\n8xQ5mzPnALtlPnEL52HNqBOwYc6/UVwWBIVCi0mTeuDrry8hO3s3DNd1Uir7A9Dnp8cei8aaNZko\nKxuEW7eKUFvbF4WFGRg8uItxoQhHWMuL5q6jZem9ted95+gGaimrBdWjjz6KoUOHIikpCSEhIdi6\ndSvatWvnjtiIWsSRFehcsTKhpSFzGzZk4fvv9Uu9yuUCtNosPPvsUJP9Jk2KQHx889epahizXK4D\nUA0AyMq6CGAgKiq64PZtAdu3O3f8uC1z5AzJcc+eW6iq6oS4uDuQn+/vsrHsLZ23Z3auwxNxQHEx\nkJ1d/1NUBMTHAyUlgEoFhIQA/foBlZWARgOo1fofS7c1GuvBLF+uXy6ZrGKeImdz5hxg0eYTNyqw\naub+HeU79kCnk8HHR0BoxwB4eelzpJeXDE98/KxxW9U/NJCN/jfuvHMcBEGAr2+WycmlzZtzUFFx\nD8rLQ1FR0RGC8At0ugCcOZOF+Ph4h3OnvfPNmntv7XnfpbgqMXkWqwVVWloa1q5di6VLl6KoqAhP\nPPEElixZUn/BOiKJMndR2uHDQ5rdx50rE+7dW4KysrGQyWSorhawZ89uPPus9f0aaxjzgw9WQBAE\n3Lp1AQEBN9G3bywA2864NT4zOGlSD6SlXW1Rb40hOZaW3kR1dSecO5eFwYMHmMaSlwf88AOwcydw\n5Yrdx99S/dRqIDAQADC+sAp1tfXH6OVdBay2cMyN5+/s3u3cwE6dYkFlI+Ypau2c0Xv+ZfwzyA1d\nZSwaBvv9P/x521uorRNQWlplUmjpdDI88MPfjft6eVcB++KBzz8HoD9h2adPAK5eLQHQA76+kQgM\nDMbVqycwZYq/1dxp6XjE6imS4qrE5FmsFlTp6elYv349FAoFAP31PV555RVs2rTJ5cERtYS5i9Lu\n3r0bI0ZY3qfhGS21uqrJkrHOHf7la+W2bSydhUtJ0aIs4zcMOJeKftnb4O+vATbJLT6P+qYGY6vl\nkAEQANz+n3KM8WmHKk016upkKPyfavTs0d54RtMScwVKsroGulpfeMmqEHQ8wGoszmTuy4KlY/Dx\nEVBdC+N74OMj2PdiXl76Yw8MBORyICjI8dthYS0+9raCeYo8nbWCyRmrDqpUftDpanHu3E3culWD\n9IpqZE9ej8uXryIsbDT8ff3x9L+HoaRUAx8fNG0Lz50zDhOceVODqVUBSGj/JcrL1QgOLkN0dAy6\ndcu1KS5LxyNWT5EUVyUmz2K1oFqzZo3J7d69e+M///mPywIi12sr80TMXZS2rCzQ5v2tJrCiIuDg\nQeDwYeDQIf3FGe2wWqVGeZkv6upk8PIS0CGvBhhaH19tnYCuN8pxwzvAaiFgzow6ASWGQsJfv39z\ndDoZDM8uA1BT4w1dTTV0tfoiS1vtg5LSKig62V4IGQoUudwHGk0NZF5a+NsQizOVllah+vdC8Vpo\nLH6N6YJhsycCgwYBHTvi/7d393FR1XnfwD/DAMMIKo4IKiqNQiiKYJSkuNmDWVpuu3dxsbdaaXtZ\nrWW26qWWubXburaFtV7r9up2vVq22u58Wl+31GplZls+pIupoKmgyCrIw8iDDgMMyLn/mGacGWY4\nM2dmzsyBz/v14lUD55z5ngP+vvM9v4dzuqjI1pMR3dKKj52KaPTAfxs9DfMUKZ1YvvFHz01cnBlf\nf21AY2MCqquLIQhT8e23KjQ3D4bBUIbMzHT8+cl/ISbmDJ55Jgkfby7F/av/ty3/ADduULWbgY6O\nq/iq48do7QAiTFFQF6uwb85Gl+/t/LmjqkpweT7sKSKlEi2oXHH13A9SDkU8q8dksgwFu3jRMgzs\n3/++8frqVY8PM+9Ki+3DtABAhUbgm+6H/Vl5NfxLgoE6LVQq+54Tx0KloaEV5vZoRCICbdeB+oYW\nr4qZsDCVbfvr9sWVm+LMuXcmIuI6zG3httfqMAEdHSL/9uPjYcjIQPQzzwDDhrksUOQu3gvyz8Bo\nvFFUx8ScwcQ7Xc9L87ImphDGPEVKIlYwifXceHKjNC8vBbt2/RMaTRIiIq5gwIA0mEyNiI6+juZm\nywgJ67FtPTbzShyOcWrmfOiqi6ECEBGhRXQfE/pozQhTdyI8XMATGxcCm+z+7W3YANx+e5fPHZWV\nu5CYmN7lfHpLT1FvubHdm0gqqHy1du1aHD9+HCqVCi+++CLS7ZZeO3DgAN566y2o1WrccccdWLhw\noeg+5J0rtWpozEb0u3oJMcZqDDx/HDB9DVy5YplgX1dn+W99fbfHsR/aFap0A6JQ39BiKySiNJ7/\nyfs8/EuEfcHjin3xogJQF6tH3ML/BUyfDgwb5tV7vW/3gENBEBwefmjlXPz8+MfDsXz5AVRU3Ibo\n6E6kpelw882nxR9KXFSEpB/iC4Xk6M0QEn/cbGCi7DmYq0guYu2UWM+NJ22XVhuFGTOGoLz8Zhw/\nbkZ9fRj69LmOtDQdamuLEBOjEu0V+vTulTBOTEV7u+Vh80MbP8VLZ3+D+EEa1yMonn0WwI0blFVD\nsvDxrP+DUaOGY8iQ3tsTpYgb2+QVjz9dCoJgW88fAMLCRB9h5dKRI0dQUVGBjz76COfOncOqVasc\nxrmvWbMG7777LuLj4zF37lzcd999qK+v73afkHL9uqV3xZOVvpxej6iosMyhcP65nx9Q+bhTr41G\n0wJ8L898Frk5Fy3NJpOrjYDJk4EpUyz/HToUQPCHf+0uKMb+/TokJibaiqAxEh9K7Hz3s7JSQEFB\ncZdtnRv0P/7xbrt5ZLWKTHpyL53LRBk8/spTQC/IVRRSxNopsZtT7tou57xgfXyGRiPg/PndGD58\nCC5eLMLIkcM8ugFkLfxOnryC+vpBgG4CXn7gK+Tk1Fvi6+wEJk7ssp/1BuXQy0VYsPFWaDR2Iy6c\nl3vvBbhMe88jWlBt2rQJ77zzDpqbmwFYEpZKpcL3338v6Q0PHjyIadOmAQBGjRqFq1evorm5GdHR\n0bh48SJiY2ORkJAAwPJskYMHD6K+vt7tPiGhvR2YNMnnw/SRqcfHudfGL/NZ+vUD4uK6fsX+MLxu\nxAjLV79+vr+XHW97A+zny7g9notCI5Axudv/8mWgrm4P9PoJGDpUhby8lG6P3d0Heee7n+Xll2A2\nzxD90O+PHiZvr4e/e3jkXjqXiVJ+/s5TQA/NVRSyfB1u7K7tcs4Ljo/PGI+CgmJ0ds6A2axCeXn3\nN4BMpla0t5tx+vQ+lJcbMHy4HmPHjkNdXf2Ndi4szOXzsHQDonDliglXr10HICAyIhydnYKlV8v5\neVnffguo1V3eWywvuNpGENDtfsEaUcBl2nse0YJq+/bt2LlzJ4b+cNfeVwaDAePGjbO9HjBgAAwG\nA6Kjo2EwGKDT6Ww/0+l0uHjxIhoaGtzuExLUauDmm4GzZ73bT6t1WNnLZDIhevhw6SuDRXi2SlwY\ngDjvz7ILseLEn9w1es7J4v33jyIyMlJy4+iP3gVfj2G//6BBOgwdWm/bv8Bu6J7zsbv7IO989zMq\najja2uT50O/qevzHf6RIKgwDzR8Topko5efvPAX00FxFIcvXds9d2+UqL9jn0yNHDEhOvo6IiHDR\nXLBlSykuXboFY8ao0NpaDaAWERFRtnbObXHyr38hDMAnP+Sve/a+hKhzn7qfF5yd7fh661Zs+coo\nen1cXUMA3e4n9jzIQOHiGz2PaEGVlJTk1yTlTOjmtoy7n3W3j7OioiKvY5Jk6VK/HMbjp/CYzZav\nxka/vK9Ucl3fwsJKVFZmQaVS4cwZARcufIZZsxJx7FgDTKaBtu0OHryApKTbu2znaczOx2tqqkFR\nkXcfiH09hv3+KpUKx47d2N/dsVta2vDNN6W4fDkcWm0Hhg9X4dq1Q7h06SJiY0249944pKdrYH2w\n8YULlais1Nk+9CcmnkFRkdGr8+yO/TV2FfOFC+Uuf59i57hnjwGNjX1s5xQVpfF7vJYpL5brdOrU\nSa+PlZLShgsXCm1xpqTE+f3fiWztmkIEOk8Bgc1Vven32RPP1V3b5M25+iP3uGq7jMZKVFbGOLT1\nr79+xtb+VleHobq6DKmp/URzgX2MAwdex6VLpWhsrEVioqWde/31zxza9bNnP0FkZITtutTVhaO9\nfSA+GPMMMOYZ9OlzCo8+OgCaixehf/FF9yf2wAO4+0oHOjstxddXYx7Dd00Ztutjvf5ffAGEhTVg\n5MhhiIiIQlNTDQB0e123by+DwTDTdn22bfsHsrLEF7Txx9+xr7lGLj3x32wgiBZUqampWLp0KSZO\nnAi1XRfsI488IukN4+PjYTAYbK9ra2sxaNAg28/q6upsP6upqUF8fDwiIiLc7iNGSQ92LJKxx8cf\n5Iz3yy9jkJh4ozCKiTEiKysVxcXFKC8fYmsMm5r6utzO05idj5eYeBnFxd71eDkfQ6+/gqws8TuN\nN4b6dcJoNEOlakBdnRnp6WakpY2FVhvl9tgFBcVIS/sPAGVobo5ARcURTJkyG5GRERAEAaWljr1C\nQ4cORWJiNZqaYn44r+l+G+bwzTcHcOqUBl98cRVAO7TaVgwdOsgWi15/BQZDpNvfU3fnKAiTEBur\nsp2TP3quAvF33N2zznyltHYCCHxC9neeAuTNVUr7fUqlxL9dT7hqm9LTzV6dq7Xd6+i4jpISA6Ki\nOlFcHOk253g6VC0tbazT8xSn409/qrC1v4MG6XDmzF40NWkBtOO224ba8o2rGK+bccgAACAASURB\nVM+eHYBTpyx5JilJi7Vrp+DUqZPIysrCV18Vo64uHCaTGn36XEdDQ3+MHXuP7bq0te1CYqKL3JiV\nBfzkJzfeyMU8rJaWFrS1RUAFYFrZ/8UDF99F3DeWAqtcPQjC/f/AwIG1qK8fhIaGk8jI0EOvvwIA\nOHt2EE