{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Uczenie maszynowe UMZ 2017/2018\n", "# 2. Regresja logistyczna\n", "### Część 2" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 2.5. Regresja wielomianowa" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Wybór cech" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Zadanie: przewidzieć cenę działki o kształcie prostokąta.\n", "\n", "Jakie cechy wybrać?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ " * $x_1$ – szerokość działki, $x_2$ – długość działki:\n", "$$ h_{\\theta}(\\vec{x}) = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ " * $x_1$ – powierzchnia działki:\n", "$$ h_{\\theta}(\\vec{x}) = \\theta_0 + \\theta_1 x_1 $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Regresja wielomianowa" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Przydtne importy\n", "\n", "import ipywidgets as widgets\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas\n", "\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Przydatne funkcje\n", "\n", "# Wersja macierzowa funkcji kosztu\n", "def cost(theta, X, y):\n", " m = len(y)\n", " J = 1.0 / (2.0 * m) * ((X * theta - y).T * (X * theta - y))\n", " return J.item()\n", "\n", "# Wersja macierzowa gradientu funkcji kosztu\n", "def gradient(theta, X, y):\n", " return 1.0 / len(y) * (X.T * (X * theta - y)) \n", "\n", "# Algorytm gradientu prostego (wersja macierzowa)\n", "def gradient_descent(fJ, fdJ, theta, X, y, alpha=0.1, eps=10**-5):\n", " current_cost = fJ(theta, X, y)\n", " logs = [[current_cost, theta]]\n", " while True:\n", " theta = theta - alpha * fdJ(theta, X, y)\n", " current_cost, prev_cost = fJ(theta, X, y), current_cost\n", " if abs(prev_cost - current_cost) > 10**15:\n", " print('Algorithm does not converge!')\n", " break\n", " if abs(prev_cost - current_cost) <= eps:\n", " break\n", " logs.append([current_cost, theta]) \n", " return theta, logs\n", "\n", "# Wykres danych (wersja macierzowa)\n", "def plot_data(X, y, xlabel, ylabel): \n", " fig = plt.figure(figsize=(16*.6, 9*.6))\n", " ax = fig.add_subplot(111)\n", " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", " ax.scatter([X[:, 1]], [y], c='r', s=50, label='Dane')\n", " \n", " ax.set_xlabel(xlabel)\n", " ax.set_ylabel(ylabel)\n", " ax.margins(.05, .05)\n", " plt.ylim(y.min() - 1, y.max() + 1)\n", " plt.xlim(np.min(X[:, 1]) - 1, np.max(X[:, 1]) + 1)\n", " return fig\n", "\n", "# Wykres funkcji fun\n", "def plot_fun(fig, fun, X):\n", " ax = fig.axes[0]\n", " x0 = np.min(X[:, 1]) - 1.0\n", " x1 = np.max(X[:, 1]) + 1.0\n", " Arg = np.arange(x0, x1, 0.1)\n", " Val = fun(Arg)\n", " return ax.plot(Arg, Val, linewidth='2')" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Wczytanie danych (mieszkania) przy pomocy biblioteki pandas\n", "\n", "alldata = pandas.read_csv('data_flats.tsv', header=0, sep='\\t',\n", " usecols=['price', 'rooms', 'sqrMetres'])\n", "data = np.matrix(alldata[['sqrMetres', 'price']])\n", "\n", "m, n_plus_1 = data.shape\n", "n = n_plus_1 - 1\n", "Xn = data[:, 0:n]\n", "Xn /= np.amax(Xn, axis=0)\n", "Xn2 = np.power(Xn, 2) \n", "Xn2 /= np.amax(Xn2, axis=0)\n", "Xn3 = np.power(Xn, 3) \n", "Xn3 /= np.amax(Xn3, axis=0)\n", "\n", "X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n + 1)\n", "X2 = np.matrix(np.concatenate((np.ones((m, 1)), Xn, Xn2), axis=1)).reshape(m, 2 * n + 1)\n", "X3 = np.matrix(np.concatenate((np.ones((m, 1)), Xn, Xn2, Xn3), axis=1)).reshape(m, 3 * n + 1)\n", "y = np.matrix(data[:, -1]).reshape(m, 1)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Postać ogólna regresji wielomianowej:\n", "\n", "$$ h_{\\theta}(x) = \\sum_{i=1}^{n} \\theta_i x^i $$" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "slideshow": { "slide_type": "fragment" } }, "outputs": [], "source": [ "# Funkcja regresji wielomianowej\n", "\n", "def h_poly(Theta, x):\n", " return sum(theta * np.power(x, i) for i, theta in enumerate(Theta.tolist()))\n", "\n", "def polynomial_regression(theta):\n", " return lambda x: h_poly(theta, x)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Funkcja kwadratowa:\n", "\n", "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 x^2 $$" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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11n4N5AOj/B/51tqN1toy4DlgonH+uXca8KL//bOBSdWuNdv/+YvA6f7zg91D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\ncK8/e3bzvXLBydH06bBvn1c+5bbb4Je/9IbBg+c8hiqZk5t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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X2, y, xlabel='x', ylabel='y')\n", "theta_start = np.matrix([0, 0, 0]).reshape(3, 1)\n", "theta, logs = gradient_descent(cost, gradient, theta_start, X2, y)\n", "plot_fun(fig, polynomial_regression(theta), X)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Funkcja sześcienna:\n", "\n", "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 x^2 + \\theta_3 x^3 $$" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 397519.38046962]\n", " [ -841341.14146733]\n", " [ 2253713.97125102]\n", " [ -244009.07081946]]\n" ] }, { "data": { "image/png": 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4fzXw60u2Ya16AoqIhFJZhZcZX24A4AZt+yZRRAlgjDt1YAfapifz3c4CVuUecjscEZGY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\nGdmzDXsKynj0Y+0TLBJuXq/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ZZm7oknTXrvD447Wf//jj0Llz0+ILJC3NmVWs7RnF3Fx4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\nREREksz/A7DOkj9lyGSTAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X3, y, xlabel='x', ylabel='y')\n", "theta_start = np.matrix([0, 0, 0, 0]).reshape(4, 1)\n", "theta, _ = gradient_descent(cost, gradient, theta_start, X3, y)\n", "plot_fun(fig, polynomial_regression(theta), X)\n", "\n", "print(theta)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Regresję wielomianową można potraktować jako szczególny przypadek regresji liniowej wielu zmiennych:\n", "\n", "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 x^2 + \\theta_3 x^3 $$\n", "$$ x_1 = x, \\quad x_2 = x^2, \\quad x_3 = x^3, \\quad \\vec{x} = \\left[ \\begin{array}{ccc} x_0 \\\\ x_1 \\\\ x_2 \\end{array} \\right] $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Uwaga praktyczna: przyda się normalizacja cech, szczególnie skalowanie!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "W ten sposób możemy stosować również inne „pochodne” cechy, np.:\n", "\n", "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 \\sqrt{x} $$\n", "$$ x_1 = x, \\quad x_2 = \\sqrt{x}, \\quad \\vec{x} = \\left[ \\begin{array}{ccc} x_0 \\\\ x_1 \\end{array} \\right] $$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Wielomianowa regresja logistyczna\n", "\n", "Podobne modyfikacje cech możemy również stosować dla regresji logistycznej." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def powerme(x1,x2,n):\n", " X = []\n", " for m in range(n+1):\n", " for i in range(m+1):\n", " X.append(np.multiply(np.power(x1,i),np.power(x2,(m-i))))\n", " return np.hstack(X)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [ { "data": { "text/plain": [ "matrix([[ 1. , 0.36596696, -0.11214686],\n", " [ 0. , 0.4945305 , 0.47110656],\n", " [ 0. , 0.70290604, -0.92257983],\n", " [ 0. , 0.46658862, -0.62269739],\n", " [ 0. , 0.87939462, -0.11408015],\n", " [ 0. , -0.331185 , 0.84447667],\n", " [ 0. , -0.54351701, 0.8851383 ],\n", " [ 0. , 0.91979241, 0.41607012],\n", " [ 0. , 0.28011742, 0.61431157],\n", " [ 0. , 0.94754363, -0.78307311]])" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Wczytanie danych\n", "import pandas\n", "import numpy as np\n", "\n", "alldata = pandas.read_csv('polynomial_logistic.tsv', sep='\\t')\n", "data = np.matrix(alldata)\n", "\n", "m, n_plus_1 = data.shape\n", "n = n_plus_1 - 1\n", "Xn = data[:, 1:]\n", "\n", "Xpl = powerme(data[:, 1], data[:, 2], n)\n", "Ypl = np.matrix(data[:, 0]).reshape(m, 1)\n", "\n", "data[:10]" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Wykres danych (wersja macierzowa)\n", "def plot_data_for_classification(X, Y, xlabel, ylabel): \n", " fig = plt.figure(figsize=(16*.6, 9*.6))\n", " ax = fig.add_subplot(111)\n", " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", " X = X.tolist()\n", " Y = Y.tolist()\n", " X1n = [x[1] for x, y in zip(X, Y) if y[0] == 0]\n", " X1p = [x[1] for x, y in zip(X, Y) if y[0] == 1]\n", " X2n = [x[2] for x, y in zip(X, Y) if y[0] == 0]\n", " X2p = [x[2] for x, y in zip(X, Y) if y[0] == 1]\n", " ax.scatter(X1n, X2n, c='r', marker='x', s=50, label='Dane')\n", " ax.scatter(X1p, X2p, c='g', marker='o', s=50, label='Dane')\n", " \n", " ax.set_xlabel(xlabel)\n", " ax.set_ylabel(ylabel)\n", " ax.margins(.05, .05)\n", " return fig" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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TqQEFcQxiANAz6R+25Adt9tysamej6WfOnsm5hcDqUZQ5IIcOLQzeknItycAG\nRqECAD9sqAaKMgdkdDQaBJLuaUuCuMnJoEahEsCVSYkKFKIc+GFDFSxVlHlN3xqdPHNStbnF17xF\nDpI8wsbTpK2mFxgBXJmUqEAhyoGrDURqczWNPz2u+x69T+NPj/NjXjJLFWU+Vz+nh088rI0PbtSx\nF45l3DKUGWVEymSp5MwC1bhBddTmatr44MYFyd2Jwf7BSiR3NxvE0Wd9DOIomeRzPu/n9eq5V5su\nU5XvPFan3TIi9MCVSWMyZl8fwRtytZKrDZSpt4pBHNWxddNWnbz3pG679jZdbM0LPJD3iW6ijEjZ\nJEFcusI0wRtylPywtXO1gbKVHGlnEMeuG3Zl3KryKFp9wXX96/TGgTfqNX+t6XzyPtFNBHBlU5IC\nhSiXdf3rlg1UylhLi0EcvVPUYD/J+2z2uVcp7xO9xynUMuECyAhYGUuOMIijN4p8anqpAQ191qex\n68cybhHKigCuTEpUoBDVU8beKn7Me6PIwf5K8j6BleAUapkkBQrTFzpOgrht24IqUIjqKeOpp+TH\nvNUoVH7MV6bowX4neZ/AShHAlQkXQEbAxq4b056je5rOC7m3ih/z7gsh2G8n7xNYDerAASgMaqah\nHdQXRJm1WweOHjgAhUFvFdrBqWmAHjgAQKDOnD1DsI/SoQcOAFBq5JmhyigjAgAAEJhcAzgzW29m\nj5rZdPz3kibLbDGzL5nZCTP7qpmNpeZ90sy+ZWbPxLct2a4BAABA9vLugdsr6TF3H5L0WPy40auS\nfs7dr5N0s6T/bGavT83/ZXffEt+e6X2TAQAA8pV3ALdd0qfi+5+StKjSrLt/w92n4/snJX1H0mWZ\ntRAAAKBg8g7g3uDuL8f3/0LSG5Za2MxuktQv6Zupyb8Wn1rdZ2Zre9ROAACAwuj5KFQz+7ykNzaZ\n9aH0A3d3M2tZ08TMLpf0u5J2ul+4CN4HFQV+/ZIeknSfpPtbPP8uSXdJ0qZNmzpcCwBoX22upokT\nE5o+Pa2hDUMau25Mg2sH824WgBLJtQ6cmT0n6W3u/nIcoH3B3X+wyXLfJ+kLkv6juz/c4n+9TdIH\n3P0fLve61IED0CtcTQLAarRbBy7vU6iHJe2M7++U9EjjAmbWL+mgpN9pDN7ioE9mZory5473tLUA\nsITaXE0jB0ZUO1u7cJ3O2XOzqp2Npp85eybnFgIoi7wDuAckvcvMpiW9M34sMxs2s/F4mZ+R9OOS\n3tekXMgBM3tW0rOSLpX0q9k2HwDmTZyYUP1ChsdCda9r4vhExi0CUFa5XonB3U9LekeT6VOSfjG+\n/3uSfq/F89/e0wYCQAemT0+pc+ORAAAWRklEQVRf6HlrNHtuVjOvzGTcIgBllXcPHACUxtCGIQ2s\nGWg6b2DNgDav35xxiwCUFQEcAHTJ2HVj6rPmu9U+69PY9WNN5wFApwjgAKBLBtcO6sidRzTYP3ih\nJ25gzYAG+6Pp6/rX5dxCoCDcpYMHo7/tTMciBHChYyNASdXmahp/elz3PXqfxp8eV22ulneT2rJ1\n01advPek9t+8X3vfulf7b96vk/eepIQIkHbokLRjh3TPPfO/U+7R4x07ovlYUq514PJSqjpwBw9G\nX/bdu6V9+ySz+Y1g/35pclK69da8Wwl0hFpqQMmlf6eS36/Gx2Z5tzIX7daBy3UUKrpgdDT6su/f\nHz1u3AhGF11eFii0dC21RDKyc+TAiE7ee5JTkUDozKLfKyn6vUp+wyoevHWCHrgySB/JJNgIUCCd\nXFpq/Olx3f3HdzctxzGwZkD7b96vXTfs6nWTW+IyWUAXuUt9qWyuer3yv1v0wFVJciSTDuAI3lAQ\nzU6H7jm6p+Xp0CLXUut0XQC5R/lco6ML98mtpldJ0vmQds89/H61iUEMZdBqI6hg7yqKZSWXlipq\nLTUuk4UVCSlZP8tBcY05cPX6fDoQv19tIYALHRsBCmwll5Yqai01LpOFFUnnKSf75KLmKWcZbB46\ntHjAwr598+9VkQLbguIUauhabQRSNH3bNkahIjcrOR2a1FJrNQo1rwEMRT61W3WFzksMKVk/y0Fx\no6NRlYT0KeTkvdq2rViBbUERwIWOjQAFlpwObTUgodXp0KSW2sTxCc28MqPN6zdr7PqxXEefrnRd\n0FtB5CWGkqecZbBp1rxzodV0LMIoVAA9U5uraeODGxeUBEkM9g8GVRKkTOtSaB0k/QfzmYRWKYCR\noblqdxQqOXAAeqZMl5Yq07oUWgd5WEHkJYaWp8yguGBwChVATxXxdOhKlWldCquDPKwg8hJDylNe\n6uoIUnF7DCuKAA5Az63rX5dr8d1uKtO6FFIHeVhB5CWGlKccUrAJcuAAAAXURh5WMDlwoaDocCGQ\nAwcACFObeVjkJXZZMgK0MUhrNR254hQqAKA4OszDIi8RVUUABwAojhXkYZGXiCoigAMAFEdISf9A\njgjgAADFQYV+oC0MYigid+ngwcWFE1tNB1aD7xsABIcArog6qEQOrBrfNwAIDqdQi6iDSuTAqvF9\nA4DgUMi3qEK7+DHCxvcNAAqh3UK+BHBF1kYlcqBr+L4BCEWJrxoRxJUYzGy9mT1qZtPx30taLHfe\nzJ6Jb4dT0682sy+b2YyZTZhZf3at77E2K5EDXcH3DUBIyN3NfRDDXkmPufuQpMfix838jbtviW+3\npKb/uqR97r5Z0ncllaOSY2Ml8np9PkeJH1V0G983AN2Uxcj2dO5usp+qWu6uu+d2k/ScpMvj+5dL\neq7FcmeaTDNJfyXp4vjxj0k62s7r3njjjV5ok5Pukvvu3e71ejStXo8eS9F89E69Hr3HyXu/3PTQ\n8X0D0E1Z7VPS/zO5pV8zUJKmvJ0Yqp2FenWT9L3UfUs/bljuNUlTkp6UNBpPu1TSTGqZKyUdb+d1\nCx/AVS2AKJqqBTR83wB0U3p/mexHGx9387XSAVwJ9leFCeAkfV7S8Sa37Y0Bm6TvtvgfG+O/10j6\nP5L+TqcBnKS74iBwatOmTd1+v1EmWe58sDoEn0AxZdE7Rg9crj1wbZ1CbXjOJyXdVupTqMhfSXcM\npVO13lIgJL3sHSvxgXa7AVzegxgOS9oZ398p6ZHGBczsEjNbG9+/VNJbJX0tXsknFAVzLZ8PrEhy\n8ew0aqIVTy8TmZ1LjAErlmyLaSsZFNVqezt4MNrO3//++X3zvn3z+4MKjELNuwdug6LRp9OKTrWu\nj6cPSxqP7/8DSc9K+vP4767U86+R9KeSZiT9gaS17bwuPXAl143Tap30wHEaL1+96i2ldw9YmW72\njrXaDt///mj6H/7h4tcOfL+rEE6h5nUjgCu51f7wdrrz4Yc+f704VVPiUzRAT3Vzn1jB7ZAAjgCu\nula7wXe686ngDqZQepmvSC4k0Llun5Wo2HZIAEcAV22r2eBXsvOp2A6mMLIInktYpqCSSHUIW4W2\nw3YDuLwHMQC9sZpBCGbSrbcuXrbV9JW8npMg3xWHDs0PWOhFIrN3KREb+ePSS9np9v6N7bC5dqK8\nst3ogauArHvEOn098ua6o5e9KpwaLxc+z+yQA7cq4hQqAVxlZb3Br+T1KrhTCg5BdvmQ6pCNLEah\nlng7JIAjgKuurDf4lb4ePybFRs5UOVUolypX3dq/VXA7bDeAs2jZahkeHvapqam8m4FecY/yWUZH\nF+agtZqe5+u5S32pVNR6nWLBQK+4zxd6TqTzJ9Fd7N9WxMyecvfh5ZZjEAPKZyWDEPJ4veTHJI3E\nXKA30sHb7t1RMNF4FQ90D/u3niOAA/LAjwmQrV6PWMY89m+ZuDjvBgCV1OrHRIqmb9sW9d4B6I7R\nUWlycmFKQ7Ldbdu2uuvmYiH2b5kgBw7IQ9Z5egCQFfZvq9JuDhwBHAAAQEEwiAEAEs6VLwCUCwEc\nUDVVDGa4jBKAkiGAA6qmisHM6OjiUXDpUXIksAMIDKNQgapJBzNSNDqs7MFM4yi4ZN0p4gogUAxi\nAKqoqhXpqQwPoOAYxACgtXSPVKIKwRuV4QGUBAEcUEVVC2aoDA+gZAjggKqpYjDDZZQAlAyDGICq\nqeJlbriMEoCSYRADUDVc5gYACotBDKiGKhalXS2zqIetMUhrNR0AUDgEcAhbFYvSAgAqjxw4hK2K\nRWkBAJVHDxzC1jiasK9vcYI+AGDlSFUpJAI4hK+KRWkBICukqhRSrgGcma03s0fNbDr+e0mTZX7C\nzJ5J3f6fmY3G8z5pZt9KzduS/Vogd1UrSgsAWUqnqiT7VlJVcpd3D9xeSY+5+5Ckx+LHC7j7E+6+\nxd23SHq7pFcl/a/UIr+czHf3ZzJpNYqjikVpASBLpKoUUt4B3HZJn4rvf0rScmH8bZL+yN1f7Wmr\nEA4q7ANA74WaqlLi/L28A7g3uPvL8f2/kPSGZZa/XdKnG6b9mpl91cz2mdnaVk80s7vMbMrMpk6d\nOrWKJqNQkgr76R1JsqNJKu8DAFYn1FSVEufv9TyAM7PPm9nxJrft6eU8uiREy2+CmV0u6YclHU1N\n/qCkN0v6+5LWS7qv1fPd/SF3H3b34csuu2w1q4QiKVJR2hIf6QGosJBTVUqcv9fzOnDu/s5W88zs\nL83scnd/OQ7QvrPEv/oZSQfd/Vzqfye9d3Nm9tuSPtCVRgMrkRzppU/npncWk5Plu8YogPIL+frJ\njW1NaoaWIH8v71OohyXtjO/vlPTIEsveoYbTp3HQJzMzRflzx3vQRqA9JT7SA1BheaSqdPOMRqj5\ne8vIO4B7QNK7zGxa0jvjxzKzYTMbTxYys6skXSnpiw3PP2Bmz0p6VtKlkn41gzYDzTFSC0AZ5ZGq\n0s3ctVDz95ZhHvgKrMTw8LB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data_for_classification(Xpl, Ypl, xlabel=r'$x_1$', ylabel=r'$x_2$')" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Propozycja hipotezy:\n", "\n", "$$ h_\\theta(x) = g(\\theta^T x) = g(\\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\theta_3 x_3 + \\theta_4 x_4 + \\theta_5 x_5) \\; , $$\n", "\n", "gdzie $g$ – funkcja logistyczna, $x_3 = x_1^2$, $x_4 = x_2^2$, $x_5 = x_1 x_2$." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def safeSigmoid(x, eps=0):\n", " y = 1.0/(1.0 + np.exp(-x))\n", " if eps > 0:\n", " y[y < eps] = eps\n", " y[y > 1 - eps] = 1 - eps\n", " return y\n", "\n", "def h(theta, X, eps=0.0):\n", " return safeSigmoid(X*theta, eps)\n", "\n", "def J(h,theta,X,y, lamb=0):\n", " m = len(y)\n", " f = h(theta, X, eps=10**-7)\n", " j = -np.sum(np.multiply(y, np.log(f)) + \n", " np.multiply(1 - y, np.log(1 - f)), axis=0)/m\n", " if lamb > 0:\n", " j += lamb/(2*m) * np.sum(np.power(theta[1:],2))\n", " return j\n", "\n", "def dJ(h,theta,X,y,lamb=0):\n", " g = 1.0/y.shape[0]*(X.T*(h(theta,X)-y))\n", " if lamb > 0:\n", " g[1:] += lamb/float(y.shape[0]) * theta[1:] \n", " return g\n", "\n", "def classifyBi(theta, X):\n", " prob = h(theta, X)\n", " return prob" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Metoda gradientu prostego dla regresji logistycznej\n", "def GD(h, fJ, fdJ, theta, X, y, alpha=0.01, eps=10**-3, maxSteps=10000):\n", " errorCurr = fJ(h, theta, X, y)\n", " errors = [[errorCurr, theta]]\n", " while True:\n", " # oblicz nowe theta\n", " theta = theta - alpha * fdJ(h, theta, X, y)\n", " # raportuj poziom błędu\n", " errorCurr, errorPrev = fJ(h, theta, X, y), errorCurr\n", " # kryteria stopu\n", " if abs(errorPrev - errorCurr) <= eps:\n", " break\n", " if len(errors) > maxSteps:\n", " break\n", " errors.append([errorCurr, theta]) \n", " return theta, errors" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "theta = [[ 1.59558981]\n", " [ 0.12602307]\n", " [ 0.65718518]\n", " [-5.26367581]\n", " [ 1.96832544]\n", " [-6.97946065]]\n" ] } ], "source": [ "# Uruchomienie metody gradientu prostego dla regresji logistycznej\n", "theta_start = np.matrix(np.zeros(Xpl.shape[1])).reshape(Xpl.shape[1],1)\n", "theta, errors = GD(h, J, dJ, theta_start, Xpl, Ypl, \n", " alpha=0.1, eps=10**-7, maxSteps=10000)\n", "print(r'theta = {}'.format(theta))" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Wykres granicy klas\n", "def plot_decision_boundary(fig, theta, X):\n", " ax = fig.axes[0]\n", " xx, yy = np.meshgrid(np.arange(-1.0, 1.0, 0.02),\n", " np.arange(-1.0, 1.0, 0.02))\n", " l = len(xx.ravel())\n", " C = powerme(xx.reshape(l, 1), yy.reshape(l, 1), n)\n", " z = classifyBi(theta, C).reshape(int(np.sqrt(l)), int(np.sqrt(l)))\n", "\n", " plt.contour(xx, yy, z, levels=[0.5], lw=3);" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/pawel/.local/lib/python2.7/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'lw'\n", " s)\n" ] }, { "data": { "image/png": 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xpuAM3lj8LJM3Ih/9c+p9CI8Ix9sjP0AoNn6QvjCBIzKS8ibG9iGJ27IyG49e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\n8MpdiIyK1Dq0ypk1y16n7HpOdp6zBw2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HZl4HvJ/qejhJmjuvgZOkNYqIDcAH\ngecAF2bmh1qukqQFZwInSZLUM55ClSRJ6hkTOEmSpJ4xgZMkSeoZEzhJkqSeMYGTJEnqGRM4SZKk\nnjGBkyRJ6hkTOEmSpJ75H6zqsn7OT0cUAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data_for_classification(Xpl, Ypl, xlabel=r'$x_1$', ylabel=r'$x_2$')\n", "plot_decision_boundary(fig, theta, Xpl)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Wczytanie danych\n", "\n", "alldata = pandas.read_csv('polynomial_logistic.tsv', sep='\\t')\n", "data = np.matrix(alldata)\n", "\n", "m, n_plus_1 = data.shape\n", "Xn = data[:, 1:]\n", "\n", "n = 10\n", "Xpl = powerme(data[:, 1], data[:, 2], n)\n", "Ypl = np.matrix(data[:, 0]).reshape(m, 1)\n", "\n", "theta_start = np.matrix(np.zeros(Xpl.shape[1])).reshape(Xpl.shape[1],1)\n", "theta, errors = GD(h, J, dJ, theta_start, Xpl, Ypl, \n", " alpha=0.1, eps=10**-7, maxSteps=10000)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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Od7ouPDgcbev7cCuOjwkKDsKND/fHJ9vn4NbHb8KSz//E/ReOwYK3foa5xKx1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\n4awjsuL71fLxM1/JpAEvnh7qwz4m37Q74+XnuUs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Przykład dla większej liczby cech\n", "fig = plot_data_for_classification(Xpl, Ypl, xlabel=r'$x_1$', ylabel=r'$x_2$')\n", "plot_decision_boundary(fig, theta, Xpl)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 2.6. Problem nadmiernego dopasowania" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Obciążenie a wariancja" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Dane do prostego przykładu\n", "\n", "data = np.matrix([\n", " [0.0, 0.0],\n", " [0.5, 1.8],\n", " [1.0, 4.8],\n", " [1.6, 7.2],\n", " [2.6, 8.8],\n", " [3.0, 9.0],\n", " ])\n", "\n", "m, n_plus_1 = data.shape\n", "n = n_plus_1 - 1\n", "Xn1 = data[:, 0:n]\n", "Xn1 /= np.amax(Xn1, axis=0)\n", "Xn2 = np.power(Xn1, 2) \n", "Xn2 /= np.amax(Xn2, axis=0)\n", "Xn3 = np.power(Xn1, 3) \n", "Xn3 /= np.amax(Xn3, axis=0)\n", "Xn4 = np.power(Xn1, 4) \n", "Xn4 /= np.amax(Xn4, axis=0)\n", "Xn5 = np.power(Xn1, 5) \n", "Xn5 /= np.amax(Xn5, axis=0)\n", "\n", "X1 = np.matrix(np.concatenate((np.ones((m, 1)), Xn1), axis=1)).reshape(m, n + 1)\n", "X2 = np.matrix(np.concatenate((np.ones((m, 1)), Xn1, Xn2), axis=1)).reshape(m, 2 * n + 1)\n", "X5 = np.matrix(np.concatenate((np.ones((m, 1)), Xn1, Xn2, Xn3, Xn4, Xn5), axis=1)).reshape(m, 5 * n + 1)\n", "y = np.matrix(data[:, -1]).reshape(m, 1)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X1, y, xlabel='x', ylabel='y')" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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9st+RACAuUcCAOFF5qF7XF5fKOelH5w3RaQM7+x0JAOIWBQyIA8453frMUu2o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\nVwaap7tzbkfT5zsldT/O49L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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X1, y, xlabel='x', ylabel='y')\n", "theta_start = np.matrix([0, 0]).reshape(2, 1)\n", "theta, _ = gradient_descent(cost, gradient, theta_start, X1, y, eps=0.00001)\n", "plot_fun(fig, polynomial_regression(theta), X1)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Ten model ma duże **obciążenie** (**błąd systematyczny**, _bias_) – zachodzi **niedostateczne dopasowanie** (_underfitting_)." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Amsn6HVW64vE52rWnTif1ydB9E45TDOULLSSPEhbWKGAA0Ay2lO3VDx+bo5KKGo3MSdfD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\nAADgsf8PQ5GyUdomDXUAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X2, y, xlabel='x', ylabel='y')\n", "theta_start = np.matrix([0, 0, 0]).reshape(3, 1)\n", "theta, _ = gradient_descent(cost, gradient, theta_start, X2, y, eps=0.000001)\n", "plot_fun(fig, polynomial_regression(theta), X1)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Ten model jest odpowiednio dopasowany." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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AGWP6SxojabHLHEA0WbSlVGt3Vqhrcry+NYbffQDABWcFzBiTIuk5SbOstRX7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\nmIB/QNmZqfrlN4+SJP38+dU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(X5, y, xlabel='x', ylabel='y')\n", "theta_start = np.matrix([0, 0, 0, 0, 0, 0]).reshape(6, 1)\n", "theta, _ = gradient_descent(cost, gradient, theta_start, X5, y, alpha=0.5, eps=10**-7)\n", "plot_fun(fig, polynomial_regression(theta), X1)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Ten model ma dużą **wariancję** (_variance_) – zachodzi **nadmierne dopasowanie** (_overfitting_)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Obciążenie (błąd systematyczny, _bias_)\n", "\n", "* Wynika z błędnych założeń co do algorytmu uczącego się.\n", "* Duże obciążenie powoduje niedostateczne dopasowanie." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Wariancja (_variance_)\n", "\n", "* Wynika z nadwrażliwości na niewielkie fluktuacje w zbiorze uczącym.\n", "* Wysoka wariancja może spowodować nadmierne dopasowanie (modelując szum zamiast sygnału)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 2.7. Metodologia testowania" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Zbiór uczący a zbiór testowy" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "* Na zbiorze uczącym (treningowym) uczymy algorytmy, a na zbiorze testowym sprawdzamy ich poprawność.\n", "* Zbiór uczący powinien być kilkukrotnie większy od testowego (np. 4:1, 9:1 itp.).\n", "* Zbiór testowy często jest nieznany.\n", "* Należy unikać mieszania danych testowych i treningowych – nie wolno „zanieczyszczać” danych treningowych danymi testowymi!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "Czasami potrzebujemy dobrać parametry modelu, np. $\\alpha$ – który zbiór wykorzystać do tego celu?" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true, "slideshow": { "slide_type": "subslide" } }, "source": [ "### Zbiór walidacyjny" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Do doboru parametrów najlepiej użyć jeszcze innego zbioru – jest to tzw. **zbiór walidacyjny**" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ " * Zbiór walidacyjny powinien mieć wielkość zbliżoną do wielkości zbioru testowego, czyli np. dane można podzielić na te trzy zbiory w proporcjach 3:1:1, 8:1:1 itp." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Walidacja krzyżowa" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Którą część danych wydzielić jako zbiór walidacyjny tak, żeby było „najlepiej”?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ " * Niech każda partia danych pełni tę rolę naprzemiennie!" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "Żródło: https://chrisjmccormick.wordpress.com/2013/07/31/k-fold-cross-validation-with-matlab-code/" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Walidacja krzyżowa\n", "\n", "* Podziel dane $D = \\left\\{ (x^{(1)}, y^{(1)}), \\ldots, (x^{(m)}, y^{(m)})\\right\\} $ na $N$ rozłącznych zbiorów $T_1,\\ldots,T_N$\n", "* Dla $i=1,\\ldots,N$, wykonaj:\n", " * Użyj $T_i$ do walidacji i zbiór $S_i$ do trenowania, gdzie $S_i = D \\smallsetminus T_i$. \n", " * Zapisz model $\\theta_i$.\n", "* Akumuluj wyniki dla modeli $\\theta_i$ dla zbiorów $T_i$.\n", "* Ustalaj parametry uczenia na akumulowanych wynikach." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Walidacja krzyżowa – wskazówki\n", "\n", "* Zazwyczaj ustala się $N$ w przedziale od $4$ do $10$, tzw. $N$-krotna walidacja krzyżowa (_$N$-fold cross validation_). \n", "* Zbiór $D$ warto zrandomizować przed podziałem.\n", "* W jaki sposób akumulować wyniki dla wszystkich zbiórow $T_i$?\n", "* Po ustaleniu parametrów dla każdego $T_i$, trenujemy model na całych danych treningowych z ustalonymi parametrami.\n", "* Testujemy na zbiorze testowym (jeśli nim dysponujemy)." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### _Leave-one-out_\n", "\n", "Jest to szczególny przypadek walidacji krzyżowej, w której $N = m$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "* Jaki jest rozmiar pojedynczego zbioru $T_i$?\n", "* Jakie są zalety i wady tej metody?\n", "* Kiedy może być przydatna?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Zbiór walidujący a algorytmy optymalizacji\n", "\n", "* Gdy błąd rośnie na zbiorze uczącym, mamy źle dobrany parametr $\\alpha$. Należy go wtedy zmniejszyć.\n", "* Gdy błąd zmniejsza się na zbiorze trenującym, ale rośnie na zbiorze walidującym, mamy do czynienia ze zjawiskiem **nadmiernego dopasowania** (_overfitting_).\n", "* Należy wtedy przerwać optymalizację. Automatyzacja tego procesu to _early stopping_." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 2.8. Regularyzacja" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def SGD(h, fJ, fdJ, theta, X, Y, \n", " alpha=0.001, maxEpochs=1.0, batchSize=100, \n", " adaGrad=False, logError=False, validate=0.0, valStep=100, lamb=0, trainsetsize=1.0):\n", " errorsX, errorsY = [], []\n", " errorsVX, errorsVY = [], []\n", " \n", " XT, YT = X, Y\n", " \n", " m_end=int(trainsetsize*len(X))\n", " \n", " if validate > 0:\n", " mv = int(X.shape[0] * validate)\n", " XV, YV = X[:mv], Y[:mv] \n", " XT, YT = X[mv:m_end], Y[mv:m_end] \n", " m, n = XT.shape\n", "\n", " start, end = 0, batchSize\n", " maxSteps = (m * float(maxEpochs)) / batchSize\n", " \n", " if adaGrad:\n", " hgrad = np.matrix(np.zeros(n)).reshape(n,1)\n", " \n", " for i in range(int(maxSteps)):\n", " XBatch, YBatch = XT[start:end,:], YT[start:end,:]\n", "\n", " grad = fdJ(h, theta, XBatch, YBatch, lamb=lamb)\n", " if adaGrad:\n", " hgrad += np.multiply(grad, grad)\n", " Gt = 1.0 / (10**-7 + np.sqrt(hgrad))\n", " theta = theta - np.multiply(alpha * Gt, grad)\n", " else:\n", " theta = theta - alpha * grad\n", " \n", " if logError:\n", " errorsX.append(float(i*batchSize)/m)\n", " errorsY.append(fJ(h, theta, XBatch, YBatch).item())\n", " if validate > 0 and i % valStep == 0:\n", " errorsVX.append(float(i*batchSize)/m)\n", " errorsVY.append(fJ(h, theta, XV, YV).item())\n", " \n", " if start + batchSize < m:\n", " start += batchSize\n", " else:\n", " start = 0\n", " end = min(start + batchSize, m)\n", " return theta, (errorsX, errorsY, errorsVX, errorsVY)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Przygotowanie danych do przykładu regularyzacji\n", "\n", "n = 6\n", "\n", "data = np.matrix(np.loadtxt(\"ex2data2.txt\", delimiter=\",\"))\n", "np.random.shuffle(data)\n", "\n", "X = powerme(data[:,0], data[:,1], n)\n", "Y = data[:,2]" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def draw_regularization_example(X, Y, lamb=0, alpha=1, adaGrad=True, maxEpochs=2500, validate=0.25):\n", " plt.figure(figsize=(16,8))\n", " plt.subplot(121)\n", " plt.scatter(X[:, 2].tolist(), X[:, 1].tolist(),\n", " c=Y.tolist(),\n", " s=100, cmap=plt.cm.get_cmap('prism'));\n", "\n", " theta = np.matrix(np.zeros(X.shape[1])).reshape(X.shape[1],1)\n", " thetaBest, err = SGD(h, J, dJ, theta, X, Y, alpha=alpha, adaGrad=adaGrad, maxEpochs=maxEpochs, batchSize=100, \n", " logError=True, validate=validate, valStep=1, lamb=lamb)\n", "\n", " xx, yy = np.meshgrid(np.arange(-1.5, 1.5, 0.02),\n", " np.arange(-1.5, 1.5, 0.02))\n", " l = len(xx.ravel())\n", " C = powerme(xx.reshape(l, 1),yy.reshape(l, 1), n)\n", " z = classifyBi(thetaBest, C).reshape(int(np.sqrt(l)), int(np.sqrt(l)))\n", "\n", " plt.contour(xx, yy, z, levels=[0.5], lw=3);\n", " plt.ylim(-1,1.2);\n", " plt.xlim(-1,1.2);\n", " plt.legend();\n", " plt.subplot(122)\n", " plt.plot(err[0],err[1], lw=3, label=\"Training error\")\n", " if validate > 0:\n", " plt.plot(err[2],err[3], lw=3, label=\"Validation error\");\n", " plt.legend()\n", " plt.ylim(0.2,0.8);" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/pawel/.local/lib/python2.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n", " \n" ] }, { "data": { "image/png": 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YuTJMnQobN2L6+LD8izVUvL8cpSoVT/sYTuCT14fRP43gkUFtWPzpMl5r9z4h\nV+2oRpwe99wD+/bBmDFQqpSVbHp4QKtWsHSptbzVnn22krnWrbP+fqcmJMRafiwiIiIi6aaEViwd\nO6Y+I+flBaNGpX8MFxd49FHYutWa6Y2OthK0nj3B3Z0Dmw7z96HTtO3TIv1jOIGrmysDPn2KIdOe\nZfcv+xl0/wj+OZzGfcb28vODQYPg+HFrX3JEBKxaBc2aZc54knbh4fYfb3X9eubGIiIiIpLLKaEV\ni80G69dbS49vn6n18LCWuc6aBfffn2khLP9iDV6+njTuWi/TxshMbfs054M1bxJyJZRB949k+8pd\nzg5JnKF0afvaeXhAxYqZG4uIiIhILqeEVv5TvDj88QdMngw1algztiVLwgsvWNe7dMm0oYMvXWf9\nt5to9kRDvHxTKB6VzVVpWJFJ28ZQuFQhXnv4feaPXYJp72yd5A716oG/f+rtDMPa9ywiIiIi6aaE\nVm7l6Qm9esHOnXD+PJw4Ye3ZLJ65e1qXf7GWqIhoOgxsnanjZAWrWNS7NOpSjxkj5jK62yeEh0Y4\nOyzJKoZhFUFLqnjXTd7e1lL7okWzLi4RERGRXEgJrThdXFwcP322mupNK1G6cglnh+MQXj6ejPzm\nBfqM6cFvC7cwuP6rnP7zrLPDkqzSubOV1Hp6Wh83ubpae9E7dYIpU5wXn4iIiEguoYRWnG7fhkOc\nO3mBNjmsGFRqDMPgsZc7MHr5q1w8fZkBtYezael2Z4clWeWZZ6ziXcOHQ2AgVK9unfO7dSvMmZPy\nmcIiIiIiYhcltOJ0q2auw9vPi/odajs7lEwR2KoaU3aM5Z4yhXnzkQ+YMWJu5p1XK9lLkSLw5puw\nfTvs2gVffGGduSwiIiIiDqGEVpwq9FooG77bTNPHG+Dp7eHscDJNkVJ3MX7juzzUtwXzxy7h5Zaj\nuHDqkrPDypmOHbMSxOPHnR2JiIiIiDiZElpxqnXzNxEZHkWbPs2dHUqmc/d054XPn+HlWQM5suMv\nnq0xjC0/BTk7rJxj0SKoVAkqV4YWLf77fPFiZ0cmkuMYhtHaMIzDhmH8aRjG8CTuf2IYxu4bH0cM\nw7jqjDhFRERSo4RWnGrll2spXaUE5QPLODuUTGNiso+1fMAjDKUKv/YczhNB1SlQ3J/X249hygtf\nERUZ7ewws7dRo6zq2wcPQng4BAdb/z1wwKoW/M47zo5QJMcwDMMVmAy0AQKAboZhBCRsY5rmENM0\nq5umWR2YCOg3RyIiki2pKok4zeEdf3F4+188N/5/GIbh7HAyRQhXeIeWnOEwEYTEXz9Zfh9scqPh\ny0P5fsJy9m44yIi5gylZsZiSY1MdAAAgAElEQVQTo82mNm2CsWMhLCzp+2Fh1tFSzZtD/fpZG5tI\nzlQH+NM0zWMAhmHMBzoAB5Np3w14M4tiExERSRPN0IrT/DB5BV6+nrTq3cTZoWSKOOIYRXP+Zt8t\nySxAJKFEel7jyISxDPzhMS6eusRztV5m6ZRVmKbppIizqTFjrNnYlISHwwcfZE08IjlfUeCfBF+f\nunEtEcMwSgKlgV+Sud/PMIwdhmHsuHDhgsMDFRERSY0SWnGKqxeu8ev8TbTo2RifPN7ODifeNc6z\nkHcZSBmeohAvEMBKJhPO9TT3tYdVnOUoMUQl2yaKcA63m8u0vR9TtXEAEwd+wevtx3D53ysZeRm5\ny+rVkFqSb5qwcmXWxCNyZ3kcWGiaZpKl2U3TnGaaZqBpmoGFChXK4tBERESU0IqTrJzxC9GR0XQY\n2NrZocTbxy8MpAyLGc05jnGdi5zmEF/zCgO4l384kKb+fmJ8opnZ25mY7GYFHkUMRi8byXPj/8eu\ntfvoU3ko67/bnJGXk3tE27m/2N52InIaKJ7g62I3riXlcWBepkckIiKSTkpoJcvFxcWx/Iu1VG0c\nkG32jJ7hCGNpTwQhRBNxy71IQrnORd6gMaHYX+jzHH/Z1c4Ndy5zBhcXFzo+35YpQR9wT5nCvPvY\nOEY/MZ7gy2mfHc5V7rrLvnaFC2duHCK5x3agnGEYpQ3DcMdKWpfe3sgwjAqAP6DfromISLalhFay\n3O51Bzh77Bxt+7RwdijxljA2USJ7u2jC+YUv7e7THS+72sUSgwf/LbsuWbEYn/4+mifffozfFm6h\nT6UhrF+w6c7dWztwIHh6ptzGywsGDcqaeERyONM0Y4CBwCrgELDANM0DhmGMMgyjfYKmjwPzzTv2\nfz4iIpITGDnxfSowMNDcsWOHs8OQdBr9xHiCVu1m/ulpuHu6p+nZWGLYwVKOshUwKM/91OJhXDNQ\nsDuOOHrgk2pCC3AX9zLZzpnXRYxmEe+m2m9BSjKF4xgkrvT8567jjOs7laM7j3P/w7UYNOlp7iph\nxz61Xbtg6VLreJsyZeDxxyF/frviTtG5czB/Ppw8Cf7+8OijEBCQ+nMZcfkyVKgAFy8mvZfWMKBg\nQfjjD8e8RrkjGYYRZJpmoLPjyMn03iwiIo5k73uzju2RLHXtYjC/L97KQ/1apjmZ3c5SJtObWGKI\nuFGkyRM/bLgzkNnUpG26YgrnOnEkWe8kkWDO291vC/qymPdSbOOBN4/wSpLJLEDZGqWZuOV9vp+w\nnFlvfEufykPp/c7jdBjYGldX18QPnDwJjzwCR45AZCTExoK3N7z4IgwYYFUCdknHwozoaHjuOfj6\nayuBDA8HNzd4/32oUQMWL868Jb/588PGjdC0qZWghyTYl+znZ338+quSWREREZE7kJYcS5ZaMeMX\noqNiaNsvbcuNd/Aj4+lGKFfik1mACK5znUt8TGd2kb4qtx54Y2LfSgUPfOzuNy938Txzkl167IE3\nVWlFS55JsR9XN1c6D23H9P3jqPxABaYOmcmg+0dyJOi2meJ//4U6dWDfPuts1tgbSXpYGEREwNSp\n0Lev3fHHM03o0gW++cbq5+YROjEx1ufbt0PdunDV/v3FaVa+PBw/DjNmQLNmULmyde7sjBlw4gSU\nK5d5Y4uIiIhItqWEVrJMbGwsP05dRfWmlShduYT9zxHLVJ4mirBk20QRzhSeIo64NMflho0qNLej\nnTsN6Z6mvuvSiTdYQwCNseGJN3nxwAd/7qEb7/ESi3Cx859hkVJ3MXrZSF6d9wIXT11iUN0RTHnh\nK0KvhVoN3noLrlz5L5G9XVgYzJsHe/em6TWwfj2sWWM9n5ToaCuZHjcubf2mlbs7dO0Ka9daSfua\nNVaibbNl7rgiIiIikm0poZUss+XHIM7/fZH2A9qk6bndrCTKjv2tEVxnH2vSFVsnRuJOyufhuuJG\nG9JeeOg+6vM2vzKZY7zOz7zPNj7jHx5isN3J7E2GYdDksQZ8eehT2vZtwZKJK+hd/nmWT15O7Ow5\nqR9dExUFn3ySthfw0UfJJ7M3RUbCpEnJJ9PZ2blzEBRk7cGNS/svRERERETEeZTQSpZZMmkFhYoX\noH77tNVdOcEuIglNtV00ERxnV7piC6ARj/F2kkmtgYE7XgxiDndRKl39A/hzN2WpTXEC0pzI3s43\nnw+Dp/Zj0rb3KVr+bj4Z9BUDox5gPwVSfjA2FrZsSdtgQUFJF2O6XUQEXLiQtr6dacsWa19uyZLW\nMubAQCheHD79VImtiIiISA6hhFayxJ+7j7P7l/10GNAGV7ckihmlwMAl2aJJSbVNr/a8xHB+pBJN\nccWGO1644U4dOvIuv1OXTunuO7OUr1WGTza8w6sfdeGaaWOI0ZRR3M+ZlPb6prUolL3t4+LSV3DK\nGZYutZLYX3+1ZpeDgyE0FM6cgZEjoVMnJbUiIiIiOYCqHEuW+Gnqajy83GnbN/W9qrcrTz3c8SKC\nkBTbueFBeeqlN0QAqtCMKjQjnBAiuI43+fCw8zxZZzEMgyYDH6Hum8+wKORuvuU+NnMP7fmL7hwi\nD1H/NbbZrEQuLR54ABYuTD3B8/e3js/J7i5ehG7d/itudbuwMPj5Z6uI1oABWRubiIiIiKSJQ6ZT\nDMNobRjGYcMw/jQMY3gS9z8xDGP3jY8jhmFcTXAvNsG9pY6IR7KX0OAw1n7zG00ea4Cfv2+an69E\nE3xJ/UiWfBSmAg3SE2IiXvjiz93ZPpmN5+6O17N96OFxjJmspCUnWEJZetKG2QQQevN3V25uMHhw\n2vp+6SXw9Ey5jZcXDBmSM2Zov/gi9SXUYWEwdqx9S61FRERExGky/NOnYRiuwGSgDRAAdDMMIyBh\nG9M0h5imWd00zerARGBxgtvhN++Zptk+o/FI9rP269+ICI2kXf9W6XrewGAw3+CRQtEmD7wZzDd2\nL03OlV57DYoWpYB7HEPZyef8TC3OMccIoCdtWGCrRMTgoVC2bNr6rV0bnnzSOs82KZ6e1rE6g9Je\nMMsp5s1LfnY2oUuXrKOCRERERCTbcsR0Sh3gT9M0j5mmGQXMBzqk0L4bMM8B40oOEBcXx5JJKyhX\n617KB5ZJdz8VaMDrrKEI5fDABxueuOOFBz7cw328yTrKUdeBkedAefNaZ8K2agWenpTyieUNj11M\n8dpEBbfrTI+pSM+v/mXhuB+JCItMW9+TJ8Pw4eDrC35+4OFhfe7pCR06wMaN1ixtTmBPMgvg6pp6\ndefbmaZ1zNGUKTBtGhw+nPb4RERERMRujthDWxT4J8HXpyDpzMIwjJJAaeCXBJc9DcPYAcQAY0zT\nXOKAmCSb2LlmH//8cZqXZw3EMDI2e3of9ZjAYf5kG3+xA4Cy1KEstR0Rau6QPz/8+COcPg0rVkBo\nKOVKleK9Nm3Yt/Uv5oz6js9fms23H/xA15fa07ZfC3zypHxcEQCGAa+/bi0/XrbM6j9PHnj4YShU\nKPNflyOVKQNHj6beLioKiha1v98VK6BfP7h6FWJirOXXpglVq8KcOVCuXPpjFhEREZEkGWYG94gZ\nhtEZaG2aZp8bX/cE6pqmOTCJtq8AxUzTHJTgWlHTNE8bhnEvVqLb3DTNv5J4th/QD6BEiRK1Tp48\nmaG4JWu8+vB7HA06xtcnpuLuYXN2OALs++0Qc0Z9x661+/DO48XDz7Si4+C2FLwn9X3KucLKldCl\nC4SkUGTMMKxkfamd2/qXLIHu3ZOe0XVxsZL/7dvTvtxbsoxhGEGmaabtTDG5RWBgoLljxw5nhyEi\nIrmEve/NjlhyfBoonuDrYjeuJeVxbltubJrm6Rv/PQb8CtRI6kHTNKeZphlommZgoZw2I3SHOnXk\nDNuW7+LhZ1opmc1GqjSsyAc/v8Gkre9Tu3V1Fn68lJ6ln+PDpyZz4sA/qXeQ07VqZe35dXdPvo2X\nF7zzjn39RURAr17JL0+Oi7OOBerbN+2xioiIiEiKHJHQbgfKGYZR2jAMd6ykNdG0hmEYFQB/YHOC\na/6GYXjc+Lwg0AA46ICYxB7BwXD+vLU8MhMs/PhHbB42Hu7TDC5cgGvXMmUcSZ/7apfltflDmXlk\nIm37tmD9t5voW2UoIx96j12/7COjqzeyLRcXWLMGqlSx9gEn5O1tXVu6FKpVs6+/775LvRpyXBxs\n2QInTqQrZBERERFJWoYTWtM0Y4CBwCrgELDANM0DhmGMMgwjYdXix4H55q0/JVcEdhiGsQdYh7WH\nVgltZjJNmD/f+mG9YEEoWRLy5bMq1J465bBhrl0MZvXsX2lVzp38AfdCiRLWXsuAAJg9O/UzTSXL\n3H1vYQZN6sM3f39G71GPczToGC+3GEWfykP4fsJyQq6GOjtEx/P3t5YAL1liFbWqVAnq1oUPPrD2\nBzdPw3nJa9emvHz5JpsNtm5Nf8wiIiIikkiG99A6g/bppFNcHPTsCT/8AKG3JSk2G/j4wIYN1sxV\nBs17cRpffvIz093WUSr60q03fXysZZ/ffWdVks0GYollNyvYxLeEEcw93EcL+nE32WvP43lOsIbp\n/MN+PPHlfjoTSDtcHVLfzRIVEcUv835n2eer+WPbn3h4udPksQa0froZlerfl+HiXrlOz57w9dep\nt/Pzg88/h27dMj8mSTPtoc04vTeLiIgj2fverIT2TjJhAowYkfJRJHfdZc3U2tK/5zU2Moqevp0p\nGnuND80NSTfy9oZXX4WRI9M9TnqEco3zHMMVG3dTHhvunGAP79GGcEKI4DoArthwwZVA2jOI2djw\nyNI4bxdDNJ/Rl018i0kcMUQB4Ikf7ngygmWZUu356M5j/PTZatbN/53wkAhKVCzKQ/1a0rJXY/z8\nfVPvIAVXOcdlTt84eql8zj1DeMoUePnlxL8kup2XF+zYYa1SkGxHCW3G6b1ZREQcSQmt3CouzjqC\n5N9/U27n5wczZlhVYNNp/fBJvPvBet42f6c+Z5NvmD8/nDsHbo6bXUzOOY7xDSPZzg+44Y6JiQsu\nNKAbG5lL+I1E9nbueFGF5rzCUqcmXOPpxnaWEkXSv4zwxJf32EpxMidZCg8JZ/2CzSybvoY/th7F\n5u5GvQ61adWrMYEPVsfVzf6Z9qNsZS4jOMIm3PAgjlh8yMcjjOBB+uPikK39WSg4GIoUSf1825o1\nISgoa2KSNFNCm3F6bxYREUfKyirHklFxcdZRIu3aQfXq0KQJzJqV+g/IabFnj337/K5fh6++ytBQ\ni75Yzz3mde5PKZkFqxjVtm0ZGsseJ9nHMGqwme+IJoJwgongOmFcYw3Tkk1mAaIIZz/r+JPk4wzm\nIt8zhpHczzBqMoknOcZOh8a/nR+STWYBIghlLq84bMzbefl60fqpZkzc/B5Tgz7goWdasmfdfl5r\nN4ZuxZ9h8vNfsv/3P4hLZW/0dpbyFk05wDqiiSScYCIJ5TKnmcvLfEwX4shh+6vz5LH23nqncJ6v\nt7e13FhEREREHCrzp8YkZefOQbNm8PfftyacQUEwdCisWgWBDpg0uHbN/v2qly+ne5iDW45w6DIM\n4M/Uf1tiGJle+TiOON6jLeEEJ3nftCN5iiKcHxnHUL5NdG8j85jK0/HtAP5mL5tZSDVaMYT5GV6u\nvIIJ8UuMk2eyl5+5xgXykrnHWpWtUZqyNUrT78OebFu+i5/nrGfZ9DUsmbSCQsUL0KhzPRp1qUeF\nOmVxcfnvb0EwFxlPt/jv0+0iCWMPK1nDNFrxbKa+BocbOND69zVsmPX3+ua/ZV9fa9XDwoWO+Xcs\nIiIiIrdQQutMkZHQsCEcP5746JybPxA3b27NrpYqlbGx7rkHoqNTb2cYVuXjdFo8/id8bPBg9N+Q\n2mr2mBi4++50j2WPPawmjKsZ6sMkjpPsTbLvqTydKEGLI5YowtjDKibRiyFJJMJpcZxdxBGbajsb\nnvzLn5me0MaP526jwSN1aPBIHUKDw9i8dAfrF2zih0krWPTJTxQqXoAmXevTuGt9ygeWYY0xndT+\nUkQSxveMoSXP5Lw9tf37w5NPWsXO9uyx9qE3awYtW1pHBYmIiIiIwymhdaZFi+Ds2ZTPgQ0LgzFj\n4LPPMjZW+fJWUnwwlVORfHysH8zT4dTRs/y2cAtdutfBa9EKCE0lgS5c2P6zPtNpC4uIwI6l1qlw\nI3GRrJkMSXa2EawZ2+0s5SxHuZtyGRjbvhlekzjccE/3OBnhk8ebFj0a0aJHI0KuhrL5xx1s+G4z\niz9dzncf/0ih4gWI6/AnEZ18cXsgAsMt+cQ2mPOc5wSFKZ2mGExMDrOJH/mYo2wBoBz3056XKE+9\nrEmQvb2tpFZEREREsoSmDZxp3LjU97XGxMCcOfbNrqZmzJiU9/nZbFC2LDRunK7uv/vwB9zc3Xh0\nbB+oWhXcU0iuvL3hvfesGeFMlNxS47Sw4UEt2t1y7W/2c4ETqT4bRyyrydgvI2rTHne8Um1nAiWo\nnKGxHME3nw8tezbmnaXDWfDvdIZ9NYByNe/l8hd5CW3WmOC72hHarS5Rc0oQdzHx3xFX3FLcL5yU\nWGKZQE/e5UG2s4QrnOUKZ9nOEt6hJRPpRawds9y52pEj8MUXMHWqdTxXDiwIKCIiInI7JbTOdPKk\nfe3i4jK0rzVeu3Ywdqx1fMjtlYV9fa1kdvXqdCWZVy9c4+c5G2jZszH+Rfxh2TKoWNHqNyE3N2v8\nN9+Exx7LwIuxT1EqOGDW0uBBnrvlyjmO4WLHAodYojlFKrPiqWjG06S2VNeGBy3o5/TjhW6XJ78f\nrZ5swtvfv0yD86F4f7cZ2yOnifm1EGFP1iG4cDuu121G+BsBxGwqgBljEEMU/tyTpnHm8grb+Z5I\nQjETfK9MTCIJYyuLmctwR7+8nOGvv6B+favg3ODB8OKL8NBD1taCFSucHZ2IiIhIhiihdSZPT/va\nxcRYSaAjDBwIu3ZB377W/tUCBaxiNdOnw+7dUCh9+y9/+uxnoiOj6fjCQ9YFf3/Yvt2qmFy3rjVO\nkSLWcszt261zO7NAM57GsOuvedJJvDte9OYTClD0lusepDDTfRtPMnZeax4K0o9pyc7SuuFBEcrS\nlbcyNE5ma+87mDyPXsP7yyDynP4J321r8XzzINjiiHyvIiEPNCW4cDtcurdl69z9BF9Kvvp0QqFc\nYxWTiUxhVjeKMFYxmTAHzNjnKMeOQe3asHWrVTU9LMz6b0gI/PMPdO4MS5Y4O0oRERGRdNMeWmfq\n1Mla/pfacuJKlayjQRzlvvtgyhTrwwGiIqL4YfJKarepQcmKxf67YbNZPzB37uyQcdKjECWoz2Ns\nZkGy+11teBFAIw6y/sbsngkY+FOEJ/mEunRM9Mx91LerUJMnftSnawZfBTSmJ3koyFcM5jJncMGq\nWB1LNA3pzpN8glcGE+fMVo0HKUJZ/uEgsS5RuAVewS3wCp5vHCLuio2YnwsTt7IYYcvvY8y8Cbi4\nGJSvXZZaLasS2KoaFeqWw82W+H9ZW1lk12y5Cy5sZRFN+V9mvLzsqW9fq5J4cscphYVBz55w4YL9\nv2ATERERyUaU0DrT889bM6MpJbQ+PjBiRNbFlA5r5/7G1fPX6Dy0XeqNneBZphNFGEEsI4bI+ETU\nWp5r8CivspXFgEEsUZjEYcODK/zLUbZQmw643DbL64E3Tfkfa/mCaCKSHdsNd2rziENeRw3aUJ3W\nnGA35ziGDU8CaIQXfg7pP7O54MIbrOUdWnKWI7cU6/Lyd8foepWXu86kUlxTjuz4i23LdxH08x7m\nvbeYue8uwtvPi6qNA6jRvAo1mlehVKXiGIbBZU4TSWiq40cSxmVOZ+ZLTLvISAgOto72cXRC+fff\nsGlT8slsQgsWQK9ejh1fREREJAsooXWmMmVg4kQYNMhaBng7b2/o0gW6ZnyGL7OYpsmiT37i3mol\nqdHM+QWJkuKGjaEs4Bg7WcZ4jrMTV2zU5GHq0Zl3acV1Lt0y4xpNJAArmUQoV3mGzxP124OxHOZ3\nTnEoiaTWwBMfRrIsyQrJ6WVgUJoalKaGw/rMSn7kZwzb2c8vLOdTznEMT3xpRE8a0wtv8oALVKhT\njgp1ytHrra5cvxLC7nUHCFq9h12/7GPLT0EA+BfOS43mVXBtFobRIi9miZSPZ3LDAy8cuNIhI7Zt\ng3ffhZUrrfNrY2PhwQfh9dehTh3HjLFli7VKIiL5X7gA1vLjtWuV0IqIiEiOpITW2Z5+GkqUgJEj\nYf9+8PCw9swWKGBd69cv0ysB2yOUa2xgDgdZD0BlmtKInuxdfoSTB0/x8qyBGNkgzpTcS00GMfuW\na9N4lhCuJLt8OJIwNjCHNgxKVEHYA2/e4XcW8Q6rmIJJHGAVNapKC7ozhuJUyqyXk2O54EJVWlCV\nFna19/P3pWGnujTsVBeAcycvsGvtPnb9so9da/dx5ZtrQAtcKgZja/Mvbm3P4vbARQz3xIW0HDVb\nniGzZ8Ozz1qJpmn+t0Jj2TL45RdrK4Ajjv6xZ2b2ptg7vAK0iIiI5FiGmQOPbggMDDR37Njh7DAc\n7+RJ61zavHmhQoVskcgCrOYzZjEUAyO+8I4HPsSZcbg/0J2YMzZmHpmQ5P7G7CySMJ6mUIrFhABc\ncKUxT/IcM5JtE00UpzhIDFHcRWnykr7iWpI2pmly4sA/jP15IH+vvEb0+gIQ5Qq+0bg1P4+t9b/Y\nWp/DvWQMVWjOSJY7N+D9+60iaWEp/J3z9rZmV6tUydhYhw5BrVpJr/5IyMfHOtJr4MCMjZfDGYYR\nZJpmoLPjyMly7XuziIg4hb3vzTkrA8ntSpa0PrKRX/iKWbyYqKBSJKFEry/Ehc1XaTu5Wo5LZuHm\n0TuuqbaLI5YjbE6xjQ13SlPdUaGJnQzDoHTlEnxUeRYjh9TlQkgQ4evyEL2sCNGrihDzQ1HCAfeK\nEeRp045dbfdR+YEK2Nwdtww8TT74wNo3m5LISPjwQ2smNyMqVrQ+du5MuV1cnFUYSkRERCQH0rE9\nkqxoopjFEKKSmcGM/Kg8xl0R7Pnfp8QSk8XRZZyBSyqnuyZsmz1my3OkqCiYNw9atIAaNeDhh63l\ntQ5c5uqLP2MJ4lHfV8jfLpq8nx2iwLF1FDm4jXof30Ol4rVYPmkdL7cYxaMFn+Ltzh+xetavXLuY\nxcf4LF6c+uuOjYVFixwz3rRp1oxvcry9rdnZvHkdM56IiIhIFst502qSZXawlDiS3ocXeyAPMcvv\nxvOtA8R6RrKLFQSSPascJ6cIZexq54qNyjTL5Ghyqf37oXlza9nr9Rvnyu7eDRs2WOcSr1sHRYum\n3IedvPCjM6/TiVcJ5gIYkKdCIVwquMAQCA8JZ/e6A2xdtpMtP+1g4+KtuLi6UKN5FZo81oCGnerg\nk9fHIbEkK7XlvwnbmWbGtx3UqgVr1sCjj1rf/5AblaV9fa3+x46FAQMyNoaIiIiIEymhlWSd4uAt\nR6skFPlxefCKwf25v4gijlMczHEJrQ0PWtCXlUwihqhk27niRlsGZ2FkucSZM9CoEVy5kvje9evW\nPtIGDeDgwZRnEdPIBRfyUTjRdS9fL+q1C6Reu0BMsy9Hgo6xcfFW1i/YxMdPT2FC/2nUaVuDpt0a\nUq9dLdw93R0WU7x8+eDyZfvaOWoPfb16cOoUrF5tFZ2KioLq1a3q6Q78vouIiIg4gxJaSZYbNlxw\nJe625cRxpz2JmlsC977HcCkYhQvuuDrwaJqs1JnX2cb3XOYUMSQ+D9gDbx5iCHdT1gnR5XCffAKh\nKZwPGxsLFy/CN99Anz5ZFxfW3tv7AstwX2AZnhrdjcPb/+SXbzayfsEmfl+yHZ+83jTqXI8WPRtR\n+YEKuLg4aHdGnz4wfryVVCbH3R369nXMeDe5uEDr1taHiIiISC6iKse5SDTW0t8rnMGbvFSnDX7k\nT3d/R9nK2zQnkluTkvBXqhD5cXn8jqzE9d7Q+ONrcmpRpGAuMpGeHGAdxo0E3g0PDAy68hYP8YL2\n0KaVaVr7Mm8uM05JhQpWRd5sIDY2lt2/7GfN1xvYuHgrEaGR3FOmMG2ebs6D/2uKf+F8yT1oneX6\n11/g5WXtFy5WLHG706chIACCU9i76+dnzVon9bxkGlU5zji9N4uIiCPZ+96shDYXMDH5nvdZwhgA\nYonBBTdiiaY+XenLVDxI+9JCE5MXqMgZDsdfi7tqI7hUW2wP/ovPt1sBgxJU5mP2OurlOM1F/mEX\nK4gklEKUpCYPYcPD2WHlTCEh4O9vnamcGl9f+xLfLBYeGsHGxVtZ+eUv7F1/EJu7G02feIAuL7an\nVKXi/zWcPRtefNGqThwTY82GxsZC06YwcybcddetHW/ZAg8+aJ0/m3BPrZcX2GywcqW1TFiylBLa\njNN7s4iIOJIS2jvIFwzgV2YmeZ6qDU9KUJl32Jiu5Owk+3idBoQTAphEvFuBiDcq4xu0BluNa3iR\nh9FsphgVHfBKJNeIjgZPT+tImNTkzw+XLmV+TBnw9x+n+WHSClbP/JWIsEjqtQ/k8VceIWDHahg+\nPOlzZW02q/DVrl1QoMCt9y5ehBkzrCrEV65Ye2b79bOWJBcsmDUvSm6hhDbj9N4sIiKOpIT2DnGU\nbbxN0yST2Zvc8aIb7/EwL6RrjFMcYjr9ORKyg0ulmuNe/xp5lm7lPurTj8+4m3LpDV9ys/r1YXPS\n5/eG5oVNj8H5ew28ytSgVueZlKRKFgeYdsGXrvPDpJV8P3E51y+HUMW4xJNx+6nGhaQfsNmgd28r\ncZVsTQltxum9WUREHEkJ7R1iHI+xhYWYyRyvc1N+ivIZ/2RoL+jsCV8z54Uf6Pd7S5rUa00hSqS7\nL3GeWGII4xrueKVrKbrd/s/efYdHVaVxHP+emWQmhSRA6B0FC00UUFFZVCyogCKo7FpX7GLvbVVU\n7Lp2xYa6dmyIICKCFRQUREBBqjQh1PSZyczdP26AJCSZSzIl5ffxmUfm3jP3vkBI5p1zzvtOnAgj\nRpQqDBUy8OYDMPkKcJ0PpqAAACAASURBVIXAlwouy02C8dCWbtzAh2RS8/eOFuQVMnn4Dbw7ZSVb\nSKKntZHzWEhXyplpTkmBDRvspdVSYymhrT79bBYRkUhy+rM5QqU7JV5+55uwySxANlnklPdm26Gi\nQBFfPP4DXQ/fl9P6XqRkthb6m2U8z0WcQzoX05pzSOc2+vIzE6Nzw5NOsmcnS7SGeeEFmHI5BJLt\nZBYgZIL4KWAFc7mZPmxnY3TiiaDk1CRO3f4zr1uTuNSax0rSudocxX0czGaSSg9OSICFC+MTqIiI\niEgdp4S2lgs5SGYBDC5HiW9Fvnl/JhtWZXHGjadU+RoSP4uZyQ30ZDqv4qeAAD5CBFnCLB5nBK9z\nfeRvagw89RQ8/TR06MDKQ5L47sxdiWxZIYrIYTPjuSfysURDMIiXEKeylNeZzDnWQr6nNedzPBPY\ni+COccY420ssIiIiIntMCW0t14EDHI3zkEwDMsMPLIdlWbz78Ce02781h5x0UJWuIfGTTzZjOIFC\ncnfrKQzgI48veJ4feC/yNzcG/v1vWL6ciZ8PpCjJXenwIIHipLsw8rFEWt++9h5ZIJkgZ/M7Y5nK\nvmzhKXMQV3M0K0iHwkLYd984BysiIiJSNymhreWGcANJVL43LxEvJ3AFbipPJiry89T5LP91Fadd\nfzIul75kaptveINgOYlsST7yojszagxLGi4i5AqGH4qLLFZGL5ZIueIKcJf+N9WGXB7kW26xfuRv\nUrjcDOC9fQYTzMiIU5AiIiIidZuyk1quOwPYjyPwkFzueTcJZNCcQVxT5Xu8++BHZLZqxNH/OqLK\n16jLctjCJzzMbRzGTfTmWUaykl/jHdZOX/EKPvLCjvubpWxmTdTiMI6/3Vh7MDaO9t7bbrWTUrqw\nlgGOZjUvmqkcnLCJFxfA7YPuZ/um7PjEKSIiIlKH1YJ3jVIZFy5u5GMOZTiJJO3sNevCjYcU9qIX\nY/iRVBpW6foLvv+DedMXcvr1J+PxJkYy9FplFb/xMxNZwPRSy2G/510uoQ3vcSdLmMlyfuZrXuM2\nDuMRhhPAH8eobflsczQugUTy2R61OLpyJG4Swo4zuGhKh6jFEVGPPw5XXWX33N2R2BoDqak03Lst\nd857nqufv4hfpy/k0l43snTeivjGKyIiIlLHqG1PHbKZtXzHm2xkFWlk0pfTqt3b89aTxvDnnGW8\nvvwZklOTwr+gjvmZibzO9WxmDW4SsIr/O45L6MqRPMpw/BSU+1oPyRzMUK7izRhHXdod/IM/+Dbs\nuES8PMdqMmgalTjW8gc3clCFf14ACcXL48/h4ajEEDVbt8Jbb8Hvv9vteQYPtvvwGrtN1pKfl3HX\n0IfJ2ZrLLf+7isNO7hPngKUste2pPv1sFhGRSFIf2prs779h7Fh44w3IyYE2beDKK+H00+2Znhpi\n+fxVXNzzes67ZwRn3jYs3uHE3Je8xKtchZ/83c7ZS7xNuedKSiSJR5lPSzpHKcrwfuA9nmMkheRW\nOi4BD+k0ZR/6MoTr6cwhEY/lDW5iCk/jK+fPLYFEGtOGh5hLKnVvz+nm9Vu5a+hDLJ69jJH3n8np\nNwzBmKr3hZbIUkJbfbX+Z7OIiNQo6kNbU02aZO+9u/9+WLoUNmyAn3+Gyy+HffaBVaviHeFO7z86\ngaRUL4MvPS7eocTcZtbwKldWmLD6KQibzAKECPIFL0Q6vD3Sh1NoQGbYfalF+NnCWn7kQ+5mAM/w\nb8dtoZw6iwc4jbtIIo0k0nDjwUsKiXjpzjE8wOw6mcwCZLZsxCPT76L/6X156eb/8eKNb1AbP1AU\nERERqUnCb2iTyJk3D047DfLLSYRyc+3j/frBkiVxn6nduHoT09/+niGXHU9647S4xhIPn/NMtfr2\n7hAkwBoWRiCiqkvEw2i+5naOII+tYQtEWYTwkcdM3qMhzTmTByIWi8FwMjdwIlfyMxPJYhVJpHIg\nJ9KEthG7T03lTfZyy5tXkdEknfcf/RRvipdz7z4j3mGJiIiI1FpKaGNp9GgoqHj/IKGQvRdv/Hg4\n66zYxVWOj56YhGVZDLtmUFzjiJc5TCCALyLX8pIaketUR1Pa8ySL+Y63+YzH2czasMWifOQziSc5\nldtIJo3tbGQKz/IFz5PLZjwkcyjDGcx1tKXrHsWTiJdDqX/L2AFcLheXPfFvfAV+/nfPeJJSkzjj\nxpPjHZaIiIhIraQlx7GSm2svNw63xDA3F554IjYxVRTCtjwmvfglR55xGM3bR6dAUE0XqWQ2iTQO\n4/SIXKu6vKQwgJE8xgLO5VFHibYLNz/yISuYy5Xsy8c8yHY2EKSIAnL4mje4mT5M57UY/A7qDpfL\nxdUvXMSRIw7npZv/x4Rnp8Q7JBEREZFaSQltrGRlQYLDCfF166IbSxifPvcF+TkFnHb9kLjGEU/2\njGP1C/YkkEgfTql+QBG2mTXlFmYqy0c+61nK3Qwgn20ESrQsAghRhJ8CXuIyFjMzWuHWSW63m5te\nG8Whg3vx9BUv8+OkX+IdkoiIiEito4Q2VtLTIRBwNrZBg+jGUonCfB8f/ncifU44kE49O8Ytjngb\nxDUkhZnBNLhIpSGJlLff2eAllZuZSCKe6ARZDSmk7+xZXJkEPKxlIUVhZqz9FPAB90QqvHojITGB\n296+hr0OaM+D5zzFxr+y4h2SiIiISK2ihDZWMjOhq4N9hsnJcPbZ0Y+nAp+//BXbsrL51y1Do3YP\nP4V8zRs8wZk8xhlM4BFy2By1+1VFF/qzN30qSFZtSTRgNN9yIleRTDrJpJFCBol4OZATGMMs9qVv\nDKN2rjfO92yu4jcHs7kW8/mSwjAFp2R3SSle7njvWoKBIPeOeJyA3+EHX2BXSL/iChg2zP6/WqaI\niIhIPaM+tLH00Ud2sppXyZv+1FRYvhyaNavevbZsgTVr7AR5773BFf6zi2BRkPP2uYLGrRrzxHf3\nVu/+FfiFSfyXf2IR2tkX1UMyFhancivDuB0TgaW+keAjn8c4nQV8RRF+QgQBe1+sl2Ru43M6ciBg\n77n9iwUU4acFe5NBNf/+YuAejmcRMyjCX+75BDx042iW8wvZbAx7PQ8pPMliMmkT6VDrha/fn8m9\nZzzGsGsGccmj51Y+OCsLBg2CBQugsNAuKOdy2dXRu3aFzz6DpvVz/3tVqQ9t9dXan80iIlIjqQ9t\nTTR0KFxyiZ20luVyQUoKfPBB9ZLZ+fPtN7qtWtktgHr2hLZt4b//hWCw0pd+9+GP/L0yi9OjtHd2\nAdN5lOEUkL0zmQV7uWqAQj7mQT5kTFTuXRVeUriFidzPTxzLJfTgWA5lOKMYxwus3ZnMgl21d296\nsS99a0UyC3A1b9GEduUuPU4kiaa05yreIpWGjq4XJECKw7Gyu/6n9WXIZcfzweMTmTd9QcUD8/Ph\n8MNh7lz716Hi9lKhkP183jz7fGUfnImIiIjUERFJaI0xA40xi40xS40xN5dz/jxjTJYxZl7x44IS\n5841xvxZ/AgzLVEHPPIIvPkm9O4NHo+d3Hq9cOqpMGsWHH981a89fTr07WtXU/b5IDvbfoO7bh3c\ndhsMHlxhUmtZFuMf+5RWnVpw6OBeVY+hAhYWY7kYPxW3LfKRxwfcS16YdjKx1o5uXMDT3MEXXMf7\nHMKpuOtAx6s0MnmQnzmFW2hAJh6S8ZBMAzIZyi08yM80oBHHcCEeksNerwv/IJn47f+OtO1k8SFj\nuI3DuZk+vMhlrOH3qN7zwofOplWnFjx24fMU5lewb/m112Dt2or35AcC9vnXVHlaRERE6r5qLzk2\nxriBJcCxwBpgNvBPy7IWlRhzHtDbsqxRZV7bGJgD9AYs4Gegl2VZWyu7Z51Z1rRli92mp0kTe3a2\nOnJz7VnZnJyKx6SkwF13wQ037HZq4Q+LufqI2xn11EhOvnxg9WIpxzJ+5k764wuzx9JLCv/kfk7i\nyojHIBULEmQ7GwDIoDlu3DvP5bCFy+lIAdkVvt5DCrcxmS78I+qxxsI0XuFlLsdgdn4I4yYBN4kc\nzggu5sVSf0aR9OvXC7n+qLs48/ZhnDd6xO4DOnWCZcvCX6hjR3v7gjiiJcfVV2d+NouISI0QyyXH\nBwNLLctablmWH3gHHFecOR6YalnWluIkdioQ+WyqpmrcGNq1q34yC/C//+1aeliR/Hx7hricceMf\n+5S0Rqkcd96R1Y+lHGtY5GhvrI98VqD2JbHmxk1jWtGYVrslamk05namkEQaCWUqNhtceEjhbB6u\nM8nsj3zEK1xBgMJSKwqCxS2KvuddXmFUJVeongP6d2XAmf147+EJrFv29+4DVq50dqFVq8L3vRap\ngXxFlW+PERERKSkSCW1rYHWJ52uKj5U1zBgz3xgz3hjTdg9fizHmImPMHGPMnKwstbbYzZtvOtsz\nl59vF5IpYe3S9Xz/0U+cdPFxJKdWXNW3Ouwlus6KPZVNmsqzmoU8xwVcSnsupjX3cQK/MQ0LvYGP\nhn04lMdZyECuIIUMwP57OoRTGc3XDOSyOEcYGRYW47gGfyVVnf3kM51X2UL0+kVf8OBZuBNcjPvP\nO7ufdFDgbec4UzMKrIk49cLXy+h25xRuGj8/3qGIiEgtEauiUJ8CHSzL6oE9C7vHm7ssyxprWVZv\ny7J6N1X1zt3l5oYfA+B220ltCeMf/ZQETwJDrzyBAH7m8ClTeYHveJtcKl397dj+9CNI+HYkSaRx\nYJhJ+nf4DzfThxmMYxN/sYV1zONzHuIU7mMgfgojErOU1oS2nMsjvMY23qGIt/FxHe+zN3VnleYS\nZpHrqIWU4SteiVocTVo15pRRJzDjnR9YuXB16ZOHHebsIk7HidQg90/+g0DQ4t05q1m3reKaCyIi\nIjtEIqFdC7Qt8bxN8bGdLMvabFnWjgonLwG9nL5WHOrc2dlsjM9nVz0utnXjdqaMm8Gx5/TnmxZj\nGUlTnuRMxnENY7mYi2jFs5yPr5JiTk5k0oYu9McVZt9hAh56U3GV5am8wEQexU/BzjY6OxSSy+98\ny9PU/dpi8Rat/aPxthFne04DFLI2ygWiTrt+CEmpXv53z/ulT9x0U/mV0ktKTbXHidRiub6ieIcg\nIiK1QCQS2tlAZ2NMR2OMBxgBTCg5wBjTssTTIbDzneAU4DhjTCNjTCPguOJjsqdGjXK2F7dPH2i9\na1X3xOe+IOALwLW/Mp7RFJBNATn4KaCAHAIU8h1vcxdHEqCCqqsOXcrLNKBxhUmthxSuZ3yFFYSD\nBHmb2/FVuhy0gDlMYCMrqxWr1E+JJDnug+wlTFJZTemZaQy98kS+fm8my+ev2nVi4EAYNqzif++p\nqXbV9BNOiGp8UruF605QPOZ0Y8wiY8xCY8xbsY5RRETEiWontJZlFQGjsBPR34H3LMtaaIwZbYzZ\nMdV2ZfEPxF+BK4Hzil+7BbgHOymeDYwuPiZ7ql8/6NHDbgFUkeRkeOCBnU8D/gCfPj+FbifuxZx9\nX6swUQxQyF8s4AteqFaImbTmIebSk4Ek4iWZdJJJx0MyHTiQO5lGV46s8PWLmEGRg6Q6RIjpvFqt\nWKV+6sqRFDlaGt+AQxga9XiGXTuI5AZJvPfIJ7sOGgOvvgq33w4NG0Ja2q5Hw4Zw660wbpz2z0qF\nirsTPAOcAHQB/mmM6VJmTGfgFuBwy7K6AlfHPFAREREHItJM07KsScCkMsf+U+LXt2D/YCzvta9A\nFDej1RfGwOTJdh/bhQtL76lNTrbPv/VWqX1137w/i60bttPpCnsmtjJ+8vmUhzmRKxzPYJUnk9bc\nwkS2sp4lzCREkDZ0pS1dwr52M2scFX0K4meDw6WjIiWlkcnBDOVHPqAIf4XjkknnAKrRM9qh9MZp\nHHfukUx66UvO++8wmjduZf/7c7ngllvg+uvh669h0ya7/Vf//pCYGPW4pNbb2Z0AwBizozvBohJj\nLgSe2dFGz7KsjbEOUh/JiIiIExFJaKWGyMiAmTPhq6/gv/+FP/+0k9kRI2DkSPsNbwkfPz2ZNvu0\nZOOx72MRpuUPsJ2N5LKFNDKrHWojWnIIp+7Ra5JJxzhYVGAwNKBRVUOTeu5CnmU5c8jir91WBBgM\nXhpwCxNxRbmmXgA/X/Ey8y54isAzXbn4zaNpesU2TuIaBnI5yaTZyesxx0Q1DqmTyuswcEiZMfsA\nGGO+B9zAXZZlfR6b8ERERJxTQlvXGAMDBtiPSiyevZQ/fvyTy584n09d7zq7NK7dCjHFUncGOKqU\n7CGFwxkRg4ikLkqlIQ8wh3e4g+m8gsGFwRDAxwEcx1k8RGv2jWoMPgoYzdGsYj6+A/Jx925J4cvt\n2DZqCePNaKbxEmOYRTpNwl9MpGoSgM7AkdgFG78xxnS3LGtbyUHGmIuAiwDatWsX6xhFRERi1rZH\napiPnppESloyx57bnw4c4Og1HpJpEIHZ2apKIZ1/cA4ekiscY3DRhHbsQ98YRiZ1TQrpnM8TvMRG\n/sOX3Mpknmc1N/FJ1JNZgJcZxQrm7dzX7jlvJaH5DQktSsdPAZv4i0f2cIWDSAlOOgysASZYlhWw\nLGsFsAQ7wS1FLfVERCTelNDWQ5vWbeHrd39g4PlHk5qewhCuJ4kGlb4mAS8DuTzu7VrO43Ha0aPc\npNZNImlkciuTqrXPV2QHL8l0og/70jdms6G5bOU73iq1rz1x6DowFoEP7QrlQQIsYw5rotw6SOqs\nsN0JgI+xZ2cxxjTBXoKs4gQiIlLjKKGthyY+9wXBohCnXGG39ejOMezLYRXOfLpJIJ2mDOLaWIZZ\nLi/JjOZrRnAvjWhFIkl4SSGJNAZyOY/yG83oEO8wRarsFz7brXWVq2Uh7r6bCXzcauexIgLM5P2y\nLxcJy2F3ginAZmPMImA6cINlWZtjGacKdYuIiBPaQ1vP+Av9THzhCw4d3IuWezUHwIWLm5jAs5zP\nj3yIhUURPly4ScBLW7pwExNqTKGlRLwM5lpO4mq2s4EgRWTQnEQ88Q5NpNry2EaQot2OJw5dS+EN\nBxBckYK7Yz4hisgmKw4RSl3goDuBBVxb/BAREamxlNDWM999+CPbN+Vw8uUDSx1PxMtVvMlm1vAN\n/yOLlTSgMX05nY70jFO0lXPhohEt4x2GSEQ1oiVuEndrpZV48joKbziAosktcF+2nAS8NCm1DVJE\nRESk/lFCW89MemkaLTo248AB3cs9n0kbhnJzjKMSkR0O5EQop9+ya+88XB3yKJrWHO9lyzEYjuDM\n2AcoIiIiUoNoD209smbJOn6dsZATRg7A5dJffU3yN8uYwWtM4yWWMAurnIRG6gcvyQzmOrykljpu\nDCQM2EDgq6YkBpM5hKFk0jpOUYqIiIjUDJqhrUcmvzQNl9vF8f8+Kt6hSLENLOdpzmUZc3Dhxp6Z\nMzSkORczlu5U3k9Y6qbh/IcsVjGT94tb99gfcCQcsxH/y3vRak4/Lj3klfgGKRJ1qgolIiLhaZqu\nngj4A3zx2gz6Du5FZsuaUdypvtvACm6iN4v5gQCF+MjDRz4+8tjAch5gML+Urtki9YQLF5fxCrcx\nmd4MogGNSaURXY7cG4A+316Gh6Q4RykiIiISf5qhrSd++GQO27KyOfHCY+MdihR7jpHksx2LULnn\n/RTwBP/iJTaqgnM9ZDDsTz/2p9+ug83hX20vYdncFfELTERERKQG0QxtPTHpxak0b9+UXsf1iHco\nAmSxiiXMrDCZ3SFEiB/5IEZRSW3Q6cCOLJ27Mt5hiESd+tCKiIgTSmjrgXXL/uaXL3/jhJEDcLvd\n8Q5HgCXMxE1i2HGF5DCfL2MQkdQWnXp2ZM3idRTkFYYfLCIiIlLHKaGtB74YNwOXy3D8v4+MdyhS\nLESQ8lqzlD+2KLrBSK3SsXs7LMtizeJ18Q5FREREJO6U0NZxlmUx7c1vOPCYHjRpnRnvcKRYO3oU\nJ7WV85JCJw6OQURSW7Tu3BKAtX+uj18QlgXLlsGCBbBtW/zikDqnp1nK44nPcIzr53iHIiIitYQS\n2jpu4Q+L+XtlFgPO7Bd+sMRMe7rTgk5hx1lY/IOzYxCR1BatOrUAYO2ff8f+5sEgPPUUtG0LPXrA\n4YdDixYwdCgsXBj7eKTO+dj7H4a6v+clz6MYf268wxERkVpAVY7ruGn/+4akFC9HDNUsH9h9Xyfz\nNEuYiQs3B3A8x3IRDWke81guZiyjGVDcZ3R3HlL4F2NIIT3GkUlNlpTipUnrxqxdGuMZ2mAQhgyB\nGTMgv8zX7CefwNSpMHky9NOHZxIZiTlrgRbxDkNERGo4zdDWYUWBIr4ZP4tDh/QmuUFyvMOJKwuL\ncVzDNXRlCk/zJ7NYzPd8xBguowOf80zMY9qHQ7mFSaTRhCTSdh73koqHFM7kfk7iqpjHJTVfi47N\n2PjXptje9NFHy09mwV6CnJcHgwbZ/xcRERGJEc3Q1mFzp/1G9uYcjhpxeLxDibu3uZ0vGUuA0pVh\ndzx/gxtJJoP+nBXTuLrSnxf5m1/4jN+YRhF+9qYXhzGCZBrENBapPTJbNYpt655gEB55pPxktqRQ\nCN55B0aOjE1cIiIiUu8poa3DZrz3A6kZKfQ+vme8Q4mrXLYykcd2S2ZL8pPP61zHEfwTN7FtbeTG\nTR+G0IchMb2v1F5NWjXmx4m/YFkWJhbNOhcsgIKC8ONyc+GNN5TQioiISMxoyXEtlstWvuddvuRF\n5jKZYIn2Ln5fgO8/+onDTumDxxu+32ld9h1vYRx8qQcoYAHTYhCRSPVkts6kMN9H3vYwM6aRkpcH\nTntY56qQj4iIiMSOZmhroULyeJlRfM87uEnEIoiLBFy4OZ27OIEr+PmLX8nbns+Rp2u58Rp+x19B\n4aWSghTxN8s4IAYxiVRHo+YZAGzflE2DhqnRv2HbtuDzhR9nDHQKX71bxImYrD4QEZFaTwltLeOn\nkP/wD9awiACFuy2jfYtb2co61oxvTVqjVA4c0C1OkdYc9l5UA1iVjjO48JAUk5hEqiOtsb2/Ontz\nLq1jkT+2bQs9e8KsWZWPS0mBUaNiEJCIiIiITUuOa5lJPMlafq9wP6iPPD7zPc33n/zI4accTKKn\nfi83BjiIk/CSEnZciCJ6cGwMIhKpnrRG9qxszpYYLu996CFIrqRaute7qzetiIiISIwood0ThYWQ\nk2O3qIiDECE+43H8VF6cpeDLDAqyffQb3jdGkVVPAB/5ZGOFmUGtqv04gka0xJ6lLZ+bRLpxNJm0\niUoMIpG0a4Y2J3Y37dcPXn/dnoUtm9g2aGDP4E6ebC87FhEREYkRJbThhELw1ltwwAH2m7bMTPtx\nxx2wKbZ9ILeynny2hx3n/6w5JjVIz6Nr7nJjC4sf+YibOZgzSeF8mnAuDXmdG9jK+ojey2C4iQmk\nkF5ucSg3iWTQnMsZF9H7ikRLSrq94qAgt+LK3VExfDisXAm33w7du0PnznDSSfDxxzBzJmRkxDYe\nERERqfeU0FYmGLTfwF10Ecyfbz8PBGDrVnj4YejWzX5zFyMWIUwls4xgTx4Xfd6C5AHba2x1YwuL\n57mQpzibZczGIkSQAAVkM5knuZZurGZRRO/Zhv15iF84mKEkkkQKGaSQgYdk+nMOjzCPDJpF9J4i\n0ZKU6gXAl++gUFOkNW0Kt95qf09csgQmToQBAzQzKxGnrygREXFCRaEqM2YMTJkC+eVUyPX5ICsL\njjsOFi+OyZu5hrTAFaZHamhxGqGVqbS90RP1eKrqC57ne97GV07l4SL85LKV0QzgOf4igcgl5c3Z\ni+sZTw6bWcsfGFy0o3tx0SiR2iMpxU5oC/PikNCKiIiI1CCaoa1IIACPPVZ+MrtDKATr18OMGTEJ\nKYFEBnARCVScrAYmtwDg9IEjYxLTnrKw+IB7y01mS44qJI85TIhKDGlksh+Hsy99lcxKreROcJPo\nSaAwL8ZLjkVERERqGCW0FfnuOzthDSc3F8aNK//cmjX20rwjjrAfd9wB69ZVK6xTuIkGNK5wpjY0\nrSXJnUP06zCoWveJllXMp4DssOMKyeErXolBRCK1U6I3kaJAMN5hiIiIiMSVEtqKbNvmfGzZ4lCW\nBXffbRdMeewx+P57+/Hww7D33vDAA1UOK4Om3M9PtKELXlJ3FjlKwEtCIJngN8046uhjw+61jZc8\ntoVdNr1DDpujHI1I7eVOcBEsUkIrdYcVpw4CIiJSu2kPbUVatHDWnsfthnbtSh977DG7Z2NhmeWA\nvuL9bvfcA2lpcPnlVQqtCW15lPksZTYzeZ88ttKMjrSY3Y87c5+k14ADqnTdWGhIC4IEHI1VCx2R\nirncLoJFDlaRiNQSlqVCUCIisuc0Q1uRQw