6dqkdzcxiSkswO5zdgwFW0tfW1xTRgQILo762n/h270tvO1ReiM3Zra2sRGRmJY8eOoaio\nyPYlVU5ODj799FMAwMmTJ5GQkIA+P8wbSkxMRHNzM6qqqtDR0YF9+/ZhypQp3e5DvUNcnNl2t9d+\nGFVeXgr0+hLExJyBXl+Ce+7RudzOU3l5KRg6tAjff/8ZTp/ehwMHKnH2bDKMxlSUl4/D5s2lHh3D\nPiZPu/KtwxWSk+9AVdVJnD/fH1ptLOLj77W9r7tjGwyRiIzUIjMzHTk5o9G//whERlqGgFqHcViP\nbzSmorIyCxERkVi2LBXz5qX7dcz4nj0GfPJJIqqr70R19b2oqxuC2trPHWJ29/sUO0fOTSJX/J2n\nAOYq8pw/2iZru1dW9jWAWiQn39FtzrFvz7vbzjqH1L6tt29/w8M1iI0FRo++E2PGTEdlZZbbY+Xl\npaC29ks0Nw9GdPQAh9wEAOfPX0R9/SCYzXGorx+Ef//7isN1GTVqOPT6EkREnEBl5S5cvmwpRlta\nWh3fyDoPy+5rwKgh0GhaEKZuhUbT4jD3W1t1EU/9+Tb86duZePfEBLyxLxf6pBPIy0v5IebP0dzc\ngOjoasTH3+UQ87Rp/RAbW4PISANiY2swbZp/53lT7yHaQ7V27Vq/vuGECRMwduxY/OxnP4Narcav\nfvUr7NixA3379sW0adPw8ssvY8mSJQCABx98EElJSUhKSuqyD/Uu7sYbOy840NLS6tO4ZK02ChqN\nBqNH3wuVSoX9++vQ2Gh54KGnidLdIghidxStSTkiIgoDBgxHTc1ltLZG4NSp04iJEbo9tvO8nYQE\no21ivrVgMRgi0dFxHSdPXoHJpMbp0wbk5bX6fYGIxsY+aGkJtyXS9vZ+GD26H5Ytu9FT2N34cU/P\nMZBzk7j0ubL4O08BzFXkOX+0TdZ2z2BwfG6eu5wjtYizX1gCaMeUKdE4frwDhw4VQRDaoNcPQ5Sb\npk6rjYJePwzV1ZdQVnYdpaVlGD3aiJSUvgCAkSOHwWA4CZMpEn36mKFWRzvkoSFDgHnzLKMNzOYZ\naGsTXwjDSr1nj+Pc7w8/BN58E4DdI05UKmj7RECj6cC8t38O/PC879/WtKJgzjdojYq1XTuruXPH\nIiLCvq0f69F1JHLmtqB6/vnn8Yc//AFTp051+YDEffv2SX5TaxKySk290XjceuutLpeZdd6HehdP\nV2rzx6p09okqOrqzywMPpRKbdGyflBsaLqK9/Q60twP19dE4f343gPFuj+1coCxePBk7d954PWvW\ncKxYcQAHDkTg+vVoDBrUH1rtQGzeXNrt9ZIyUTo21gSttgNtbdYisA1xcY5tiJTfk5yTeLn0uTIE\nMk8BzFXkGVdtk9Q5MZ4WZ55u53xzqL3dbFtYQhAEHD++CxUVo3HtmqU9PXv2BAYPrgTgur0rL7+E\ns2d/hLa2GAiCgPPnd+Hzzw3IyQGGDlUhI+PG8w4TE9sQGenZQhlemz3b8gXLI072/PkQ7nzjWZcr\nF4eHC3j0vWmOj4q55wNgwoSQeFYi9QxuC6qXXnoJAPDhhx/KFgyRvzknk5SUNtF97BNVdw889LYX\nQyyJ2CflUaM0aGu7hrq6Vuh0JowaNbzbmF0lhXnzYm3/X1BQjPj4u6BSHUV7+0CYTEWYOvVuGAwV\n3R5XSuK79944JCZWYs+e7wG04557dMjLGye6nxg5Ex+HFyoD8xSFAn+2TZ7cOHLuZequjXW+OXT6\n9D6MGXOjbaupiYFO1x8tLbVob1cjMrIeI0cOs72Pc44bNWo4Dh6sxfXrbYiIuA6dbgQaG2vcxD7O\nZU7092gDrTYKP3vuTuC5khvfFATgttsAuHlUzIIFjgd5+mngP//Tpziod3NbUMXFWTpX7SeOEymN\nczK5cKFQdMEA56SwevXdLpOCJ70Y9gnp9OlziI8faVucwTmJ2CflggIzysuH4PLlyxgyJB5DhtT6\ndB2sc6xSUpLR0BAPjUaF8HCNaCKTkviiojSYM+fGMIrISOUtG86lz5WBeYp6Gk+KM/vlywVBQGRk\nidubec43h4B2h2F4CQlG1NUJtmeqxcYOxNChKtv7OOe4IUOA5ORoNDYOxPXrnaivP4tTpwwoKChG\nXl6KR4WlLKMNVCrb87Bsj4p57z3gv//b9fbvvGP5skpOtgwr9OHh4FJwuLlyic6hIlIy52TS2Cg+\nQdzTu42e9GLYJ6T4+BGorf0co0ePEk0i1oTT1FQDvf6KzwnHWiCMHTsQJSU1iIqqgF4vnsgsQwV3\noaYmBgkJRixePNmj91P6kDk+I4SIQpWnPegmUytOnz6HigoB0dHtSEtLxj336ByG4S1ePBnbt59z\nOaLA1fs880wS2ttPYs+e71FeXouhQ0ciPn4iysv1HrfzQRtm99hjli+rEyeAJ55wvW1ZWZeVBrFn\nDxAb63p7P1F67uzNWFBRj+bc0xAba/J4X7E7RZ70YtgnpMhILUaPHuWwOIM7XjxqzSP2BcJPf2pG\nXt4dHt31Kiy8iMTEGRg2zHKOO3eWOAwldEfpQ+Y4rp6IQpWnPehbtpQiPv5eGAyWJcNra790OeJi\nwYKsLiPg3L2PVhtl2z4/37KARlVVVZd2PpA9LX479vjxtl4sAMDVq8Ddd7vffto0AMBokwno0wfY\nuhXQ671/324oPXf2ZqIFldlsxtatW3H58mUsW7YMx48fx+jRo6HR+OeBmkSB5NzTkJISJ77TD8Tu\nFHnSiyF16Jj1vU2mgSgvH+L1XSpXCUdKgSC1ceeQOZIT8xT1Jp72oFuGXEcgM9MynC8mZpRXhYfz\n+8yaNRwFBcW21/36teHaNdePvwhkT0vAjt2vn2OBJQjAvHnASTcLjOTmOr5+/fXuCzIPMHcql2hB\n9corr6Bv3744evQoAMuzNQoKCvDWW28FPDjqffx9V8u5p8GbZ9OIFROe9GJIHTrmSSHT3bXyV8KR\n2rhzyBzJiXmKehNPcs+N4X46REd3Ii1N5/WHc+f3KSgodsgrw4YdhV7vemh6IHtaZOvFUamAv/4V\nwI18q/32O/zo//0G2igtwsKcVhZdvtzx9dy5wOLFluN4iLlTuUQLqvPnz+Ojjz7Co48+CgCYPXs2\nPvnkk4AHRr1TKI0f9uezRbzVr58RX39djZqaVtTUVOPBB41dtunuWvkr4Uhp3Fta2rB5MyfVknyY\np4gcWYb73QWDoQzNzRGorS3C6tXSe09Mplbs2nUZDQ2WZ0yNHZuCpqYYLFuWiqIiM7KyHPOcc/7s\n2/eaQ++WL3khGL04tnybkI49D9yDnJx6S76tqAAeftj1Th98YPmyGjcOePtty3BBNzjcXLlEC6rw\ncMsm1g9nJpMJra2t3e1CJFkojR8O7p0iAUAtgFYAUban2tvr7lr5K+FIadx37apCScnNaGkBtFoB\nZnMJnnzy1m734cpG5AvmKSJH1pVdMzMt7XdMjMqnNnXLllK0to5HW1sC2tqAkpJi/PSn7ntenPNn\ne7sK5eXj0NFxHV9/bcCuXf/EjBlDXLb1YvkgGLnZbb5NSnIcJmgyAYsWAcePdz1ISQlwxx2O39u2\nDbjppsAETbISLajuv/9+PP7447h06RJ++9vf4p///Cdm//AwNSJ/C6Xxw2LFhLtG3x/FwdWrfTFh\ngmWy79ChQ3H16pku23R3rdwlHDkKlyNHOtDWlg6VSoW2NgFffPE5nnyy+31CqWeSlId5isiRfX4w\nm9tx+vQ55OfD63bfmjO2b28AMBD9+l1GW1skoqKuIC9vktv9nPNnfv4ZqFQqnDx5BY2NCdBoklBe\nfrPLtl4sH0jtxfEl/3n82aRPH+B//ufGa0EANmywDR3s4pFHHF/7YR4WBYdoQTV37lyMHz8ehw8f\nRmRkJN58802MG+f7QzqJXFHS+GF3jb4/igNr4w10nexrZX+t+vUzwmwWkJ9/pttFKOQpXCJEXncV\nSj2TpDzMU0SO7POD5RmId8Fo1Hrd7ltzhlpdgvr6wdDp6jBp0kDo9XFe3Yyz5jSTSQ0A6NPH7Lat\nF8sHUgsjX/Kf/fVMTDyDvLzpHu0HlcrSY7Vo0Y3vffkl8F//5Xp7P8zDouAQLaiOHDkCAMjIyAAA\ntLS04OjRoxgxYoTtoYpE/hKs8cNSGmh3jb4/igNPnkPl+CDgG5OF6+tbsGjRXofnXVnPRY7C5bbb\ngJKSGrS0hEOr7cC0af1E9wmlnklSHuYpIkf2+SE/HzAatQC8b/cNhkh0dFxHR0c/XLlyEE1NDXjg\ngSHIyxvrVTzWnHb6tAGtrQNx880j8N13JxAVdQUFBY55SiwfSC2MfMl/9tezqMjo28iOu+5yHCbo\n53lYFByiBdWGDRtw9OhR3PTDGM+KigqMGTMGlZWV+MUvfoE5c+YEOkaigJPSQLtr9P25mIWryb6u\n2CeKU6fKcPXqLTAYVGhuDsM33+zFH/9oefaIP2ITKz5nzhyClJQ6u5+LJ14l9UxS6GGeot5Cys0/\nX9r9uDgzvv7agGvXRiAubgRiY4sREeH9fCxrTsvLa8XmzaXYteswgPFITk5DebnaIefm5aXg/feP\n4osvrgJoR2KiDi0trT7fGAzZG3ech9UjiBZUN910E1avXo3k5GQAQFlZGT744AP89a9/xdy5c5mo\nqEeQ0kC7KwKCURzYJ4rm5gg0Nl7D9evJUKlUqKgYic2bS39IZu5j8zRRixWfUVEaSXPPOGeKpGKe\nop7Kub00m9tQWZnl1c0/+3a/b99raG9XOQwP7644ystLwa5d/4RGk/TD6n43w2CokHw+1rbeYIiE\n0TjY9n37nKvVRiEyMhKjR98JlUqFykrH8+zxj/PgPCxFEi2ozpw5Y0tSAJCcnIyzZ88iKioKYWFh\nAQ2OSC5SGmh3RUAwigP7RJGUdB7Xr9+Czk7LuURHt9uSVXexedpL5+uwQX/M4+KqgGSPeYp6Kuf2\n8vTpzzFmjHftr7vh4Z60v1ptFGbMGILy8pv90rNjbbuPHLmM1tb+GDcuDuHh6i7H7C7PSC2MFHvj\nztd5WI89ZtmX87ACSrSgiouLw/PPP49bb70VKpUKJSUliIyMxOeff46BAwfKESNRwIX6nSuxAsI+\nUbS0JGHRor2oqBiJ6Oh2pKUlIy6uTPQ9PC2UfB024Y95XFwVkOwxT1FP5dxeAhEQBPnaX5OpFe3t\nZpw+vQ9AO+65R4e8POkLvljb7uTkFJSUnEVZ2feYMSOuS87tLs8otjDyJ2/mYb33nuXLKj0d+NOf\nOA/Lz0QLqjfeeAM7d+7E2bNn0dnZibS0NKxatQrNzc3IycmRI0aigAtUA+2vnhRvCgitNgp//OPd\ndg/XLfOoQPS0UPK1+PTHOHauCkj2mKeop3JuL6dN64eICPna3y1bSnHp0i0YM8ayfWRkiU+jAaxt\nd0REFCZMGI+YmDOYNy+1y3Ziq9hyRIITb+ZhFRffmIcVHg7Mnw/k5QGxsfLE2kOJFlRarRYzZ87E\n5MmTbd9raGjA8OHDAxoYUaiRUhz5qyfF2wJCSoHoaaHka/Hpj97AkJ1cTEHBPEU9Vdf2cqxPxYS3\n7a+/b1552nZb84zJ1IrnnrOOuDAjLS3ZNieYuuHpPKyODuDPf7Z8Wc2aBTz+OBe68JJoQfXb3/4W\n27dvh06nAwBbV/MXX3wR8OAotDgXFCkpbcEOSVZSiiN/JSM5Cgi5hlH4431CfYgmyYt5inoqf7fL\n3h7P37nH27Z7y5ZSVFTchvb2QWhoEHDqVAl0OmWMSAipub6u5mGVl1uGAhYWOm5bWGj73miTCfjJ\nT4BXXwXUahkDVh7Rgurbb7/FoUOHoNFo5IiHQphzQXHhQiGCPZomEA2Wu2NKKY78lYxYQDjiGHqy\nxzxF5Blvc6YnK8MeO9aA4uJij/Kvt223wRCJ6OhONDTcWMVWKSMSQn6ur14PvPyy5QsAGhuBzZuB\nv/zF0nNl9dlnwNSpwH33BSdOhRAtqJKSkpikCEDX3pbGRvknNPpjCVkx7hpBKcWRvwohFhBE7jFP\nEXnG2w/5nqwMazINRHn5kIAUDHFxZqSl6XDqVC2am8OQlHQeeXnKWBJcygIgQe3Rio0FnnrK8gUA\nZjMub9iA5JgYS0FF3RItqAYPHow5c+YgKysLarvuvsWLFwc0MAo9zgVFbKxJ9hj8sYSsGHeNoJTi\niIUQUeAxTxF5xp9zouRYHMiSd09Dp7Pm3bsVsyCFlAVAQqpHKzISTVOnAllZwYtBQUQLqtjYWEya\nNEmOWCjEORcUKSlxssfg7yVkXXHXCIoVR0G/u9SL8FqTPeYp6q28bQvt85vZ3I7Tp88hPx+S2lHr\nsQAofm5vIAR7ARCSl2hB9eyzz3b53u9///uABEOhzblhKyoqkj0Gfy8h64rUYXohd3epB+O1JnvM\nU9RbedsW2ue306fPIT7+LhiNWkntqPVYTU010Ouv9Pq5vc6CvQAIyUu0oNq/fz/efPNNNDY2AgDM\nZjNiY2OxYsWKgAdH5MzfS8i6IvWOGO8uyYfXmuwxT1Fv5csjNfLzAaNR6/G+7o5VVGRGVhZvaPmK\ni08pm2hB9Yc//AGrV6/G7373O6xZswaffPIJbrnlFjliI+oilLv/eXdJPrzWZI95inorX9pCtqOh\nJZQ/35C4MLENYmJikJmZiYiICKSkpOD5559HQUGBDKERKUteXgr0+hLExJyBXl8i+e6SydSKgoJi\n5OefQWFhJVpaWv0cqfL561pTz8A8Rb2VL22hr+2oNVe9/34DCgqKmauoVxPtoTKbzTh8+DD69euH\nHTt2YNSoUaiqqpIjNiJF8deiFfZj4isrY/hUeBd4J4/sMU9Rb+VLW+hrO+rrsulcXIh6EtGC6tVX\nX4XBYMDy5ctt///000/LERtRj+Lp5GHODyLyDvMUkfx8zVVcXIh6EtGCauTIkRg5ciQA4N133w14\nQEQ9lafJh+PaQxvvqoYe5ikiz/mrDfN12XTePKSeRLSgKiwsxMaNG2E0GiEIgu37+/btC2RcRD2O\np4VSXl4K3nuvCHv31qOh4RomTrwJLS2t/NAeInhXNfQwTxF5zl9tmK/Lpst185A3wUgOogXVhg0b\n8Lvf/Q6DBw+WIx6iHsvTJVG12ihoNBqMHn0vLl++jEuXvB+bToHDu6qhh3mKyHP+asN8XTZdrmXC\neROM5CBaUI0YMQJZWVl+e8OOjg6sXLkSVVVVUKvVWLt2LYYNG+awzc6dO/Hee+9BrVYjNzcXjzzy\nCHbs2IH169djxIgRAICcnBw89dRTfouLKNC8mQDMD+2hi0MyQw/zFJHnQqUNk2txIeZTkoPbgurg\nwYMAgFGjRmHdunXIzs6GWq22/XzSpEmS3vDjjz9G//79kZ+fj/3792PdunV46623bD9vaWnB22+/\nje3btyM8PByPPPIIpk+fDgCYOXMmli9fLul9iZTE17HpFDh8+GLoYJ4i8l5va8NCpYCkns1tQfX2\n2287vD527Jjt/1UqleREdfDgQfzkJz8BAEyePBkvvviiw8+PHz+O8ePHIzo6GgBwyy234OjRowDg\nMDaeqCfzdWy6v3DseVdcsj10ME8Rea+3tWG9oYBkrg4+twXV+++/b/t/o9GImJgYAEBdXR0GDRok\n+Q0NBgN0Oh0AS8ILCwtDR0cHwsPDu/wcAHQ6Herq6hAeHo4jR45gwYIF6OjowPLlyzFmzBjJcRCF\nMl/Hpkvh3CDPmjUcK1YcQEXFSERHm5GWlsxnYlFIYZ4iCg77fGE0ViItbazPH+ADVRT0hgKS88SC\nT3QO1d/+9jfs37/fdidwyZIluO+++zB37lzRg2/duhXbtm2zjV0VBAEnTpxw2Kazs7PbY1jv9mVm\nZkKn02Hq1Kk4duwYli9fjsLCQtEYiMgzzg3yihW7UFFxG9rbB6GhQcCpUyXQ6Tj2nEIP8xSRvALx\nAHoWBdJxnljwiRZUO3fuxN/+9jfb63fffRdz5871KFHl5uYiNzfX4XsvvPACDAYDUlNT0dHRYQki\n/EYY8fHxqKurs72uqanBhAkToNfrodfrAViSVkNDAwRBsP0BuVNUVCQaZyhhvIGntJjlivfYsQaY\nTANtr8+c6YBaXY+rVzVQqVRobTXBaCxHUZFR9Fi8xoGltHgDjXlKOXiuPYN9vlCpVDh2rAZFRb7N\nTXLOQU1Nvh8zUELtd2s0VqKyMsY2Tywx8YxHudoToXauoUq0oLp+/bpDIgkLC/PpDXNycrB7927k\n5ORg7969yM7Odvh5RkYGVq9eDaPRCJVKhe+++w6rVq3Cpk2b0L9/f+Tm5qKsrAw6nU40SQHw68pP\ngVZUVMR4A0xpMcsZb3FxMcrLh9ga5M7OcMTHj8SpU/Vobg5DUtIVrFgxXXQIxjffHEBZWV/FjOXm\n30TgBTohM08pgxL/dqXq6edqn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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -398,75 +425,58 @@ } ], "source": [ - "def linreg_r2(X,Y, plot):\n", - " # Running the linear regression\n", + "# Choose which dimension we want to model using the others\n", + "exog = 'xlp'\n", + "\n", + "# Defining our linear regression function\n", + "def linreg_r2(X,Y):\n", + "\n", " Xc = sm.add_constant(X)\n", " model = regression.linear_model.OLS(Y, Xc).fit()\n", " params = model.params\n", " Y_hat = np.dot(Xc,params)\n", " \n", - " # Plot results\n", - " if plot:\n", - " plt.scatter(X, Y, alpha=0.3) # Plot the raw data\n", - " plt.plot(X, Y_hat, 'r', alpha=0.9); # Add the regression line, colored in red\n", - " return model.rsquared, Y_hat\n", - "\n", - "print 'rsquared', linreg_r2(data['Year Built'], data['log Price'],plot=True)[0]\n", - "plt.xlabel('Year Built');\n", - "plt.ylabel('log Price');" + " return model\n", + "\n", + "# Creating a figure with a grid of regressions\n", + "ncols = 2\n", + "nrows = (len(data.columns)-1)/ncols\n", + "fig, axes = plt.subplots(ncols=ncols,nrows=nrows)\n", + "\n", + "# iterating through and plotting regressions\n", + "for i, dimension in enumerate(data.columns[data.columns != exog]):\n", + " \n", + " model = linreg_r2(data[dimension], data[exog])\n", + " \n", + " ax = axes[(i)/ncols, i%ncols]\n", + " ax.scatter(data[dimension], data[exog], alpha = 0.5)\n", + " ax.plot(data[dimension], model.predict(), alpha = 0.8, c='r')\n", + " ax.set_title(dimension);\n", + " ax.set_ylabel('Pct change in %s'%exog);\n", + " ax.legend(['r2 = %5f'%model.rsquared]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Using only `Year Built` in our model explained only 1.9% of the variation on `log Price`. Using only one dimension to try and understand a multi-dimensional dataset is equivalent to trying to categorize a 3-d object as a cylinder by only approaching it from a single perspective. It cannot be done. In this model alone we ignore many features of the data and it can be improved by adding another dimension or 'view'.\n", + "None of the above four models explains a satisfactory amount of the variance in returns of `xlp`. `fx`, the USD-EUR exchange rate, explains the most with an $R^2$ value of 9.81%. The least insightful dimension is the change in the price of gold, `gold`, which only explains 0.1% of the variance in `xlp` returns.\n", "\n", - "Let's see what `log Price` looks like from the perspective of `Number Of Stories`:" - ] - }, - { - "cell_type": "code", - "execution_count": 145, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "rsquared 0.0561128798813\n" - ] - }, - { - "data": { - "image/png": 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SDJk2rUTr1m1WPO5XZWVUixdb/5yKsrJBvflmWLt29WtoKKz5862+1TXOyS9+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\n+OOP8vHxUbt27QxOhTuqqqq0atUqbdmyRe3btzc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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "print 'rsquared', linreg_r2(data['Number Of Stories'], data['log Price'], plot=True)[0]\n", - "plt.xlabel('Number Of Stories');\n", - "plt.ylabel('log Price');\n", - "plt.xlim(0,15);" + "Using only one dimension to try and understand a multi-dimensional dataset like in this example is equivalent to trying to categorize a 3-d object as a cylinder by only approaching it from a single perspective. It can not be done. In this model alone we ignore many features of the data and it can be improved by ensembling independent views.\n", + "\n", + "Each of these dimensions provides unique insight into the problem of predicting the returns of `xlp`. Let's now average the predictions of all four models, combining their unique insights, to see if we can build a more accurate model:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "`Number Of Stories` explains about 5.6% of the variation in `log Price`. While better than `Year Built`, it still provides a mostly incomplete understanding. Let's take a look at the final dimension, `Total area`:" + "*Note: In the below plot, the blue line is not the model but the line $predicted=observed$. Points along this line mean the combined model perfectly predicted the observed returns of `xlp`.*" ] }, { "cell_type": "code", - "execution_count": 146, + "execution_count": 293, "metadata": { "collapsed": false }, @@ -475,14 +485,14 @@ "name": "stdout", "output_type": "stream", "text": [ - "rsquared 0.168804441783\n" + "rsquared: 0.909701113542\n" ] }, { "data": { - "image/png": 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KNXFinrc/5l76579zZrc75HA4tHPndkkuVVRke7c895w3YoTnvGne8zo6jHI4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\nh5S82p9euX//vsaNGxc5NnjGioqKNHz48LfWAPH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"text/plain": [ - "" + "" ] }, "metadata": {}, @@ -490,124 +500,37 @@ } ], "source": [ - "print 'rsquared', linreg_r2(data['Total area'], data['log Price'], plot=True)[0]\n", - "plt.xlabel('Total area');\n", - "plt.ylabel('log Price');\n", - "plt.xlim(0,200000);" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`Total area` was the most insightful dimension, with its model explaining 16.8% of variance. Still, however, this is not a great result and we are still attempting to understand a complex, multidimensional dataset from a single perspective. Let's see if averaging the models, combining information from all 3 dimensions, can produce a more accurate model. \n", + "combined = np.mean([linreg_r2(data[_], data[exog]).predict() for _ in data.columns[data.columns != 'unemployment']], axis=0)\n", "\n", - "*Note: In the below plot, the blue line is not the model but the line $Y=X$. Points along this line mean the combined model perfectly predicted the observed `log Price`.