6x2/SE4/XChRfuep6fD3feWfne2/x8eymy31+tEDvR\nh7N5iEt4kVO5lRVfbQTggCO7Vuu60dSafcmkXdhxSTTgOC6JQUQitZM7wU0wUORs8JIlcNllsNde\n9gdwgwfbe/81IyY1mL46RUTECSW0FXG5YPRoSEmpeIzHAwceCAcdtOvYhx86q3hsWTAhskWP5n+7\niI7d25HRJD2i1420fzEGDxX/ubpIoCnt6c6AGEYl4kwBucziA6bxEj8zkQDV+2Aq6saMgZ494aWX\nYMUKWL0aPvvMTmoHDtx9JYlInCiBFRGRqlBCW5kLLoCrrrKTWleZP6oGDWC//eDTT0sfX7rULhQV\nTkEBLFsWsVCDRUF+n7mEbkfsH7FrRsshDOUM7sZD8m77aZNIpSntuYMva+w+YKmfAvh5lau5gOY8\ny795lat5gn8xkqZ8wH1YMX47blkWJtyHZ6++CvfdZ3+/CZRY6m9Z9vepb7+Fs8+ObqAiDpXdQ6s9\ntSIi4oQS2nDGjLGX5g0fDo0bQ3q6PSs7dizMng2NGpUen5wMCQ62JrvdkJQUsTCXzltJQW4h3fvV\n/IQWYAjXM4ZZ/IOzSaMJyaTTlm6cz9M8ym80okW8QxTZKUgR93MSX/IifvIpIAcfeRSQQwHZfMT9\nPMcFMU1qLQuMHoy96AAAIABJREFUq5KENhSytzZUtv2hoAAmToTlyyMfoIiIiEgMqCiUE336wLvv\nOhs7cKC9VLkozN42l8seGyELv/sDgO799ovYNaOtPT24nFfjHYZIWN/yJkuYib+C/sk+8viBd+nP\nOXSlf0xiskKhymdov/sO8vLCXygUgpdftmdyReJI87EiIlIVmqGNtAMOgH333X2Jcklut72nbd99\nI3bb33/6k6ZtM2nSOjNi1xQR28c8iI/Kk0Mf+XzCQzGKCIJFIdyJlbTAWr3aWdEnvz+i2x9EIkUJ\nroiIOKGENhrGj7eXIrvLebOZkGAvXX7nnYjecsmcZezbp1NErykiEMDHOhY7GGmxmO+jHs8ORf4i\nEhIrWWSTluasQJ0x9vckkTjTllkREamKiCS0xpiBxpjFxpilxpibyzl/rTFmkTFmvjFmmjGmfYlz\nQWPMvOJHZMv+xstee8HcuXDaafY+2YwM+5GUBGecAfPm7d67thrytuexbunfdD5or4hdU0RsIUKO\nC5SFCEY5ml0C/iISPJUktEcdFX7rA0BqKpx+euQCE6miWBdWExGRuqHae2iNMW7gGeBYYA0w2xgz\nwbKsRSWGzQV6W5aVb4y5FHgIOKP4XIFlWT2rG0eN07YtvP02bN0Ki4r/KLp2hYYNI36rZb+uAqDT\ngR0jfm2R+s5DEuk0ZRt/hx3bmtgUZbMsi2BRkITKlhynpcG558Jrr9nFn8rjckHz5tA/Nvt+RURE\nRCItEjO0BwNLLctablmWH3gHOLnkAMuypluWtaOayiygTQTuWzs0agSHH24/opDMAqxatAaADt3a\nRuX6IvWZwXAS15BI5VXJk0jlZG6MSUz+Qrv3rTfZU/nAxx6DHj3s6utlJSTY358+/9zZ0mSRKNOS\nYxERqYpIJLStgdUlnq8pPlaRkcDkEs+TjDFzjDGzjDGnRCCeemf1H2tJSvXSpLX2wYlEw/FcSmNa\n4Sax3POJJNGW7hxMbL6F+QrshNYTLqFNToavv4a774YWLeznqan245JLYP586KS991JTKcMVEZHw\nYtq2xxhzFtAbSvW1aG9Z1lpjzF7AV8aY3yzL2q3kpjHmIuAigHYR3H9aF6xevJa2+7bCVVll5SgL\nEmQ5P5PHVhrRknZ0d7zvUKSmSyaN+5jJg5zMKuZThI8QQdwk4sJND47hat7BHaNvqf4ChzO0AF4v\n3HADXHcdrF1r76tt1co+LiIiIlLLReLd11qg5FrXNsXHSjHGHAPcBvS3LMu347hlWWuL/7/cGDMD\nOBDYLaG1LGssMBagd+/e+ti2hNV/rKPLYfvE5d4hQkziCT7iAfwU4MJFkCIyaMa/GMPhjIhLXCKR\nlkEzxjCTVcznO95iOxvJpC39OYcW7B3TWBzP0Jbkctl7+0VqqLJLji1LH4qKiEh4kUhoZwOdjTEd\nsRPZEcC/Sg4wxhwIvAAMtCxrY4njjYB8y7J8xpgmwOEQw0aOdUCwKEjWms207Ni8ytcoIIdveIOp\njCWXzaTRlOO4mH6cRRKpFb7OwuJpzuEnPsJHfqlzG1nBc4zkb5YyjNurHJtITdOeHrSnR1xjKMyz\nPxNMSq18X69I7abPrkVEJLxqr1G1LKsIGAVMAX4H3rMsa6ExZrQxZkjxsIeBBsD7Zdrz7A/MMcb8\nCkwHHihTHVnC2LR2C6FgiObtm1bp9SuYy6W05w1uZBW/spk1rGQur3Edl9GBVfxW4WtnMZ6f+Hi3\nZHYHH/l8yBhWMK9KsYlI+XYktMkNlNBK3aG2PSIiUhUR2fBlWdYkYFKZY/8p8etjKnjdD0D3SMRQ\nX238axMAzaqQ0G5lPXdxFPls3+2cjzx85HEn/XmCxWSw+/U/4gF85FV6jyL8TOQxruD1PY5PRMpX\nkFsIKKGVumW3JceqwyAiIg7Er4qQRMTOhLZdkz1+7SSeJEBhpWP8FPAFz5dzvJBV/Br2HiGCzC39\nWYeIVNOOhDYpVYWdpC7TjK2IiISnhLaW27phGwCNW+x5j9svGUsAX6VjAhQyhWd2O16EH+Pwy6eI\nwB7HJiIVK8gpACAlrZz+siK1VNn0VX1pRUTECSW0tdz2rGwSEt2kZqTs0essLHLZ6mhsDpt3O5ZM\nGl6c3bMZHfYkNBEJI784oU1O05JjERERqd+U0NZy27KySW+SjjF7ttfIYEjAWcuPRHZf1mgwHMsl\nYa+RRAMGc/0exSYilSvI0R5aqXssTcmKiEgVKKGt5bI355DRJK1Kr+3FSWGXDbtwczCnlHtuENeQ\nTDqmgsIdbhJpTGsO4/QqxRcN+WQzhWd5inN5hn/zLW+GXXYtUtPk5xTgcrvwJO1BH1qRGm63Jcfa\nQysiIg4ooa3l8nMKSK7iPrpTuJlEKp/hScBb4QxrQ5pzHz+QSVuS2JVUGwxJNKAd3RnNt+XO8MbD\nZJ7mQlrwBjfyDa8zg3GM5RJG0ow5fBrv8EQcy8/OJzUjZY9XZojUZBuz9eGiiIjsOSW0tVxhnq/K\nlU470Yd/ch+eCvbCekjhHB6hIz0rvEZLOvM0y7matziEU9mff3AEZ3Irk3mQOeW2+4mHKTzLm9yE\nn4JSrYYKyaWAbB7nDH7lizhGKOJcfk6BCkJJnbN0Y06p51qBLCIiTkSkD63ET2FeIZkt97zC8Q6D\nuJp2dOM97mIZs0nAQxF+9qEvp3En3Tgq7DXcuOnFIHoxqMpxRJOPfN7gRnzkVzjGTwEvcDHPsLzC\nJdQiTm1hHVN5noXMAKArR3Isl9CYVhG5fn52ASnpSmilbnG79Bm7iIjsOSW0tZy/wI83pXpLentw\nDD04hhw2k8sWGpBJGo0jFGH8/cC7jpLUHDaxmB/Yj8NjEJXUVR8yhvHcA1g792cvZTaf8DDDuJ1h\n3Fbte1Rnq4FITZXg0oeJIiKy5/RxaC0XClm43JH5a0wjk5Z0rlPJLMAK5lJIbthxIYKsZkEMIpK6\nahJP8iH3EaCwVLEx+3khHzGGSTxZ7fvkZxfscasukZrOXSahtbRaRkREHFBCK3VegsOiVAaDS4sW\npIr8FPI2t1W6tN1HPm9zO34Kq3Wv/Ox8UrXkWOqYsjO0RptoRUTEASW0Uud14yiSaBB2nIXF/vSL\nQURSF83mk6iMLU9+topCSd2z+wytEloREQlPCW0tZ4zBCumHfmV6MjBsQmtw0YEDaMU+MYpK6pq/\nWVrp7OwOPvL4m6XVupf20EpdlOAus8RYbalERMQBJbS1nDfZg6/AH+8wajQXLq7lfbwVtCcyuEgh\nnVG8EePIpC7xkIQLd9hxbhLwhOn/XJlgMEhhnk8ztFLn7FblWEuORUTEASW0tVxSqpeC3Ortx6sP\n9ucI7mQ6HeiJh2SSSCOJNBJJYn/68QBzaEmneIcptdgBHI/bwR5sF24O4Pgq36ew+N+7ZmilrvH6\nt5d6rnxWREScUAWcWi4p1UthnhJaJzpzMA8zl79YwCrm48JFZw6lGR3iHZrUAe3oRhu6soJfsAiV\nO8bgog1daEe3Kt8nP8f+956SVvVZXpGaKGXbH6UPaMmxiIg4oIS2lktOSyZ7ZVa8w6hV2tGtWgmF\nSEWu431upjd5bCNEsNQ5F25SaMi1vF+texRohlbqqBbpZT6k0RStiIg4oCXHtVxGk3S2ZWXHOwwR\nAZrRgYeZx6GcRiJJpJBBChkkksShDOcR5tGcjtW6x86EtoFmaKVu8SaG34MuIiJSlmZoa7mGzTLY\ntnE7oVAIV9mCGiISc5m04RreJoctrGEhAG3oShqNI3L9HVsM6k1Cm5cHa9eCxwPt2oG+z9UfWnIs\nIiIO6J1BLdeoeQahYIjcrXnxDkVESkijMfvTj/3pF7FkFnYVhUpK9UbsmjXSypVw3nnQtCn06gVd\nu0Lr1vDww+BXZfe6qUwfWq04FhERBzRDW8s1btEQgM3rtpCemRbnaEQk2grzfAAkpdbhGdrffoN+\n/SA3F4Il9iLn58Odd8KECfDll+Ct40m9iIiIhKUZ2lquRcdmAPytwlAi9cKOvtPeFE+cI6nAH3/Y\nyeZPP5VORp0KBuH442H79vJfX1AAP/8Mt91W/VjrMWPMQGPMYmPMUmPMzeWcP88Yk2WMmVf8uCAG\nQZV6aqEpWhERCU8JbS3Xcq/mAKxfviHOkYhILPjyi2doU2rY7OSnn0KXLvby4OHD4ZhjoEULuP/+\nPUtsJ02yZ2YrU1AAL7xg/1/2mDHGDTwDnAB0Af5pjOlSztB3LcvqWfx4KaZBioiIOKSEtpZLz0wj\nuUGSElqRemLHDK0nuQbN0D77LIwYAb//bi8L3r4dcnJg0ya4914YNgxC5ffm3c3bb9uvDcflgu+/\nr17c9dfBwFLLspZbluUH3gFOjnNMlN1DKyIi4oQS2lrOGEPLvZuz9s/18Q5FRGJgZ0KblBjnSIot\nWwbXX28nsuXJz7eXII8b5+x627c7v3e4mVypSGtgdYnna4qPlTXMGDPfGDPeGNO2vAsZYy4yxswx\nxszJyors1hcVhRIRESeU0NYBHbu3Y8Vvf8U7DBGJgYAvgDGGhMQaUtPvySehqKjyMXl59tJjJxlK\n586Q4OD3FgzabXwkWj4FOliW1QOYCrxW3iDLssZaltXbsqzeTZs2rd4d1aZHRESqQAltHbBX9/Zs\nWruF7C0OlumJSK0W8BWR4EnA1JQ3/598AoFA+HGrV9tLkMO56CJIdDD73Lw5HHhg+HFSnrVAyRnX\nNsXHdrIsa7NlWb7ipy8BvWIU264YYn1DERGplZTQ1gEdu9uzFJqlFan7ivxFJHpryOwsgM8XfgyA\n2w2FheHHdeliF5RKqqQtUUoKPPSQZvSqbjbQ2RjT0RjjAUYAE0oOMMa0LPF0CPB79MPS36eIiOw5\nJbR1wF4HdABg6S8r4huIiERdwF9Uc5Ybg71E2KlmzZyNe+cdOPxwSE0tnbR6PHai+9BDdqEpqRLL\nsoqAUcAU7ET1PcuyFhpjRhtjhhQPu9IYs9AY8ytwJXBefKIVERGpXA16VyRVldmyEc3bN2XhD38w\n7JpB8Q5HRKIoVBTEnVCDPou87jqYO7fyAk0JCXDWWeB12GooJQWmToWvv4bHHoMFC+xkdvBgGDUK\n2rePTOz1mGVZk4BJZY79p8SvbwFuiWlQZWfcVRVKREQcUEJbUyxfDq+9BitWQGYm/POf0KeP4yV1\n3f+xP3M+n4dlWTVnb52IRFwwGMLlrkEJ7Ukn2bO0CxeC31/+mNRUuPXWPbuuMXDkkfZDREREpAI1\n6F1RPVVQYC+d69rVrgL6xht21dCjj4aePWHNGkeX6fGPLmzLyuav352NjzUfBaznTzaykhAO+1GK\nyG5CoRDuBHe8w9glIQGmTYODDtp9iXBamr3M+OuvNasqDpT+MNbSnloREXFAM7TxFArZsxszZ5Yu\nlhIK2W0uFi6Egw+G336zZ20r0fOobgD88uVvtO9SbrvAuNjMGsZzD9/yPwwuLEIkkcYgruEkriYR\nh0sQRQQAK2ThctWwN/qNGsEPP8CsWfDcc/ZKk4YN4Zxz4JRTnFUtFhEREakCJbTxNGUKzJ5dceXP\nYBC2bLH3kN13X6WXarlXc9rs05LZn89l6JUnRiHYPbeOJdxGXwrIJsiuPpU+8nmfu/mRD7mLGXhJ\ndnS9LP5iCs+yhJm4cNOTgQxgJGlUnuyLSAwYA3372g+RqtB2GRERqQItOY6nRx6pvJAK2C0xnn3W\nTm7DOOTEg5g3fSGF+Q7baESRhcV9DCSPraWS2R38FLCK+bzOdY6u9QY3cRX78hmP8zvfsJDpvM9d\nXEwbpvJiNH4LIjWWauVIfaAvcxERcUIJbTz99puzcYWFsHlz2GEHn3gQAV+AeV8tqGZg1beAr8gm\nC6uStyQBCpnBOAqoPKl/n7uZwtMEKKSIXUVn/BQQoJBxXM13vB2x2EVqNE1iSZ2lL24REdlzSmjj\nye2wsEsoZBdeCaNbv/1JSUvmh09mVzOw6vuedykMk6gCuElkIdMrPJ/HNj7mQXzkVzjGTz7juEbF\npqSULP7iDW7kKvbjcvbifgbzG19V+iFLbeAyLkLBGvC1vnWrvR2iRw/o2BGOOALefbfiSscie8qq\nAV/nIiJS42kPbTwdfTS8846dsFamZUu76EoYHm8ihw7uxfcf/8Rxz+7P5sRVeEimG0fHfJ9pHtsc\njbOwKk18v+NtXA4+d/GRzwK+ogfHOI5R6q4pPMdrXItFaOes/kZWsIgZ7EUvbuEzkkiNc5RV405w\nESwKvwUhqmbMgCFD7K0Q+cUfNq1cCb/+CjffDN98A21rTnE6ERERqbs0QxtP110HSUmVj0lJgRtv\ndFwso9mwENmbcxj99bm8xOU8x0gupjWPM8JxkhkJLelEAs4qm2ZS8Rvf1SysdHZ2hxBF/M1Sx/FJ\n3TWbCbzO9bstUQcoJJc/+ZFHGR6n6KrPnZhAUSCOCe0ff8CgQZCTsyuZ3SE3F1avhn79Ki52JyIi\nIhJBSmjj6aCD4LLL7KS1PMnJ9pgLLnB0uS94nmkD/wMNAuS9n0khuRSQQwAfP/Ext3Aw+WRH8DdQ\nsaMZiSH8kupk0tiXwyo87yUVJ/uqDC61ABIsLF7nOvyVfAgSoJBFfM0qHO5hr2ESEt0UBXYvtBYz\n99xTebIaDNp7/t97L3YxSZ1kqfqZiIg4EJGE1hgz0Biz2Biz1BhzcznnvcaYd4vP/2iM6VDi3C3F\nxxcbY46PRDy1ykMPwf33Q+PGkJYGqamQnm4ns//+N3z5JXg8YS+zlb8ZxzUEknNJHLKewPg2WL5d\nf71F+MjiL97jzmj+bnZqwd70ZjCeSlryeEnhTB6odEnxQZzoaGloiCK6a7lxvbeK+WxlfdhxRfiZ\nyvMxiCjyEj0JBHxxSmgLC+GDD8JXXc/NhSeeiE1MIiIiUq9VO6E1xriBZ4ATgC7AP40xXcoMGwls\ntSyrE/A48GDxa7sAI4CuwEDg2eLr1R/GwJVXwoYNMH48PP00jBsHGzfCM8+A19ms45eM3flrzzmr\nsLZ6CHzSqtSYInxM4yX8xGYp4Chepwv9d5tlTSARD8mcxl305+xKr9GFf5BO00rHuElgf/rTpJKl\nyzsE8BEkzvsPJWo28RduB6UBQgRZz58xiCjyvCleAr4AoXB776Nh82ZwOfyxsWZNdGMRERERITJF\noQ4GllqWtRzAGPMOcDKwqMSYk4G7in89HnjaGGOKj79jWZYPWGGMWVp8vZkRiKt2SUiA446r8st/\n4TMCxYlqwoANuDrk4X9hLzynl35TaXCxmoXsTa9qheuEhyRuZRJ/8B2f8iir+BUXCRzIiZzIlbRg\n77DXMBhu5BPu4AgKydmtQq2bBNJpyiheq/AaOWxmMk/zOU+TyxbAYm/6cAo3czCnYNQqos5IJs1x\nFeMUMqIcTXR4ku0VG/7CAEkpMV5m36ABFDmcHa5oK4WIY1pyLCIi4UUioW0NrC7xfA1wSEVjLMsq\nMsZsBzKLj88q89rWEYip3gmy602mcYPnouUU3tqd4KI03F1ydp3DEIrhDKXBsD/92J9+Vb5Ge7rz\nALN5neuYz1QSsQtpBfDRl9M4h0fIoFm5r93ACm6jL/lsI4Bv5/Gl/MRTnM2hDONyximprSM6cyhO\n3gQnkUY/zox+QFGwI4n15ftin9BmZED37vDLL5WP83phxIjYxCQiIiL1Wq0pCmWMucgYM8cYMycr\nKyve4dQ4e9MbV4nPJzwjV4A3iO/JTqXGBfDRgk5lX17jtWIfbuZTnmUVN/ARN/IJL/I3V/B6hcls\niBD3cAzZZJVKZnfwkccsPuAz/hvt8CVGPCRxPJdVuncb7P3bvRgU/YDWroXPPrMf68Pv7XUiKdVO\nYgty41RF+Pbb7b3+lXG74fLLYxOP1B1lPldUTSgREXEiEgntWii1ebFN8bFyxxhjEoAMYLPD1wJg\nWdZYy7J6W5bVu2nTyvdU1kcncmWpNjmupn48Z63C/3oHQln2EkWDi4M4iTQaxyvMamtIc7pxFF3p\nT2qYJaO/8SXb2YhFxXsNfeTxEfdrX20dcjqj6cTB5Sa1Ltwkk87tTHG017bK/vwTjj8eOnWCM8+0\nHx07woknwvLl1bp0aoa9lDc/uyASke65oUNh5MiKk9rkZHj9dWjTJrZxiYiISL0UiYR2NtDZGNPR\nGOPBLvI0ocyYCcC5xb8eDnxl2fX4JwAjiqsgdwQ6Az9FIKZ6py1dOYwz8LBr35r3mj+h0I3/eXuv\nahINOJMH4hVizE3nVQrJDTsuQCFL9WVXZyTi4Q6mcgb30JCWeEghiQZ4SKYfZ/Iw8+jAAdEL4Pff\noU8fmDrVrgq8fbv98PlgyhTo1ctOeKsoJd1O1POzw/dnjpr//hdeeQW6dbN7aael2cuMjzsOpk+H\nYcPiF5vUHZqiFRERB6o9RVG8J3YUMAVwA69YlrXQGDMamGNZ1gTgZeCN4qJPW7CTXorHvYddQKoI\nuNyyLE2VVdElvISHZKbzin2gSw4JJ6zH/0wnWt6Qy21Jn9GyFi43rqrtbHQ0zuAij61RjkZiKYFE\nhnAdg7iGTfxFEX4a09pRC6hqGz4csrPLfzMeCtnnzjgj/D7UCqSk2x9a5cVrhhbs6uynn24/1q2z\nf0/Nm0OjRvGLSeocpwXeRESkfovImjvLsiYBk8oc+0+JXxcCp1Xw2vuA+yIRR33nxs2FPMtw7mA6\n41jL72Rf72HGgO2c9OpY2l/aPd4hxlQmbTCYsG+KQgTJoHmMopJYcuGiGR1id8M5c2DVqspnlkIh\nWLwY5s+HHj32+BZpjeykPHdrXlWjjKxWreyHiIiISBzUmqJQ4lwjWnIqt3AFr3PrkS/Spe8+vPfg\nJwT8gXiHFlMDuLDUEuyKpNKIvTgoBhFJnffll/bS4nCKiuyxVZCemQZA9uacMCNFajlN0IqIiANK\naOs4Ywxn33k6G//axGcvVO0NdI20fDm8/Ta8+SYsWlTukP04nJbsg7tEsayyvKRwBqPVtkciw++H\noINdE6GQPbYKUhum4HIZtm/KrtLrRWoufR8WEZE9p4S2Huh1bA96HtWVN+8dT148C8lEwp9/Qv/+\n0LUrXHwxXHop9O4NBx0EP/9caqjBcDuf04wOeMvsnTS48JDCiVzFUZwXw9+A1Gn77QcNGoQfl5xs\nj60Ct9tNWuMGZG/SDK3UcVbFFepFRER2UEJbF2Rlwb33Qrt29pvpVq3g5pthzRrAnqW94IGz2JaV\nzbsPfhznYKth8WK7euy339rVY3Ny7EdBAcydaye6s2aVekkGzXiYXzmfJ2nN/nhIIYV0DmYodzKN\nfzEmTr8ZqZNOPtkumBROQgKcdFKVb5PRNJ1tWdur/HqR2iBzeS3+eSUiIjGjhLa2++knu9flfffB\n6tWQlwfr19ttNfbbz24TAuzbpxMDzuzHB49PZONfWXEOuorOOqvi6rFg/96HD7eXc5bgJZmjOZ//\nsog3yeM1tnM949mHQ2MQtNQrXi88/DCkVLJ3OyUFHn8cEiteCh9