*" - ] - }, - { - "cell_type": "code", - "execution_count": 147, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "rsquared: 0.185624465575\n" - ] - }, - { - "data": { - "image/png": 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w+6gGYLSSEpOWLGnQihV1WrKkgaGWOSxmMDp06JCuv/56mUz+g/ypT31KLpcr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\nZeqrOPzbAkRGMAIwIVZrb1jnbfPmgzK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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "combined = (linreg_r2(data['Total area'], data['log Price'],plot=False)[1]\n", - " + linreg_r2(data['Number Of Stories'], data['log Price'],plot=False)[1]\n", - " + linreg_r2(data['Year Built'], data['log Price'],plot=False)[1])/3\n", - "\n", - "plt.scatter(data['log Price'],combined, alpha = 0.3);\n", - "plt.plot(data['log Price'],data['log Price'], label='Y=X **not model**')\n", - "plt.ylim(6.5,7.5);\n", - "plt.xlabel('log Price');\n", - "plt.ylabel('Predicted log Price');\n", + "plt.scatter(data[exog],combined, alpha = 0.3);\n", + "plt.plot(data[exog],data[exog], label='Y=X **not model**');\n", + "plt.xlabel(exog);\n", + "plt.ylabel('Predicted %s'%exog);\n", "plt.legend();\n", "\n", - "print 'rsquared:', np.corrcoef(combined,data['log Price'])[0][1]**2" + "print 'rsquared:', np.corrcoef(combined, data[exog])[0][1]**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "By taking a simple equally weighted average of all the models we saw $R^2$ increase to 18.6%. While still indicative of a poorly fit model, the result is still interesting considering the $R^2$ values of the individual single-dimension models were 1.9%, 5.6%, and 16.9% respectively. The $R^2$ of the combined model was higher than any of the single models alone.\n", - "\n", - "Simply averaging the model outputs ignores some of the interplay between variables which can be better captured by using a multiple linear regression. Let's run a single multiple linear regression model on the pricing data:" - ] - }, - { - "cell_type": "code", - "execution_count": 181, - "metadata": { - "collapsed": false, - "scrolled": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "rsquared: 0.188016012536\n" - ] - }, - { - "data": { - "image/png": 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+bVS3SCruxBHZMPJ6LcAOMgajG2+8UWvWrNFrr70mh8Ohc889V8uWLStGbQAA\nAEV1/YPPF+25CCKAtaQNRgMDA2poaND27dt1/PHH6/jjj4/f5vP5dPjhhxelQAAAgGLZtGV3fNvI\nbhEA60kbjO666y7dd999+tznPjfhNofDoXXr1hlaGAAAQDElTs8N+7PadOiwvrTB6L777pMkPfPM\nM0UrBgAAwAroFtkf6zIhV2mD0fXXXz/pHb/3ve8VvBgAAAAz0C0qPVabDh3Wl3be7dh1RdOmTdOe\nPXs0f/58tba2avfu3aqqqipmjQAAAEVDt6g0WG06dFhf2uh84YUXSpL+8Ic/aMWKFfGfX3bZZfrS\nl75kfGUAAABFQLeoNFltOnRYX8ae4vvvv68PPvhAhxxyiCQpGAzqvffeM7wwAACAYqNbVDqYDh25\nyhiMLr74Yp111lk67LDD5HA4tH37dl155ZXFqA0AAMBQdIsAxGQMRp/+9Kd1/vnna+vWrYpGo5o7\nd268ewQAAFAq7NYtYjpqoLDSTr4Qs2fPHj3wwAN65JFHtGDBAr388ssaHBwsRm0AAACGSewWndp+\nmImV5Cc2HXUk0ii/v1le74CGh8Pq6vJp7dp+dXX5NDwcNrtMwDYyBqMbb7xRc+bM0fbt2yVJw8PD\n+uY3v2l4YQAAAMVy7Wc6zC4hZ6mmo04VlgBkJ2MwGhwc1KWXXiqXa7Q1+/d///cKhUKGFwYAAGCU\nxG7RPf+02MRK8pdqOmrW7gHylzEYSVI4HJbD4ZAk7dq1S/v27TO0KAAAgGKZf0S92SXkpbOzQR6P\nT05nvzwenzo7G1i7B5iCrCZfWL58uXbu3Kkrr7xSPT09+ta3vlWM2gAAAAousVv0X3eda2IlU5Nq\nOmrW7gHylzEYnX322Tr++OO1ceNGVVZW6tZbb1VDAx8yAABgP9FoNGnf5czq5BnbYO0eIH8Zg9FX\nvvIV/eAHP9CyZcuKUQ8AAIBhzrt2TXzbbtNzG43pv1HuMgajuXPn6rHHHlN7e7sqKyvjPz/88MMN\nLQwAAKCQ3t8VNLsES4vNaCdJfr/k9froPqGsZAxGTz755ISfORwOrVu3zpCCAAAAjHDF956Obxe7\nW2SHbgwz2qHcZXzHP/PMM8WoAwAAwDD/+fs3TX1+O3Rjamoi8vuT963CDsES9pf2isNAIKC7775b\nV155pR566CFFItb5cAAAAOTiF797I75txrVFdujGpJr+2ypYuBbFkDYY3XLLLZKkT33qU3rrrbf0\nwx/+sFjrR4H5AAAgAElEQVQ1AQCAMjQ8HFZXl09r1/arq8un4eFwQR43cXpus9hhfaHYjHbLljVq\n8eJmS3Vk7BAsYX9p31U+n0/33nuvJOmUU07RZZddVqyaAABAGSrG6WZmzUTH+kJTY+XT/FA60gYj\np3PspoqKiqIUAwAAypcRXQErdIsk1heaKoIliiHtvzgOh2PSfQAAgEIyuivAukX2RbBEMaQNRhs3\nbtRpp50W39+9e7dOO+00RaNRORwOPfvss0UoDwAAlItCdwWs0i2yEmZ3A9JLG4yeeuqpYtYBAADK\nnJFdAbpFo+wwbThglrTBqLmZDwkAALAnukWpMbsbkF7a6boBAABKAd2iMXaYNhwwC8EIAACUlMRu\nUbWbjkgiKy/iCpiNfy0AAEDJevT2j5tdgqUwuxuQHsEIAACUjMRu0dX/8FETK5kcs8MB1kMwAgAA\nJWnZ3x6Z1/2KEVqYHQ6wHq4xAgAAJSGxW/Szm5fm/Tix0BKJNMrvb5bXO1CI8pIwOxxgPQQjAABQ\ncuoOced932KEFmaHA6yHYAQAAGwvsVs01em5ixFamB0OsB76tgAA2BQX8I8KHShscOnsbJDX60t6\nXQuN2eEA6yEYAQBgU1zAP+rCG34b3y7EYq7pQgtBFChtnEoHAIBNcQG/9PL/9BftuYoxKQMA8xCM\nAACwKS7gl77zk/Xx7UJ0iyZDEAVKG8EIAACbKvcL+G948IWiPh9BFChtfNUBAIBNlfsF/D1bdsW3\nje4WScWZlAGAeQhGAADAdhKn5y4WKwZRJoQACodgBAAAbCExBCQqRrfIqpiZECgcghEAALCk8d2Q\ncDisYPAIrXi2+N0iq2JCiNJB9898fHoAALCJchs4je+GvPHGJs2fn/w7du0WFepY1tRE5Pcn78Oe\n6P6Zj1npAACwiamsozM8HFZXl09r1/arq8un4eGwgZUWxsTuR7RkukWFWhOp3GcmLCV0/8zHKw4A\ngE1MZeBkx2+jx3dDOjpq9dxvx/Z//b2zi19UgRRqEGzFCSGQH7p/5qNjBACATUxlHR0rfBuda9dq\nfDfk/t++mnS7nU8jZE0kjEf3z3yG/6u4Zs0aPfTQQ3I6nfrKV76iU089NX7bz3/+cz3xxBOqqKjQ\nggULdP311xtdDgAAtjWVdXSm+m10Ia6JybVrNb4bcvfjL8e37XptUQxrImE8un/mMzQY+f1+PfDA\nA3r88ccVDAb1gx/8IB6MAoGAHnroIa1bt04Oh0OXX365XnvtNX30ox81siQAAGxrKgOnqQ7EC3Eq\n3lS6VonrFp3aflhOz2tFDIIB6zE0GL344otatGiRqqqqVFVVpVtvvTV+W2VlpaZPn65AIKCqqiqF\nQiEdeuihRpYDAEDZmupAvBCn4hXqGoprP9OR1/2k8pvZD0D2DL3GyOfzaf/+/brqqqv0mc98Rn/+\n85/jt1VWVuqf/umfdOaZZ+qMM87Q8ccfr5aWFiPLAQAAeSrENTH5XkOR2C26558W5/y8iQo1GxyA\n0mNoxygajcrv9+vBBx/U9u3bdemll+qPf/yjpNFT6R588EH9/ve/V3V1tT73uc+pt7dXra2tkz5m\nd3e3kSXDYBw/++LY2RvHz96scPxcroj6+9/Qvn2VmjFjWLNn16i7e0fOjzNjxuj/JKmnJ/f7B3e/\no+7d7+R8v5iNG/dpZGR/fL+i4n3NmJF7HdmayrELhyPatCkQf80XLKiRy8WEwsVkhc8eisfQT9es\nWbPU3t4uh8Ohww8/XNXV1RocHFR9fb3efvttHX744fHT5zo6OrRp06aMwaijI//2OczV3d3N8bMp\njp29cfzszUrHb+HC4j9nYrfov+46Vy7n1E522bfPF79WSpI8nip1dBhzrc9Uj11Xl0+NjWO1hcM+\nLVzIdUnFYqXPHnKTb6A19FS6RYsWyev1KhqNamhoSPv27VN9fb0kqbm5WW+//baGh4clSZs2bdLc\nuXONLAcAANhINBpN2p9qKJLsNSWyFaZYB8qJoZ+wxsZGLV26VBdddJEcDoe+/e1va9WqVaqtrdWZ\nZ56pyy+/XJ/97GfldDrV3t6uE044wchyAACAjZx37Zr4dqGm57bTbHAs+AkUl+FfPVx00UW66KKL\ncr4NAACUL9/OgNklmI61joDioicLAAAs58o718W37b6Ya77s1N0CSgHBCACAMpJuHR8rre/zk9Wb\nTHleAOXN0MkXAACAtaRbx8dK6/usfm5LfDvfbtHwcFhdXT6tXduvri6fhofDhSoPQImiYwQAQBlJ\nN9OZ3y9t3rxbodA0ud0H1dY28b65dJXy7UAlTs89FbGgJ43+bV6vz/KnpRnZtbNSRxCwKjpGAACU\nkfEzm8X2t24dUDA4UyMjdQoGZ2rr1okdo1y6SoXoQE3l2qJsp7q2Umcp3WtWiBqt1BEErIqOEQAA\nJS6xWzB9eljV1e/qwIGqpJnO5s6drUDAp1DIKbc7orlzZ094nFzW1clnDZ5CdYuk7Ke6TtdZMqPD\nku41K0T3izWRgMz4VAAAUOISB9aRiOTx+LRkSWPS79TVOdTWNjbY9nh8Ex4nl3V1proGz1Rnost2\nqmsjw0iu0r1mhQg1rIkEZEYwAgCgxGUzsM4mSOSyrk6ua/AUslskZT/VtZFhJFfpXrNChBrWRAIy\nIxgBAFDishlYZxMkcllXZypr8BRz3SIjw0iu0r1mhQg1rIkEZEYwAgDAhnK5Bsbq3YJCd4tyYWQY\nyUe640qoAYxHMAIAwIZyuQbGTgPrYnaLJmPWa2bHacaBUkEwAgDAhkpllrGpdotKbX2eUjmugB2x\njhEAADaUbj0iO3vivvNzXrOn1NbnKcXjCtgFwQgAABvq7GyQx+OT09kvj8dnueuGspHYLTq17TCt\nXduvFSs2aefOxqyDTql1WErhuAJ2Ze9/PQAAKFN2um4oG8fM7lAkIu3aJQUCe9TWNlNS5qCT7+xx\nVj0Fr9SOK2AnBCMAAFB0id2iS08+Pr7tdkcUClXG91MFncRQM316WNXV7+rAgaqcZo9jkgMA4xGM\nAACwKat2PXL1oVnT4l2f1tYG9fVtktM5nDboJIaaSETyeHw6+eR6eb0DWrduMKvXotROwQMwdfwr\nAACATdm165HYLYpNuBBbM8jjieiccxbkHGpyfS3MWMAVgLURjAAAsCk7dj32H5gYQHK9riZVqMn1\ntZjqAq6l0q0DMMb6/4ICAICU7Nj1uOiG38a3813MNVWoGe0Yjf1O7LVIF2CmOsmBXbt1ANIjGAEA\nYFNT7XoU2wuv9RXkcVKFmnSvhVEBxo7dOgCT41MMAIBNWXFq58lOMbvzpy/Ffy/fblE66V4LowKM\nHbt1ACbHAq8AAKBgYh2a8Qu0Xnnn06bUMz6wFCrAsBArUHroGAEAgIJJ16Hx7QzGf1bobtFkjDrd\ncLJuXaxrtnHjPu3b52NiBsAmCEYAAKBgUp1iljg9txEmO33PjNMNY12zkZH9f+2aMTEDYAcEIwAA\nSlixp5VO2aF5fOz2bLpFudZcjBnicqmJiRkAe+KTCgBAiRoeDmvFik3atatJbndEra2j01rnEhpy\nDSnjOzT5dItyDTrFCCLZ1jQ8HNaWLX3atatSu3cH1dISkcfDxAyAHTD5AgAAJhoeDqury6e1a/vV\n1eXT8HC4YI/t9Q5o164jNDLSqGCwWb29AzmHhnSTKeQj22uLcg06Rk2wkE9NXu+AmpoWyO3ep1Bo\nRH19PUzMANgEwQgAABMVMniMFwg45XYfjO+HQs6cQ4PfL23evFvd3UPavHl30vVDmeR7bVGuQacY\nM8RlW1Mg4JTL5VJbW7OOPfYQzZvXxMQLgE1wKh0AACYy8jSwmpqIWltnqrd3t0KhaZo1q0+dnQty\neoytWwcUDLZLkoJBaevWjZJyv34nl5nocp1JrhgTLLS312nlyo0aGnKrri6k008/JuXvsb4RYF8E\nIwAATGTkQHo0YPSrqioWMBbk3L2YO3e2AgGfQiGn3O6I5s6dndX9pjITnRUXrt24cUgtLe1qaYnt\n+7R48YwJv5cY6mprt6qz85QiVwogXwQjAABMlKo7kjjhgc/n13HHhfM6HasQAaOuzqG2trHH8Hh8\nOT9GMdctMkq2nb3E17y7e3va41bs2QIBZEYwAgDARKnCS1eXLz4D2t69e3OeSa6Q8lkgNbFb1N6a\nXYcpE7ODRKE7e8WYYnwqzH69ATMQjAAAsBgrrYMz1a7TrV/824LUYVaQiAUEv3/0+qq5c2errs4x\n5QkerHSMU7F6cAOMwKx0AABYTDGmnzZKYrfojqsWFexxzQoSYwGhWS0t7aqrc2jx4uYpd0+sfoyt\nHtwAI/AuBwDAYsy6gD/V6VOS8j6l6rijZhWstsRT2cLhiLZu7dPatTL8NC+jAkI+pygWE7ProRwR\njAAAsJhsL+AvtFSnT41uZ3dKVWK36L/uOregtSUGia1b+9TUtECRiMvw07yMCghWnHkvkdWDG2AE\nghEAACUm3wvns+mOpOuYRKPRpH2Xs7Bn6ycGibVrpUhk7O8x8jSvcg0IVg9ugBEIRgAAlJh8L5xP\n1x3JpmNy3rVr4ttGT89dzNO8CAhTw+x2sBOCEQAAJSbf62LSdUcydUy2D+zN+NiFHCCXaxfHjpjd\nDnZCMAIAoMTk21FJ1x3JNJC96q5n4tvpukWFHCDTxbEPZreDnfDuBADAptJ1YYrZUfnJ6k1Z/V6u\nA+RMHaZCz6CXDbNPCzP7+fPB7HawE4IRAAA2la4LU8yOyurntsS3J7u2KNcBcqYO01Rn0MtH7DnD\n4bBefXVA69e/qYUL64oWUJ5/3qcNG2oVCk2T2+1UOOzTkiVHGP68U1GokG7HUAj7IRgBAGAh4weA\nLlf6AGH2aUqJ03NnkusAOdPfNpUZ9DJJNwiPPV5v74CCwWZVVMyQ319XtOtmursDCgaPkCQFg1J3\n9/tassTwp52SQoV0rlVCMRCMAACwkPEDwP7+N7RwYerfzec0JaO+ec80E12uA+RMf9tUZtDLJN0g\nPPacodDo8MntPiipmIE0mmG/dJn9JQDKQ2EXGQAAADkbHg6rq8untWv7tX79oMLhcPy2ffsq096v\ns7NBHo9PTme/PB5fVqcpxQb9kUij/P5meb0DedWcS7coH5n+tlS35/N6pJJuEB57/OrqAVVX71Zr\n66GSinfdTEdHraqrfaqo6Fd1tU8dHbVFed7E92dXl0/Dw+HMdyqwVMEYKDTiNgAAJkvsUIyMONXb\nO6C2ttH9GTOG094vn9OUjPjm3Yh1izL9bfnOoJeNdN2o2HOOnhY4oEAgUtTpwk8+uVku14ACAamm\nRursLM6pZIU8jS3fjiVTtKMYCEYAAJgsMZy0th6qLVvel9M5OgCcPbsmq8dIHHBOn75fknTgQNWE\nwWchZgkzsls02cC5WBfgZxqEmzVduFnPW8gwnW/IYop2FAPBCAAAkyWGFZfLqYUL67R4caMkqbt7\nR1aPkTjgfPXV3ZJCamtrTBp8Dg+HFQ6H9cYbmyRF1dFRO+WuQ6xbVKjQMtnAuVgX4DMIT1bIKbe5\nVghWxrsRAACT5XqaUKoQkjjADIWmKfE/8bHbvN4BBYNHaP780Z+7XL6cw0u6blGhQstkA2cG1eYo\n5GlsrGsEK+NfFAAATJZrh2J8CHn++Xe1ZcuQdu2qlNt9UE5nRE7n2IAzNvgsdLBIvLaoUI892cCZ\nQXXhZdPpK2QHjWuFYGUEIwAAbGZ86OjuDmjevAUKBAYUCjnl8WzTRz86WwcO9Gv69P0Kh6W1a/u1\nZUufmppmyuUavX+uwWKya4sKFVomGzgzqC68Yq8PxGmKsDKCEQAANhMLIeFwRL29e/TWW36NjHyg\n1tZGuVxOOZ3SkiWj1yh1dfniA9+mpnr19fVo3rymKQeL8TPRFSq0WHXgXKyJH4qN0xOBMbz7AQCW\nV6qD0nzFQsj69UOS6nTEEYcpGJyp3t7damubmdStSRzoulwuzZvXpGXLGnN+zsRu0efPOXbC7cUI\nNMXubhj53FZ5T3N6IjCGYAQAsDwzB8RWFAshgYBTkUijwuGwent9Coc/kMcTSurWGDHwveD0o6f8\nGPkoVncj0+QWhXhuq7ynOT0RGEMwAgBYHqf7JIsN3DdtGtLISEStrQ1qbW1UX9+AAoF6eb0D8Q7E\n+IFve3udurp8OXUqErtFK2/6O6P/vLSK1d1IFVpqalTQ5zbiPZ1PF8qqpy4CZphmdgEAAGQyfhBa\n7qf7xAbu8+bNl+TWli1vqK+vR01NCxSJNMrvb5bXO5ByoLxx45D8/uak38vFzEOrjPmjstDZ2SCP\nxyens18ej8+w7kaq0FLo5zbiPR17X+R7bIFyV95fuQEAbIHTfcYMD4e1fv2QgsEZcrsPqrX1UFVV\njQ6qI5Gx7kAg4EzZ+ci1U5HYLRo/4UKxFau7kaozVejnNuI9TWcVmBo+MQAAy+N0nzFe74BGRuo0\nMlKnYFDq7d2tRYtGg9H4wXyqgXIup6PtC4ULWrtdFCOIG/GezubYWmXSB7vUhfJCMAIAwES5DggD\nAadaW+vV2+tTKORURcWAOjvnS9KEwfxox2jsvmM/z27Q/6lvPRnfNrtbVExmBPFCBINsjq1VJn0Y\nz6p1obwQjAAAMFGuA8KamogiEZfa2kZ/x+OJxAfQ4++XaqCc7aD/uY3b8/2Tis6O3YbxNYfDYQWD\nR0jKPxhkc2yterqdVetCeeFdBwCAibIdEMYG0kNDUW3btlEtLQ3yeDRpxyfbEJQqWNzzf7vjt1ux\nW5RY85YtfWpqWiCXy2WbbsP4QPzGGz2aP3/sdqOCgVXXLbJqXSgvBCMAAEyUaUAYDkfU1TW6mOvI\nSJ1aWxvV0nKYPJ7cBv+TdVXGD9I/e/NvJ9zXah2YxJp37apUIDAQ76LZoduQWGM4HNbbb/sVDPbL\n7R6dft3jMSYYWHUiE6vWhfJi/X85AAAoYZkGhJs2BdTY2KxgcIZGRurU2+tTW1tzzoP/yU7Ziz1W\nOBxRb+8e7RseG5Rfcdr5luzAJP79bvdBhUJj+8XsNuR7Gl9iIO7tHVBzc6ucTqdCoUr19W3SOecs\nMKReq05kYtW6UF4IRgAAmCjTgHDfvkpJo4P/YFDxAJDr4H98kPL7FV/odfRUtJnq7d2jF3Y+n/G+\nVpAYLFpbD1VfX4+cTuXUbSjEtUn5ThqQGIgrKobU2jpfLtfo6+x0DluuQweUA+v9SwcAAOJmzBiW\nNDr47+3drYqKAXk8o4P4XAb240/Z27p1QFK7JKmpqV59fT0Kh91J9+moXRi/r9XEgoXfL/X1DWju\n3Nk5h5tCzISW76QBiYF49NiY0/ECMIZgBACAhYwPO8cc45Y02llYtCiizs758YF/V5cv64F9Z2eD\nnn/+XXV375Xk0MjI6LUtLpdLLpdL8+Y16cGn1yfdp7p6LIRZTSxYdHX5FAt4uYab8SFmaCga76Jl\nG7IKMWkA19cA1kAwAgDAQsZ3Mfr739A//mPqgX4u3YrKytEANH/+cZKkzZt3q7d3bMKC8QP6b3zi\nhKJPe53PqW1TmeZ5fKjZtm2nHI7cQlYhQg3X1wDWQDACAGAcM9fFGT+wj11jlKq22LVBsWtTMnUr\nEh979NS87XrjjUFJDj23Y0vS75oxUM/n1LapdGzGhxopOdRkE7IINUDpIBgBADBOIa49ydb4EDZ9\neliRhLF97BqjxNp27mxQb++AAoEGvfVWl5YsOVp1dY6kbkWqcJcYIlwup2pqDqql5X9JUlIwMmvd\noqGhqF5/3adQyCm3O6Jjj41mvM9UOjbjQ83oqYljt3OtD1BeCEYAAIwzldOzxsvUfRofwqqr35XH\nMzbQnz27ZkItvb0DCgab5XBIHs8M1dXtmxDcUoW7xAkLtm4d0M6dFQoEdqecic5I6V6Tbdt2Khgc\nPZUtGJS2bdso6bBJH6uQHRuu9QHKG8EIAIBxsj09K5tT7jJ1n8aHrmDQJY9n8toS1+xxuw+mDG6p\nwt34CQsCAZ+CwZlJv/eNT5ygtWv7DT2FMN1r0tLSoEBgt0KhaXK7D6qlpTjBJPk4SmecUZ/T323m\nqZcACodgBADAONl2DrI55S5T92myabRjky8sXJhc26uvbtKuXZVyuw+qtfVQ1dT0x2+PDdI3bRrU\nyIhTra2H/vW0ubFwF6uhtbVBj7ywOv5z18g0PfxwWPPmOXXssY3yevsNOYUw3Wvi8UhtbWNBzePx\nZf2YqcKJpLSBZeK1WsfJ5XLmdepkPqdemhmmCHJAagQjAADGyfb0rGxOucvUfRofwqLR2Um3j598\nobLSpSuuWJAwsO1PCm6xQfq8eaPXIW3Z8r4WLqxL+p1YTS5X8mB4ev+J2newUX/5y245nXtUVTX2\n9xRyMJ3uNUl8LaZP369wWFl3r0avvWpUb+8ehUKVevXVTTr22DoFg0dImhhYEsPMrl1SILBHra2H\nqLd3QOHwB/F6svkb8zn1spjXsVnpuQErIxgBAJCnbE65y9R9SjUBwM6dYfX2DigUcmr//kEND4eT\nBuiTBTe/f3Qq7tHT0dyaP79uwu/Garr78ZfjPzuqaoEGKyMKhaTh4WkKhUb/nkBgn1aufFMbNw7L\n6azUkiXHKBKZMaXBdLrXJPHvymWNJil27dWe+KmBu3YNq7t7QPPnJ/9Oqm23O6JQqDJ+7VZ1tVt+\n/8yk55wsGOYzM14hr2PLlZnPDVjZNLMLAADArjo7G+Tx+OR09svj8aU85S422F+2rFGLFzdn7EB0\ndjaor2+TQqEZcrudmjVrvrzegaxr2rp1QMHgTI2M1CkYnPnXU/NS15SoscajpqYGud0+ud0+zZr1\nrjo7G/STn2zWSy/N01tvfVh/+csxevrp1yVNbTCdzWuS6+B99NqrsWGN2x2R5JjwO6m2W1sbNGvW\nuwqHP1B19W61th464TljXZZIpFF+f3PSMcnmfZCq3sn2jWTmcwNWZvhXBGvWrNFDDz0kp9Opr3zl\nKzr11FPjt+3YsUNf//rXFYlEdOyxx+qWW24xuhwAAAqmEDOipepEzJvXpJaWOknSW28N5RRC5s6d\nrUBgbMrruXNnp/y9c68Zu7bo0duWyrt+h7q731d9fVQf/ahbLleN1q0b1O9/v1czZlSrokIKh2fo\n3XdHw4bRg+lcuzBj114Ny+2OqLW1QR5PWC5X6m5dYtfK44nonHMW/DX8jF3jlOq6rFT72bwPxh/n\n9vY6bdxozgx4zL4HpGZoMPL7/XrggQf0+OOPKxgM6gc/+EFSMLrzzjt1+eWX64wzztBtt92mHTt2\n6EMf+pCRJQEAYCmprveoqVHe6+nU1TnU1tascHj0dLw33/Srq8sRP/VreDis9ev7k+5TPcOtJUuO\n0JIlo/uJp7FJf9HgYFD19dUaHPxA06dn3xWZilwH7xOvvRpQZ2f6Dl2qMJPqOccmsxjSgQMhSdMV\niUzXrFl9Gh7Ofva68cd540bzruthUVogNUOD0YsvvqhFixapqqpKVVVVuvXWW+O3RaNRdXd36/77\n75ckffvb3zayFAAALClVJ+KMM+rjA/Ta2q3q7Dwl68eLDe7Xrx+U1KR58+bL73fGr5fxegd0z+ru\n+O9/4xMnpKwpHI6ot3eP6upmasuWLjU0tOjoo8O64IKjCzqoTnftTj6D96kO+FPdPxYS581r1O9+\nt1XDwx/omGPq1dQ0GsKyfT6u6wGsz9BPpc/n0/79+3XVVVdp7969+tKXvqSTTjpJkjQ4OKgZM2bo\n9ttv1+uvv64TTjhBX//6140sBwAAy0l1yljiAL27e3tOs7/F7hsIOBWJjJ0WFhuIb9sxnPT76WbS\ne/XV0YkM5s71qKbmoI466qAWLmwoeKfIjBnScplhL/b6uFxOzZlTL6lGbW2NSbdlI58JGgAUl6HB\nKBqNyu/368EHH9T27dt16aWX6o9//GP8toGBAV122WVqamrSFVdcoT/96U9Jp9ql0t3dPentsDaO\nn31x7OzNzOMXDke0aVNA+/ZVasaMYS1YUCOXi2/LY1yuiPr734i/PrNn16i7e0fS76Q7fpO9tj6f\nX3v37o3/bm3tVnV3b9ej67fHf7bksDb5fJvU3b096XFdroj6+nZp//45crvDOuqoQzR9+qBmzBhW\nT09ybVO1ceM+jYzsj+9XVLyvGTMK+xwTn9OvvXtb4vtvvvmc2ttTr6qb+Dru3h2UFNJbb43ux17T\nycSOXTbHGdbDf/vKi6H/ZZo1a5ba29vlcDh0+OGHq7q6WoODg6qvr1ddXZ2am5t12GGHSZJOOukk\nvfXWWxmDUUdHh5Elw0Dd3d0cP5vi2Nmb2cevq8unxsaxDkA47NPChVzfkChxAdfxJjt+k722xx03\nvityin60alPS/U84oUqdnaek7JaEw4nXGY0uttrRUfjjtm/f+OepMuR5Eg0M9CsSaYzvO5216uho\nTPm7ia/j//pfTkmH6sCBqvhrOlk3b/yxG3+cWWjV2sz+txP5yzfQGhqMFi1apBtuuEFf+MIX5Pf7\ntW/fPtXX10uSKioqdNhhh2nbtm2aO3euNm/erHPOOcfIcgBgyhjI5I5rK4yT60xpf9iwLb79xH3n\nT/rYsWuV/P7RKcCj0dnq6vKlfM9P5XNR7BnShofD2rKlT7t2VcrtPqjW1kPl8aQ/rc3IiQpYaBWw\nFkP/69TY2KilS5fqoosuksPh0Le//W2tWrVKtbW1OvPMM3XDDTfouuuuUzQaVWtrq5bEpsMBAIsq\n5kCmVEKYkddWlMprlK/p0/fr1Vdji7ke1Ikn7k/7u4nTc2cjFgi6unyS2iWlf89P5XNR7BnSvN4B\nNTUtUCAwuoBuX1+PzjlnQdGePxFfGgDWYvgn8KKLLtJFF12U8ra5c+fqF7/4hdElAEDBFHMgUyrf\nJhvZESiV1yhf4XBY77yzTYGAWzU1IbW312R1v0zdokTZvOetMsDPJigHAk65XC61tY2+T5xOGR6m\n019zo9EAABqISURBVNXFhAyAtfDVBIC8DA+H9fzzPnV375XkUEdHjU4+Of2aIaWimAOZVINNO3ZI\njOwIWGVAXmiJx9nn8+u448Ipj/Nrr4XU0NCuhobYfo+WLp34eOO7RWvX9ie9f2LPNzQU1bZtO9XS\n0iCPZzTUjnalxhaMPfHE8ITHt8oAP5ugbHStqY5durra2+u0cuVGDQ25VVcX0umnH1PQWgDkZprZ\nBQCwJ693QBs2uPTBB8fpgw8WaMOGWnm9A2aXZbjOzgZ5PD45ncYvcjl+wFZTE4kPsCKRRvn9zWXx\nmk8m1WtkN8PDYXV1+bR2bb+6unzxgXXsOO/d2zLJcXZk2J/oitPOn/D+iT3f66871N/frs2b3ePe\nX25JlX/9/4mK+bmYTDZB2ehaUx27dHVt3DiklpZ2fexjH1FLS7s2bhwqaC0AclMaX60BKLpAwKlQ\naGw/FJpWMt/WT6aY10OkOgVt3brBpN8ph9d8MsW+cN8IqboJ2XbCOjpqtGHD2DVGHR0TT6Wb7Nqi\n2OPG/j8Uiv3/tISfO9XWNrYe0oEDE8OnUZ+LXDuk2XSDjP4Mpzp26eoq1Y4nYFd8AgHkpaYmIrdb\nCgZH993ug5b/tt5Kp6El1jJ9+ugF82NTAI/WlWoAZ5VTlqyi2BfuGyHbgXSq98zo725TW1vs1LfJ\nX4tvfOKElO+f2CQOW7cO6uDBKh199LDC4bC2bu3T/v0ujYxE1NraIJfLVdT3XK7XkFkhKKc6dunq\n4vMMWAvBCEBeOjsbFA771N3do9g1RpkGZWaz0oX6ibW8+upuSSG1tTVmrMsKAz8UVqaBdG3tVrW3\nn6QVKzZp164mud0RRSJuOZ0jamtrVkvLYfFTwsYH/3+4/smk55r8/RNSc3Otdu7cIqdzmvr6+tTU\ndJwkqbd3j7ZseUMLF9bH71OMLxpy7ahYISiPP3axtY5S1WW3z7OVvlwCjEAwApCXykqXliw5Qnaa\nZd9Kp60kPvfoaUvOlLeNZ4WBHwor1eA48Th3d2/Xxo1D2rXrCI2M1CkYlLZv/x+1tNTHHyMQcKYM\n/oliM9Glev8cOFCltrbYAqeHyenslyRFIqPvxba2mXI6I1q8eGwR1GJ80WDHjkplpSseUvftq5TX\nO5A2QNjt82ylL5cAIxCMAJQNKw2yEmtxuw9KiiTdhvKRzeA4EHDK7T4YP3VVGp0hLhwOq7d3QBUV\noxftz5vXKJdr9D/tdz/+8oTHSfWNv6S/Lngqud2jp8zFFjz1+6VwOKLe3j2qqBhICm7F+KKhUB2V\nYnU6Ys+zfv2QRkbqVFEx66+TWJRGgLDSl0uAEXhHAygbVjptJbGW2KKcBw70m14XrKmmJqIPf9ij\ndeu2KBCo1MyZ76q9/Qi99tobkpo0b9589fb2q7d3T9JECTGxblG6rlJT03EKBPYoFKpUX9+m+IKn\nXq9PL7ywS++849Ts2Y164YUKhcM+LVlyRFK4j12PtHatMgaPXELKVDoqic+zZcvoaYEulzOrTsf4\nGtvb67Rx41DGmmOvbzA4QyMjdfL7t2v+/NIJEFb6cgkwQml8UgFMSSCwTytXvhlfS+Oyy45RTc0M\ns8sqOLNPW7Hj+fl2rLkUdXY2aMWKTZozp0lO535JR+u11wKSpNbWQ+RyOdXa2qAtW96Q0xnRg0+v\nj9/3wjOOjm9n843//v2jxzf2eXn++QGFQh5t2RJVZWVI0eiQliw5Iincb906GjwikczBo1inYyU+\nz65dUiAwFhrTBZXxHZ/W1npFIi6tXLlRLS3tGWuOPW6suxcKjb6WpRIgrPTlEmAE1jECoJUr31R/\nf7uGhz+i/v52rVz5ptkllSQrr0GUai0dabTmvr46Pf54n370ow/0jW88r0Bgn8nVlp/KSpfmzWtS\nR0ejnE6XDhw4QsFgs0ZGmtTbO/o+crlcWriwXsuWNSbdd7ZjZvyYplr3qaZm9FS5YHCmRkbqNDJS\nl/Te3LZtr0KhZh082KhQqFnbtu2N17R4cbPOOKNe+/c79dpru7V5s0/hcHjSDkmxTsdKfFy3OxKf\nglxKH1TGOj6j/4u9tkNDyes3pas59ritrYequnq3qqreN3Vdp0KLHfNlyxq1eHHpL+iN8kMwAjDh\nP/rj91EYVj4/P11oCwSceuaZN+X3tysS+Yj6+/+G4GySioq9Wr36DT366Nt68snX9d57W3XkkTNU\nUTGUtFhp4rpFlyw8S5FIo3buHO04DQ1FtWXLS9q8+VW98UaPwuGw2tvrVFHRp4qKflVX+9Ta2pD0\n3mxpOVRu925NmzYkt3u3WloOTarL6x3QyEiTRkYa42Fisg5JsRblTXzc1tYGzZr1bsZFXRM7PtLY\nuk51daGk30tXc2zx2Kqq3Vq0KKRLLplFgABsxDr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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "dimensions = [data['Number Of Stories'],data['Total area'],data['Year Built']]\n", - "mlr = linreg_r2(np.column_stack(dimensions), data['log Price'],plot=False)\n", - "\n", - "print 'rsquared:', mlr[0]\n", - "\n", - "plt.plot(data['log Price'], data['log Price'], label='Y=X **not model**');\n", - "plt.scatter(data['log Price'], mlr[1], alpha=0.3);\n", - "plt.xlabel('log Price');\n", - "plt.ylabel('Predicted log Price');\n", - "plt.ylim(6.45, 7.5);" + "By taking a simple equally weighted average of all the models we saw $R^2$ increase dramatically to 90.97%. The $R^2$ values of the individual single-dimension models were 0.4%, 1.7%, 0.2%, and 9.8%. The $R^2$ of the combined model was dramatically higher than all of the previous ones combined. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "This model performed slightly better than the aggregated model explaining 18.8% vs. 18.5% of variation in `log Price`. For more information on regression models with more than one explanatory variable, refer to the [Quantopian Lecture on Multiple Linear Regression](https://www.quantopian.com/lectures/multiple-linear-regression).\n", + "### More Dimensions Exist\n", "\n", - "Despite our best efforts with the data we were given, the best model or combination of models we could generate only explained 18.8% of the variance in `log Price`. What this means is that the dimensions we were given (`Number Of Stories`, `Total area`, and `Year Built`) were not enough to give us a good understanding of what drives multifamily development prices. While dissapointing, this makes perfect sense as none of our models included important dimensions such as:\n", + "We got a relatively good $R^2$ of 90.97% with the above model using only four data dimensions. However, there are still many more dimensions beyond the four we used (`fx`,`cpi`,`unemployment`, and `gold`) that could help fill out the last 10% such as:\n", "\n", - "* Location desireability\n", - "* Lot size\n", - "* Number of family units\n", - "* Occupancy rate\n", - "* ...and probably many more\n", + "* Broad market ETFs like SPY or IWM\n", + "* Models which take into account interactions between dimensions like [multiple linear regression](https://www.quantopian.com/lectures/multiple-linear-regression)\n", + "* ... and probably many more\n", "\n", - "Furthermore, oftentimes datasets do not have obvious principal dimensions. In this situation you must develop a set of many possible influencers and whittle it down to only the most significant ones through [dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction). " + "Furthermore, oftentimes datasets do not have obvious dominant dimensions. In this situation you must develop a set of many possible influencers and whittle it down to only the most significant ones through techniques like [dimensionality reduction](https://en.wikipedia.org/wiki/Dimensionality_reduction). " ] }, { diff --git a/notebooks/lectures/Model_Ensembling/preview.html b/notebooks/lectures/Model_Ensembling/preview.html index 40e11fb2..49d19452 100644 --- a/notebooks/lectures/Model_Ensembling/preview.html +++ b/notebooks/lectures/Model_Ensembling/preview.html @@ -1,6 +1,6 @@ - Model Ensembling Lecture + Model Ensembling Lecture V3