O45aN2Lx+W5VfL1IbtP795XiH\nICIitYAS2ngJhZwVj6nMhg1w7LF2kldYWPqcz2cneKeeCkuWAHD+ff8E4JXb3q7efeNh0SJYuDB8\nX8Lt22HatNjEJFKeiy6C+++3+7OWTGxTUuxjjzwC555b8esdaNyiIVvWR7jVlGXZ30fU+1NERERq\nESW0sTZtGhxzDHg89hvcjAy48Ua7l+Oeev758IVl/H77DTTQrF1Thl87mGlvfsvvP/5ZheDj6Jtv\nnI3LzYUZM6IaikhYV14Ja9fC3XfDoEH249577dUTl15a7cs3btGILeu3YkUi+fzzTzsJT021H16v\nvdKhzJ50ERERkZpICW0s3XYbDBliJ7XBoD1Lm50NTzxhFzn69dc9u97YsbvPzJZVVARvvLFz1uWM\nm06hcctGPHnZiwSLHFRjrSkCAeczR4H61Z5IaqjGjeH66+HTT+3HNddAw4YRuXTTNpn4CwPkbMmt\n3oWmToWePeHVV+296KGQ/e/no4+gXz94WUs+JYac7D8XEREpQwltrIwfb+9rzS+nyrDfD9u22TO3\nBQXOr7lli7NxgcDO5c0pacmMevJ8ls5dwfuPfur8XvHWrZtdSCecBg2gR4/oxyMSR03bNQFg41+b\nqn6RNWtg6FD7e1JRUelzoZD9vejKK2H27GpEKiIiIhJdSmhj5a67yk9mSyoshPfec35NJ+1BwP7U\n2+vd+bTfsEM54tRDeP2u91i9eK3z+8XTkUfay7OdGD48qqGIxFuzSCS0zzyzeyJbVkGBvR9YRERE\npIZSQhsLq1bB8uXhx+Xm2suInTrzzPCVUl0uOOWU3ZZyXfH0SLzJHh678HlCoVrQ688YeOEFu39n\nRXZUj01Kil1cInHQvL2d0G5YVY2K5a+9Fr4wnWXZy6WDtWh7goiIiNQrSmhjYcsW5y06Nm92ft2r\nrgp/3aQkuydtGY1bNOL/7N13fBP1G8DxzyVNmy42lL03BWRvBESmAooCAqKiIAoqe4koslQQQUQB\n8ScgqKAgoICALBEQWbL3BtmrK03X/f64QlfSpM1sed6vV17N3X3vvk9KGu7Jd705/RUO/3WcX2as\nsb9OT2rfHhYvhuDglK3TgYFaovvpp/Daa56LTwg3yZkvB8ZAP66du5H5i4SH21dOUbQZ04VwORlD\nK4QQIuMkoXWHAgVsz0b8QKFC9l+3VClYskRrmdTrUx5TFG3/zJlQq5bF01u+2JT6T9fif+9+z8Xj\nWaTr8TPPwI0b8NVX8PLL0KuXNovzjRvQr5+noxPCLRRFoXCZgvx35lrmL5I7t72V2T+8QQghhBDC\nzSShdYciRbRJjWwJDoY338zYtZ96Cv75B154QRsn6+OjPTp10pav6d3b6qmKojBozusYA41M6j6d\nmGg7k25PMxqhZ09tZtYFC7REVm64xSOmcNmCXDntQELbt6/t7vl6PXTpog1dEEIIIYTwQnKX4i4T\nJmgtptZ/9FruAAAgAElEQVTodNqkR506ZfzaVapoS/NERWndm6OjYflyqFPH5ql5CuZm+Pz+nPn3\nPHOGLsx43UIIjyhcOoRrZ68Tn9nxra+/rq2HnR4/PxgxInPXF0IIIYRwA0lo3aV1a/j4Y22sZ+ru\nwQEBWrfkrVvtH2triU6ntfKmvr4N9drX4rnBT7Pqy3VsXboj8/ULIdymSPnCxMbEceNCJmc6zp9f\nW4c2R460LbUGg/a59MMP9vUuEUIIIYTwEElo3WnAAPj7b2124ly5tJvI0qW1ZTFOnNCee8irk7tT\nuUF5pvWZzeWT/1kv+Ndf0LGjNv4uZ06oV09bY9fW8h9CCKcqXqkIABePXc78RerWhZMnYdQoKFxY\n+0zKl08b+nDoEHTo4KRohRBCCCFcQxJad6tWTRv3efeutsbjmTPw9ttaK4kH+Rh8ePfHQegNesZ3\nmUZ0VKrlPFRVu8lt3VpbxuPePQgL08bvvvIKNG6sLTskhEjjAof4jc9Ywcf8wwriiHX4mg8S2gtH\nHUhoAUJCYOxYuHJF+0y6eROmT/foF2ziEaXILMdCCCEyThJa8VCBYvkY+d3bnDt0kSmvzEq5Pu3U\nqbBwoTZOV1VTnhgRAf/+C127ujdgIbzcVU4znFqMph6LGcUPjGEmvXiNAmziW4eunSNPMLlDcnLx\nWBaZoVwIIYQQwgUkoRUp1G1bg1cn9+DPn3by3biftJ2xsTBpUvprUZrNsGkTnDrlnkCF8HI3OM8o\n6nKef4nBRBxmEogjmnAiucf/GMBavnCojpKhxTl/5KKTIhZCCCGEyHokoRVpdBnWgdYvN2fR+J/Z\n9MNfsHEjJG+ttSYuDubPd3l8QmQF/+MtoriPiuW/HTNRfMcwwrmT6TpKVy3O+cOXMj/TsRBCCCFE\nFicJrUhDURTemd2Hqk0rMbX3lxzdfsz+hPaitBa5SyxmrnOO21wmwUrSJDzjHtc5yAaryewDCgqb\n+SbT9ZSqVgKzKYarZ65n+hpCCCGEEFmZJLTCIoOvgfd/Hkq+InkYO3MvlwiyfZJOp00wI1zqDv/x\nNW/yCnkYQlXepjyvU4RVTCUWs+0LCJc7x34MGG2Wi8HEITZnup6SocW1+g5fyvQ1hBBCCCGyMklo\nhVU58+Vg0prRKL6+jIyqxQ380z/BaITu3d0T3CPqKqcZSjU2Mg8zUZiJJAYT97jGEsbyPo8TQ7Sn\nwxQZotouYkXxSkVQFIXzh6VnhMgOZJZjIYQQGScJrUhX0fKFmfT7GCIMAYzUPc59fC0X9PGBSpWg\nZk33BvgIUVGZSBsiuEu8hWVfYjBxgYMsYLAHohPJlaS6Xa3lvvhThWaZrsc/0Eih0gU4f0RaaIUQ\nQgjxaJKEVthUrmZpPlw9hmtKIO/qmxKFT8oCRiMUKQK//eaZAB8RR9nKfa6nOy4zBhNbWIAJWRPY\nk3JTiFCao9j4iFVRacGrDtVVMrQ45w5JC60QQgghHk2S0Aq7VH+iGmN+HsYpcjMm4ElMOl8wGCB/\nfnjvPThwAAoW9HSYXsOMic18y2jqM4CyjKYBW1iAGVOmr7mdJUSTztJJifT4cJhNma4nuzIRwXpm\nM4LaDKAsY2jMX/xALDEuqa83M/EnGMVKN0o/AniBieQgn81r3eYy3/MugwjlLcrxCZ04wlZUVEqF\nFufKyf+IiXbN6xBCCCGE8GY+tosIoWnYqR6jFr/D5J6fM7rBUCb+NJCAgvlAcc+4p/Mc4DJH0eND\nRRqTm0JuqTejLnKYcbQgBhPRiS2l1znDJQ7zHcP5gM0Uo3KGrxvJHewZb6miPqxXaM6wh/E8SRyx\nmBO/FLjOGS5wgO8YzodsJYTSTq2zIGWYxN98ynPc4ByxxJBAHEaCUYAefExr3rB5nY18wzcMANSH\n3ZivcYaD/EE56tG42nskJKhcOHqZcjWd+xqEEEII8QhQVYiPhfiYxIeF5wmxVspY2JenNFRo67bw\nJaEVGdKsayMURWFSjxmM7jKDSWveJSDYxmRRDjrGNubyBjc5h4IeBYgjllBa0I+vyUNhl9afEfe5\nwViaEsndNMeiiSCaSMbSlBkct6tlLrmClEWPweL42dTyUjRD187ObnGJcTyBibA0x6KJwEwUY2jM\n55zAn2Cn1l2EikzjMGfYy0E2EIeZwlSgLs9gwM/m+XtZzf94i9g0E32pmInkBDuIq/4pYOTMgQuS\n0AohhBDeIiEhMQm0kvSleR5nR5lUz9O9fnrXSFUmwfa9ZYZU7iQJrfBuj3dpCIrCpO7TGdV2IpNW\njyIwZ6BL6jrAej6hEzEWuuoeYB3DqcEn7PeapPZ3ZhFDVDoltERkPbN5jjEZunZzevMr02wmtEYC\nqUjjDF07O1vFFIvvnwdUEjBxny0spC39XRJDGWpRhloZPm8hQ9KNPZZozpTZiG9AJ878ew5o7kCU\nQniYm3r7eL1YE0Rch4gb2iP6HpjDEx9hiT8jIN6c8sY0IS7pBhVA0SX+ThXtp6JL+VxvAL1v4iP5\nc0v7kj338QW9H/j4JW77JR5Pvc835fMHP+XfWWREQnyyxC028X2e/D3/4FhcylZEq+ViLV8vzbG4\nVMmivYlpsiQzIc7Tvz3PiU//XtXZJKEVmfL48w3Q6RQmvjCdIc0/YPLad8kdksupdcRiZhpdrN7Q\nJxBPOLeZQ19G4R0TUq3nK5uz28YSzTpmZTihLUgZatKe/ayx+jvxJYDuTEYnw+MBrfv1Jv5n80sA\nM1GsYbrLEtrMuMAhbmN79uJ4fQzB1VTOHrzg/CASEmDTJti/X1tnulEjqFdPbkiFcISqQtgVuHEc\n7pxNetw9B+HXtKQ1O9MnJsR6Q6pk1y8pWbZ6zNdy+YfHUl1D0YFOD4o+1c9M7H/4BcEDyZ47sl9V\nQU2w8LC2PyNlkh1PiNMearyWJD7YTohL3La070H5VPsePhLsPydN8hiTLGl8cCwmbTnV+kSYwsl0\nD7648rH9xdbD54k/dYaUx0MyPrTOEZLQZhXx8dpPvd6zcSTTpHN9xq8awbjOUxnY5D0+WjeGQqVC\nnHb9XSwngfh0yyQQzyH+4C5XrY6pjSUGHwxWJ+dxFhWVcG7ZVTaMm5mq420W8TEdOMEOzETxYEyt\nHgN6fHiW0TTn5UxdOzuKJpI4O5bPAbjLVRdHkzG3uIgeg81yCcRjrB7JmR/Po6oqirOSzXXroHdv\nCA+H6GjtBsxggMKF4fvvoXZt59QjRHYXeRsubIfL/8DVg3DtEJjueDoqz3nQoiXEo8BSMqizlDDa\nkzjaKmMt0bSzniz8ZbUktN7MbIaFC2HKFDh9WttXvjyMGAE9e2o3lx5Wp00NPvljLGOemszAxu/x\n0e/vUqpqCadcez9r7ZrcyAc/TrCD+nR+uO8mF/iVaWzmf5iJRIeeWjxNJ0ZSjrpOiS81BQU9vnYl\nUD7W1vO1wRcjY1jHUbayik+5yEF06KlOa9ozkCJUyNR1sytfjKh2TKT1oKw3MRJod+x5ahq4NieK\na+duUKi0E75UWrMGnnsOTKl6AsTEwKlT0KwZbNkiSa0QlsTFwPk/4eR6OL8NbhzN2Pk6HwgKgaAC\nEFgAAvKAX3CyRw7tZ4qbVp+kbd2DWzs18TtPNam1DjWx1S4+VTdKO8fsxZnTPo8za92f42JSHXuw\nL7FrdJzZ+eP0xKPhYWLmk6wl0JD0PMUx35TlUv9tJD8vxTV8Uv09GdK2OqZ5biNJ1Plk6SQxK5GE\n1ltFREDz5nD0KEQlG5N54gS89RZ8/TVs3Aj+rp2QyR6VG1Rg2p/jGdl6PIOajuX9ZUOp0aKqw9eN\ns3s5FZV4ksYpHGc7E2lDLOaHXU3jiWM3K/iXdfTkE5d1La1JO3azIt1EREFHLZ7OdB0KClVoRhWa\nZfoajwo9PlSiCUfYYrNcfZ5zT1B2Kkd9uxJaI8E8XqMNR1nP6f3nHE9o4+LgxRfTJrPJRUZCr17a\n55MQTpOFb/ziY+HkOjiyHE5tsN1t2C8HhFSBvGW12UDzlIY8pSBnMTDm0rr4Z0cJCYlJb/JkNybp\n+cOfyRPnVPviHowdTr0vVcIdH5vUvVZNSPwZn+xnQqrt9PYnpOz6qib/bFYd2/+wO7MuZddmi/sz\ne1zRkjNdYhdqnU+yx4Ou1cm20zxPtk+xcg2L+3ySrp0iyUydUCZPVFMllDq9JIXCJklovdXLL8Oh\nQ1orbWqRkdqYtj59YNEit4dmSckqxZixfSJjnprM6LYTGTjndVq/7NgENWWozR5WpTspDkA88RSj\nCgDh3GYSbS227KqoxBDFIoZTgqpUpqlD8VnSkeH8y7p0J4YyYKQDQ51etzcL4xYmwshBfqfPJGzL\nM4zmNP8kdtG2TI+B9gx0Y1S2+WKkFf34nS/S/RvwxZ+2oT2Y67ORU/vO0qRzfccq/u03iLWjFeXC\nBdi3D2rWdKw+IbKymydg30I48CNEWRlyovOBwjWhREMoUhMKVoVcJbNv0poenQ50RjB4V48YIUTW\n9gh+mmYBV67A6tWWk9kHoqNh2TK4ccN9cdkQUiI/n20bT9WmlZna+0vmv/cjqmpfl0lLmvOKXS1U\nBSlLcUIB2Mi8FK21lsQQxc+Mz3Rc6SlPfZ5nLH4EWDzuSwBd+ZCy1HFJ/d5mF78wjBq8ThGGUI3e\n5ONjOnKO/W6LoTpP0o530v036c1MilDRbTHZqxsTKE0tfC3ErqDDn2DeZS3+xgBKVC7K6X/PO17p\njh3auFlbVBV27XK8PiGyGlWFCzvg+64wqy7s/CJtMpurONTvDz2Xw8iL8NoGeHIcVO6otcY+isms\nEEK4iHyieqNly+wrp9PBihWujSWDgnIFMmnNaNq++gSLJy5jQrfPMEWmXkPTPsHk5RlGWU1EQEtG\n+vDlw+2NzLPZogtwlK2Y7BifmxmdGMFgfqI0tTHghz/BGPCjLHUYys90YIhL6vU2CxjCTF7kPP8S\nRwxmIokjhr38yhgas9eNM1N3ZxIDWEhxqmHA+PDfpCKNGMVvPMGrboslIwz4MpaNPM/75CQEPwIT\nYzfSkK58zD5Ko7WQlqtZmlN7zzr0JRKQqmucECKFCzvhf23g27Zw8veUx4ILQ5Mh0G87vHMQ2kyC\nsk+Ar2uWtRNCCKGRLsfe6PZtrQXWFrNZK+tlfAw+DJr7OsUqFGbeyEVcPvkf434ZTsGSBTJ8red4\nD4BfmIyC8jBZNRKMHj2D+YmKNHpYPpJ7dl1Xjw8mwvAnKMMx2aMm7ahJO+5ylXBuE0w+clPQJXV5\no39YwQZmW+zm+6Dr92d0ZSanrc5O7Wz16Ux9OnObK0RxjxzkJycZf09mlJkoLnKIOGIpTPkM12nA\nl04MpwNDuc5Z4oghH8XSdN0uW7MU6+Zv5taVO+QvmjfzAderB8HBtltpdTrpbiweHbdOwx/vw/HU\nX8QpUKEd1OkNpZtr4/2EEEK4lSS03qhAAW2yp/QmZQEwGrWyXkhRFJ4f2oGSocWY+MJ0+tcZyXtL\nB/NY89CMXQeF5xlLG/qzmfmcYx8++FKDttTlGXxSLWsSTD67ls5JIJ5AnLturiW5KeS2hM2bLGNC\numNWARJIYD2z6co4N0WlyUsR8lLE5fVEcp8feJctzEeHHgWFWMxU5Ql6MTXDXZx16ChEWavHy9Us\nDcCpvWcdS2g7drRvebAiRaCua2YMF8JrxMXA9hnw5ycpl5rRGeCxF6DBW5C/vOfiE0IIIV2OvdLz\nz9vX7S8+Hp591vXxOKBOmxp8sWsyuQrkYESr8fw0dVWmukQGk5cODOEdFtOfb2lIlzTJLEAr+qXb\nRVmjUJ1WdpQTmRHBXS5w0Ga5WKLZxmI3ROR+EdxlJLXZyNeYicREGFHcJ5Zo9rOGkdTlLPucWmfp\n6iVQFIXT+885diGDAb79Nv0Z1AMCtDIy86RwJm97P109AHMfh80TUiazVZ+Ht/ZAh5mSzAohhBeQ\nhNZdrlyBn3+GJUvgyJH0yxYoAF27pn9D6e+vzYScO7dTw3SFouUL8/nOSTRsUZG5w79jXP1BRB45\n6ZK6mvEyPvilW8YXfzondmUWzhdNBHoLXzZYK5sdfc0b3OKixaWnVFSiCecjniKeeKfV6R9opFjF\nwpzaf9bxi3XqBD/8AHnzat2PFUXrYhwUBEWLwrp10LCh4/UI4Y1UFXbNhXktU64hW7gG9NkMnedB\n7pIeC08IIURKDiW0iqLkURRlg6IopxJ/psmuFEV5TFGUnYqiHFEU5aCiKF2THZuvKMo5RVH+TXw8\n5kg8XunyZWjbFsqUgd69taV26tSBxx6DnTutnzdnjnbDGGRhjGdQEDz+OHz+uevidqa9ewls0ZSx\nf07hdd/j7Nx9iTervsOZeq3hnIOtSakEkpP32UQguTCQclkAHT74EkA/5lIO6SrpKsHkJcHORC2P\nG7r+uls4t9nNCpvrKJuI4ADrnFp3uZqlOb3PSX9THTvC9euweDF88AGMGwcrV8LFi9C4sXPqEMLb\nmCNgaS9YOyypVdYQAK0nwWsbtWV3hBBCeBVHW2hHAhtVVS0HbEzcTi0K6KWqahWgDTBdUZTkgxeH\nqar6WOLjXwfj8S6XLkGNGrBhgzaBU3i49jCZ4MABaNkStmyxfK6fn9YKsmCBNkmLv7/2aNhQW3t2\n9Wqta6C327EDmjaFvXtRok08Zz7Mp+pWzKqet3YHsiK0I+qZM06tshSPMYOTdGYMeSiMD34Ekosn\neJVP2EcTeji1PpGSHwHUoQOKjY8XI0G05x03ReU+R9iCD742y0UTzj84d5byUlVLcOvKHcLu2LHs\njj30enj6aRg7FsaMgRYtvK9bqBDOEvYffNsGjq1K2lewKvT7Cxr0lwmfhBDCSzk6KVRHoFni8wXA\nFmBE8gKqqp5M9vw/RVFuAPnBzulos7LeveHuXW2sqyVRUfDcc3DtGvhY+KfQ67Uxsl4+TjY1ExHs\nZgV3E67gv3IStXNGkSfZ/ECh3OYr/mCqWptZpgrsrTuQIccXkSt/TqfFkJP8dOZdOvOuw9cyY2IP\nK7nFRfwIpBZPkZ8STogy+3qOsexjtdWJoRR0BJKbBnRxc2SuF0u0XesnA5iJdGrdJasUBeDisSuE\nNvK+dXWF8FrXDsHiLhD+X9K+On2g1QQwGK2fJ4QQwuMcbaENUVX1auLza0BIeoUVRakL+ALJm+Qm\nJnZF/kxRlPQHP2Ylly7BX39ZT2YfiImBVavSL5NFJJDAYkbxGgX4mjf4gXdZMDaMAWdhyjKISrbK\nSG7MTGA7b6r/sveugddDB7F3wwHPBW+BispyJvMaBZhNX37gXb5jGO9QkfG0JsyO2ZQfVcUJZRgr\n8CMQX1KOBTcSRF6KMp5t+JL9bhRDKAN2JLQGjBShklPrLlGlGAAXj1526nVF9qMoShtFUU4oinJa\nURRLvaselOusKIqqKEptd8bnVlf2wfz2Scmszgc6fAHtp0oyK4QQWYDNhFZRlD8URTls4dExeTlV\nm7rW6l2coiiFgO+AV1RVTUjcPQqoCNQB8pCqdTfV+X0VRdmjKMqemzdv2n5lnrZtm31dgsPDta7F\nWZyKypf0Zi2fE4OJaCKI18UTEwixRtjXDsbsAHOy3EYBnuE0M407CfZRGdl6ArPe+R9mk9ljryO5\nhQxlOROIJoJowoknjhhMxBLNUTYzirp2r3v7KKrOk8ziHJ15j8JUIA+FKUsd+jKbzzmZbVu5y1GP\nIPLZUVKlBb2dWneB4vkwBvhxQRJakQ5FUfTALKAtUBl4QVGUyhbKBQPvALvcFFmaPXHxCRbKOdHl\nPbCwE0Tf17b9ckCPn6Hmi66tVwghhNPYTGhVVW2pqmqohcdK4HpiovogYb1h6RqKouQAVgPvqqr6\nd7JrX1U1ZuBbsD5Tj6qqc1VVra2qau38+fNn7FV6QmysfUvvgNZKm8WdZCd/85PVLqZxRrheGtYO\nSHusDPeZNbIOnd5qy4qZa3mj1ghO7HHuuNqMusRR1vOV9ddDLHf4j+VMcnNkWUtO8vMso5jBceZw\nhcn8QxN6YLAxE3VWpqDwCtPTtEwn50cALXiVPBR2at06nY5ilYpw4ZgktCJddYHTqqqeVVU1BvgR\nbQhRauOBj4FodwaXnDnOhQnt1QPw3TNgTkxm/XPDy79Bmeauq1MIIYTTOdrleBXwUuLzl4CVqQso\niuIL/AIsVFX151THHiTDCtAJOOxgPN4jNNS+hDYgAGrVcn08LraKqcRgSrdMTAD8NhgSUn8Jr9fj\nV6Ma/Wf05qN1YzCFm3i7wWjmj/2R2JhY1wWdjtV8Rhzp1x2HmQ3MJtbGbLbi0VOXTrzGlxgwpkhs\n9fhgwJ9GvMAruGaW8mIVCnP5xH+2C4pHWRHgUrLty4n7HlIUpSZQTFXV1e4MLDWXJbR3z8Pi58Ec\npm0H5IWXfoVC1V1TnxBCCJdxNKH9CHhSUZRTQMvEbRRFqa0oyrzEMl2ApsDLFpbnWawoyiHgEJAP\nmOBgPN6jZk0oYseSJAkJ8GLW79p0gh12TYQTlQvC86bamTcvNGoEQK0nqzP34Ke06N6YxROW0b/O\nSE7tc8K6mhl0lD9JIM5mORWVm5x3fUAiy2nOy8zhMs/zPhVpTDnq0ZLXmcJ+3mAeelwzY2rR8oW5\ncfGW13TdF1mPoig6YBowxI6yLh0OFGm2/TmcYVF3YNFzEHFd2zbm1JLZglWdX5cQQgiXc2iWY1VV\nbwNPWNi/B3gt8fkiYJGV81s4Ur9XUxSYPRueekqbzdiSgAB47z3I6bzZfZ3u4kX46ivYswd8fbUl\nPHr2tLw+rj1S57wBAdr1ky0FEpw7iBEL3qLpcw2Y/vocBtQbxQsjn6H7mM74+mWBpYqESBRMXjox\ngk7WpwdwuqLlC6OqKv+duU6p0OJuq1dkKVeAYsm2iybueyAYCAW2aB2oKAisUhSlQ+L/7w+pqjoX\nmAtQu3ZtO8fZ2O++KTZFoA6Lj9PWmb19StvW+0K3HyCkijNrEUII4UaOttCK9DRvDj//DDlypEwA\nAwLAaNTWdRzhvhvdDElIgHfegQoVYNo0+OMPWLMGhg6FkBD45ZcUxctSB0sTeqRmjIDg22i/j6Ag\nbU3dtm0tlm3wdG2+PjxNa62duIx+NYZxaNsxJ7w42yrQEJ2dLWj5kKRBeI+i5QsBcPnkVRslxSNs\nN1BOUZRSicOCuqENIQJAVdX7qqrmU1W1pKqqJYG/gTTJrDuEmZw87GTTh3B+W+KGAs/OhZKNnFuH\nEEIIt5KE1tXatoUbN7TW2l69oFs3GD8erlyBUaNStEx6laFDYd48iI5OOWlVZKTW4tyjh5bkJnqa\nofgRkO4lDbE+tNtcDV3PF2HWLLh5E555Jt1zcuQJZsSCt5i0ZjSx0TEMfnwsn/WdTfjdCIdeni3t\nGYiPjYmLfPClBa9my6VnRNZVsFQBAK6dszhHnxCoqhoHDADWAceApaqqHlEU5UNFUTp4LDAL/x/e\nd2ZCe3QlbJ+RtN1sJFRJ//8gIYQQ3s+hLsfCTn5+WgLYo4enI7HPtWtaN+DodCa2NJngrbfgmNZi\nWpmmPEYb9rOWGAszA/vgS15Dcdp3+Qu6BKc5bkudNjWYe2ga332wlGXTV7Pz1z30m/Yyzbs1QnHB\nlwIlqU5TerKNRRZnOtbjQzD56MwYp9cthCOCcwcRmDOAa+euezoU4cVUVV0DrEm1b6yVss3cEROG\ntDODh0U7KaG9dwlWJptmv1wraDrcOdcWQgjhUdJCK9L65hv7yl26BPv3A9pSJYP4kea8jAHjw9Za\nH3wxYKQiTZjE3/iT8WT2Af9AI32n9GLWPx9RoHg+JveYwai2E7ly2jVdK/vwFW15C1/88SMQAD0G\nfPGnDHX4iN3ksGu9USHcq2CpAly/kAXW6xYiudwl0+wKMzlhUqiEBFjxRtKMxrlKaF2NdXILJIQQ\n2YG00Iq0Dh5Mv3X2AZ0OTp6EGjUArdXyNWbRlQ/ZyU/c4QoB5KQuz1CQMk4Lr2yNUszYMZFfv1rP\nt+/+QJ+qQ+g6vCPdRnbCz99565vq0NGDj+jEKP7mJ25yASNB1KYDRanktHqEcLaCJfNz5dQ1T4ch\nhMOc0uV41+ykcbOKDjrP09acFUIIkS1IQivSMto5JlRRtJmPUwkmL63o5+SgUtLr9XQa0JbGz9Zj\nztCFLBr/M398t5V+016mYcc6Tu2GHEhOntAm7RYiS8hTKA8H/3TPBGpCuNI9k4PrfN86BX98kLTd\neBAUq+vYNYUQQngV6W8j0urQAYLt6BocEwNNmrg+nnTkK5yHd78fyNRNH2AMMvLBs1MY3W4il05c\nsX2yENlU3kK5Cb8TQUy0g8mAEB52O8KB97CqwurBEJ+4JnPBqvD4SOcEJoQQwmtIQivS6tjRYstr\nCgaDtiZtPu8YQ1q9WRVm75vCG5+9zLG/T9Gn6hDmDltIZJiVNYCFyMbyFMoFwJ1r9zwciRCOuRVh\nzvzJh5fBuT+154oOOn4JPjb+bxNCCJHlSEIr0vLxgRUrIDDQ8nGDAQoX1mZC9iJ6Hz3PvtOeb098\nzpO9Hufnab/xcvm3WTNvI/Hx8Z4OTwi3yVNQS2jvXr/v4UiEcMytzLbQRt+HdaOTtuv1g0LVnBOU\nEEIIryIJrbCscWPYtk3rUmw0Qs6c2sNohBdegH37IG9eT0dpUe4CORky7w1m7ppM4bIF+azvbN6s\nPYL9mw55OjQh3CIodxAAEfciPRyJEI65FZ7JFto/p0BE4tJVwYWg2SjnBSWEEMKryKRQwroaNeDP\nP+H8eTh+XGu5rVNHS2yzgAq1yzB923i2Lt3BvJGLGd7yQxp0qE3fT16kaPnCng5PCJcJyq31roi4\nKwmtyGoUQH24FW6OIzo2HqNBb/8l7l2EXXOStltNAGMO54UohBDCq0gLrbCtZElo0wZatswyyewD\niqLQrGsj/ndsOq9O6s6BzUd4LXQws975H2G3wz0dnhAuEZQrMaGVFlqRDdyOzGC3400TIT7xnCK1\nIWdIZkYAACAASURBVLSz84MSQgjhNSShFY8EX6Mv3UY+w/yTn9OmdwtWzfqdXmUHsOSTlZhNFrq0\nqSrs2AGvvAJPPgk9esCGDZCQ4P7ghciggGBt6S1TuMl6oYQEWL8eunfX3uO9e8POndp7XwgvcjMj\n3Y6vHoCDS5K2n/xQW2JOCCFEtiVdjsUjJXdILgbO7kunt9oyb+Qi5o1cxMpZa3lpXFdavtgUvV4P\nN29C27ZaN+uoqKQb/FWrICQE/vhDa7UWwkvpDdpHe1yslcnQzp3Tktjr1yEiQtunKLB0KVSsCGvX\nQv78bopWiGQUJc2XKtfum6BYLvvO3zyJh12Wy7eFko2cG58QQgivIy204pFUskoxJvw6iqmbPiBP\nwVxM7f0lb9Qczj8rd6E2bgIHD0JkZMobq4gILRFo0ABu3/Zc8ELY4JM43jA+zkJCe/u29h4+dy4p\nmQXtvR4Zqb33mzSB6Gg3RStE+i7fTaenQXJXD8DJ3xM3FGj5vstiEkII4T0koRWPtOrNqjDz78mM\n+XEQ5igz7z4zleFnCnMiNsjyCQkJcPcuzJrl3kCFyACdToeiKJYT2s8/h/v3rXefj42Fy5dhyRLL\nx4VwqbTdg6/cszOh/XNq0vPKHaFAJSfFJIQQwptJQiseeYqi8HiXhsw78hn9C17jfHwgA5QnGEd9\nLhCc9gSzWUsKhPBSqqpqPTcT1NQH4IsvbLe+RkbC1KnplxHCFSyMd7WrhfbGMTi2Kmm76TAnBiWE\nEMKbyRhaIRIZfA10ur+PVsSwTC3HT5RnB0VoyQV6cZQQopIK37unJQVGo+cCFsKKuNg4EhJUfP19\nUx4wmbTWWXucO+f8wITIhCv2JLTbpiU9r9AOCoa6LiAhhBBeRRJaIZIzGAggihc5xtOc4Ucqsooy\nbKYY7TlLd46TGzMJCfG85lMIFT2VaEIHhlKBhigWussJ4W4xJm3JEr/UCa3BYP9M3T7y34PwDja7\nHN+/AkeWJ203HeragIQQQngV6XIsRHItW4JO+7PIRQz9OMh8fudJLrCKMvSiLfOpzKEaBsJ97hHB\nbfawkgm0YjZ9SMA5y/rc5SobmMsqprKdHzEnbx0WwoboqHQS2lq1bF9Ap4PWrV0QmRC2pP1S8L4p\nlrDoWOun7J4HCXHa8xKNoYgd73EhhBDZhiS0wvUSErLO2pbDhqXpRlwAE4PYxzespy5XWaxUZuTJ\ntkRPqogaoUdFxUwU2/mBZUxwqPpI7jOFZ+lPKRYwiO8ZzWz68ioFWMo4VLzn95hAglfFI5I8WH/W\nP9g/7cGRIyEwMP0LGI0wZIgLIhMic87ejLR8ICYK9s5P2q7/hlviEUII4T0koRWucesWfPghFCgA\nej34+motPps3ezqy9NWrB2+/DQEBaQ4VJYJhAbt4rc0f8PhtoseEEla6HdGflkON0mMmilVMIYbM\nLXcSTSRjaMA+1hCLGTNRxBNLNOGYiWQVU5hLP0dfoUPuco3veZdXyEtX9LyAHx/xNMfZ7tG4REp3\nrt0DIE9BC2t3PvssdOxoPakNCICBA6FuXRdGKIQVFiaFAjh1Pdxy+UNLwXRHe56rBFRo66LAhBBC\neCtJaLOb69dh2jTo3x9GjYLdu90fw8mTUKkSTJ4MN29q++LiYP16eOoprYXIm02eDDNnQtGiEBQE\nOXMSG+xHWD5Y8iEs++0eQb9tJ2jHJvQ17hE9rDphZdtg/qIMmHXsZ02mql3NdG5wnjjMFo+bieRP\nFnEaD/ybAhc4yCAq8yufEoF2AxlPLHtZzXhasZxJHokrXaoK27bBiBHa38TMmXDnjqejcrm7iQlt\nbksJraLAd9/B++9DvnwQHAw5c2rv9aJFtVmQJ050c8RCpO/0jYi0O1UV/p6dtF3vddDp3ReUEEII\nryCzfmQXcXEwYAAsWKBtR0dr4+A+/xzKlIFff4USJVwfR2wstGgBt29b7mYcFaXdMFevDi+84Pp4\nMqt3b3jlFdizB65fZ22eb1lcbzkJye6VfOrfIWjdNuL+zIdpbBVMb9fAPDWKbWP3U+vFDvgY7P/z\nSiCB1UwnhvQnP4klml/5lEH8mNlXlilmohjHE0Ry18JRlRiiWM5EilOV2jzt1tisOnoUOnSAa9e0\n952qaq2Pw4drLZATJz4cL53dpNtCC9rrHjYMBg+GXbu0tZVDQrTxtVZayIRwD8vvP4sJ7YUdcPOY\n9tw3CGr0dGFcQgghvFX2vJt71Kgq9OyptbpERyetMZmQoN3IHz0KdepoN/autnIlhIWlP2Y2MhLG\njvX+cbWKov3ennoKU8NQreu0BT5NbxG0eSuBv29DHxLDuteO07vSQNbN30x8XLxdVd3nOtFYuGFL\nRSWB4/yVoZfhDNv50WZXajNRLOUD9wRky9mz0LCh9jMyMum9FhWl/X18/rmW1GZT1y/cxNdoIDhP\nUPoF9Xrt99S+PdSuLcms8Dwr78ETlroc7/8u6XnV58GY00VBCSGE8GaS0GYHu3drLbBRVmbCjY/X\n1k2d4NiERXb5+msItzLWKbn//tO6JmcRDemCD75WjysKGFpdJ+fffzF61QCCcgUwtfeX9K70DusX\nbLGZ2KqoGVjyx/1fBGxgLmY7Eu7LHOUuV90QkQ3Dh2vvQ2tfmkRFae/VM2fcG5ebXDx+haIVCqPL\npi3Q4tHhq9few5fvmrgbGZN0IPo+HFmRtF2zl5sjE0II4S3kbic7+OyzpFZZa2JjYf582+UcdeOG\nfeUMBq1bchZRjCqUogZ6DFbLGPCnifICzZ96nFm7P2bciuEE5AhgyiuzeLXKIDYu3kZ8vOXENich\nGPCzGYeCQhnqZPp1ZFY4t+wq54OBcDz873r7NqxebXu91fh4bUxtNnTp2GWKVyrq6TCEcFj9gkmf\nmf9evpd04PAyiEscohESCoVruDkyIYQQ3kIS2uxg927bN++gNSNevOjaWAoVsq9cbKw2A3IWMowV\n5KUoBoxpjvkSQCmq8yqzAFAUhYYd6vDlno/5YPkw/AJ8+ejFz3m9+lC2Lt2RJrHVo6cNAyxeO3U9\nHRjmvBdlp5zY928VRwzB5HNxNDacOAF+tr8cIDYW/v7b9fG4WXSUmesXblG8YhFPhyJEJqTsqVIv\n2UfPgUvJEtp9ybob13hRussLIcQjTBLa7MDK2M40VNX+spn1+uvarKm2lCgBZcu6NhZnUVXYvJmc\nnfows5KBWTVz0+WTAHLdNqDHh/yUpBdT+ICt+JFy3U9FUWjUqS5f7f2EMUsGo6oqE7p9Rt9qQ9j0\nw18pEtunGUIuClptBfYlgJq0pwINXfpyLWnFGxixMR4TKMlj5KagGyJKh15v//jsbNgl98y/51FV\nldLV3DAJnBAuVqFg0ufOw4T2+hH4b5/2XO8L1bp4IDIhhBDeIvvdzT2KWrTQuvDa4uvr+pmO27eH\nPHnSTxQCAmD8eNfG4SxhYdC4MTz9NKxcie74SXLvv8pzH6jMLebDghULmMVZWvMmhnTG2Op0Oh5/\nvgFzD37K6O8HotPpmNxjBn1CB/PHoj+Jj4snkFxMZhcVaIAB/4eJrS8BGDDSnFd4h8UZGGvrPA14\nHj8CsTYDKWhxduVD9wVlTZUq2qzfthiN0KaN6+NxsyPbjwNQuUF5D0ciRCakammtEJKU0O67eI/4\nBDVl62zFpyAgj7uiE0II4YUkoc0OBg4EHxtLxBiN2rI+tso5yscHtmzRlgDxT9laiaJoyeyoUdC5\ns2vjcAZV1RL0vXu1mXKTUUwmFJMJvx59UHbstPuSer2e5t0aMefAVN5bOhgfXx8+7jWTPlUHs+mH\nvwiKz8s4tjKVf+nGeDoxkl5MZQ6XeY0v0HtopS1fjIxjC8HkxTd1KzQ6fAmgO5OoTiuPxJdCUJA2\n67c9X/L07ev6eNzsyI4TFC5bkNwhVpbsESILKZrLSIFgbQjBfVMsRy7egIPJli2r+aKHIhNCCOEt\nJKHNDipUgKFDtWTREj8/KFUKRoxwTzwlS8KxY9o6n8WLa4lFYCA8+yxs2gRjxrgnDkft2AH794PZ\nbL1MVJQ2o24G6XQ6mj7XgNn7pzD256H4+PowuccM+lYbwuYftxMSX4ZOjKAHk2nNGwST14EX4hxF\nqMgMTvA875OHIugxYCSIRnRjAn/Rnnc8HWKSyZO18dzWktqAAJgyBQp6uHu0k6mqytEdJ6jSqIKn\nQxEik5Q0W43LJo3Lv7prGZgS18POWRxKNXNfaEIIIbySJLTZxYcfwiefQK5c2hhWf3+tpcrPDzp2\n1Ca/CQx0Xzw5c8KgQXDhAsTEQEQE/Pwz1KvnvhgcNXOm9aWQktu7Fy5fzlQVOp2OJs/WY/b+KYxZ\nMhhFUZjUfTqvVRnE+gVbiIu1o+usGwWTh06MYA6X+ZEYviOcd1hMKbxshtE8eWDPHnjySa13QlCQ\n9jcRHKxNRjZnjtZjIZs58+957t0Mo1rTKp4ORQgnUWlSPimhLXjmp6RDNXpky3HwQgghMsYz/ReF\na/Tvr3Wh3LBBm804MFAbI5g/v6cjy5pOnrRvciE/P+33XTTzy6Q8GGPbpHM9tv/yD4snLmPKK7P4\nbtxSuo18hlYvN8Pga0cXWpEkf35t+Z4rV+CPP8BkgjJltDHnrp4czUN2rtqDoijUa1/T06EI4Rxq\nAo0SW2iLcJOq5v2JjbgKPNbDo6EJIYTwDpLQZjcGA7Rr5+kosgd7ZmsGbckkJ7V+63Q6mnSuT+Nn\n67Fr9T4WT/iZ6f3m8sPkX+g++llavdwMH4P82WZIkSLw0kuejsLlVFVly9LthDapSO4COT0djhCZ\nk3r5HVWlQLCROiVz0/DSMnRK4peMZZpDrmLuj08IIYTXkb46QljTvbt9iaqfH4SGOrVqRVGo/1Qt\nPt85iYmrR5M7JCefvT6HVyq8zW9zNhBjjnVqfSLrO3vwAhePXaF5t8aeDkUIB6RKaMOuAPB01RC6\n+GxJ2l9DJoMSQgihkYRWCGt62DE+KyAAhgxxWRdWRVGo27bGw8Q2V4GczHhjLr3K9Ofnab9iiox2\nSb0i61k9ZwMGPwNNn6vv6VCEcJ41wwDoEHycIsptAG6rwVwo0MyDQQkhhPAmktAKYU1QEKxcqSWt\nqbvBgba/cWNthmkXS57Yfrz+PYqWL8ycoQvpWfJNvp+0nMgwOyavEtlWxL1INizcSosXGpMzXw5P\nhyOE8yS20OY69sPDXcvim7Lwn2ueikgIIYSXkYRWiPQ0b64t39Ounda1OEcOrRtyoUIwfrw26ZCr\n1/ZNRlEUarasxtRNHzD9rwlUqFuWb8f8wIul3mTR+J+JuBdp+yIi21n37Waio8x0equtp0MRwkEW\nJuK7fwVOrH24uSS+GUv3XCLC7F2zwAshhPAMSWiFsKV6dfjtN2223D//TFqmZ/BgtyazqVVpWIFJ\nq0fzxT8fEdqkEgveX0LPUm8yf+yP3L8V5rG4hHvFx8ezctbvhDauSNkapTwdjhCOsTSz/N9fQoKW\nvB7QVeGMWoTw6Djmbz/n5uCEEEJ4I4cSWkVR8iiKskFRlFOJP3NbKRevKMq/iY9VyfaXUhRll6Io\npxVFWaIoiq8j8QjhUnnzaslthQpetfZhhdpl+HDFCL7a+wmPtQhl8YRl9Cz5Jl8O/Jabl297Ojzh\nYpsW/8XVs9fpPOgpT4cihBNYSGj/mfvwaVjNNx4+n/PnWe5FxbgjKCGEEF7M0bvykcBGVVXLARsT\nty0xqar6WOKjQ7L9HwOfqapaFrgLvOpgPEI8ssrWKMUHy4Yx7/A0mjxXn5WzfqdXmf5M6zObS2eu\nsIdfmUAbBlKZ0dRnA3MwEeHpsIUD4mLjWDhuKWVrlKJRp7qeDkcIx1lqoY1PTFoLVKZBmxconU+b\nfT48Oo7pf5xyY3BCCCG8kaMJbUdgQeLzBUAne09UFEUBWgA/Z+Z8IYRlJSoXY/j8ASw4NZO2r7Xk\nj0Vb6V3hHcb1msy+Yzu4wjFOsYsFDKEfRTnBTk+H7FWucYZdLOcfVnCH/zwdTrp+m72Ba+du8PKH\nXVEsTVyW2p078OuvsGwZHDrk+gCFyDALCe0DrSfh4+PDkFYVHu5asPM8+y7edX1YQgghvJajCW2I\nqqpXE59fA0KslDMqirJHUZS/FUV5kLTmBe6pqvpgVofLQBEH4xFCJCpYsgBvzHqR4mf3Yxx4mujl\nIYSHtiKyS33i9ubCTCRR3GcCrbjKaU+H63HnOcC7NGIwocziFb7gJQZQhom05QbnPR1eGndv3GfB\n+0uo2bIqddvVTL/wnTvauspFikDPntC7N9Svr62fvHmzewIWwh5qguX9zd+FMs0BaFe1II+Xz68V\nV2HI0gOER8va3EII8aiymdAqivKHoiiHLTw6Ji+nqqqK9a9WS6iqWhvoDkxXFKVMRgNVFKVvYlK8\n5+bNmxk9XYhH0t8sI7LQFYxTD5Dj/Br8Rh4ndn0IEXVaEvFkE2L/KIBZNfELkzwdqkedZjfv0YiT\n7CCWaEyEYSKMWKI5yAZGUIvreM8ENKqq8vmbX2OOMvPm9FfSb529cwdq1dJaZaOjISxMe0RFwZEj\n0L49rFpl/Xwh3Cl1QtvjZ3hjJzw+/OEuRVGY+EwoAb7a+t/nbkUy7KeDqJa6KwshhMj2bCa0qqq2\nVFU11MJjJXBdUZRCAIk/b1i5xpXEn2eBLUAN4DaQS1GUB9PEFgWupBPHXFVVa6uqWjt//vwZeIlC\nPLpW8xnRieNkdfli8J94hJwXV2P8+CDxR3MQ2aopYXWasfGnLUTHmzwcrWtc5xzrmc1qprObVcSR\nsiVHRWUqzxKN5SWPEognknt8Tk+nxhXJfbbyHb/xGVtZSCT37D5384/b+Wv5LnqN60qJysXSLzxo\nEPz3H8RYmTzHZNJabyNlySfhBVInpeWehJDKaYoVzR3AR52rPdz+/cg1Jqw+JkmtEEI8ghztcrwK\neCnx+UvAytQFFEXJrSiKX+LzfEAj4Ghii+5m4Ln0zhdCZN5NLqbZp+SIwzjsJDnOrsV/7h7UcB/C\nutaib5Uh/P7tZmJjskfXvbtcZRwtGERlFjCYRYzgc3ryGgX4g68fljvMJpvJpEoC59jHVRyfgCaW\nGL7mTfpQkHm8ySJGMo/+9KEQX/MmsaQ/a+vtq3f5YsA8KtUvx/NDn06/svv3YelS68lsct9/n4FX\nIYSr2J+QdqhemJcblny4/c1f5/h0/UlJaoUQ4hHjaEL7EfCkoiingJaJ2yiKUltRlHmJZSoBexRF\nOYCWwH6kqurRxGMjgMGKopxGG1P7jYPxCCGS8cVo9Zjil4Dfa+cJPrqOoKX/4B9o5NNXv+Slcm/x\n87RfiQyLcmOkznWfm4ygFkfZRizRxGAijhiiCSeSe8xnIKuYCsBBNjxsxU6PDh1H2OJQXPHE8zEd\n2MJ8YokmmgjiiSGaCGKJZgvz+ZiniSfe8vnx8Uzr8xVmUwzDvu2PXq9Pv8Ldu8HXjtXQIiOl27Hw\nDhlMRse0r0Tb0IIPt7/YfJoRyw4SG29lLK4QQohsx6GEVlXV26qqPqGqarnErsl3EvfvUVX1tcTn\nO1RVraqqavXEn98kO/+sqqp1VVUtq6rq86qqmh17OUKI5BrQBR/ST2gUPZR5Ljez93zKpDWjKViq\nAHOGLqR78X7MGbqQG5duuSla51nMSMK4RQJxFo+bieJH3uMO/9lsEX1ARSXOzrLW/MMvnOAvYrDc\nvTsGE8fZzi6WWTz+9bDv+GfNfl6f+hLFKtgxh15sLNgz+zGAWT5+hTfIWELro9cxo1sNmldIGoq0\ndM9lus39m0t3su6XckIIIeznaAutEMKLtWUAOtJvxfMjkGcZjaIo1GlTg2lbPuSLXZOp264my2es\n5sXS/ZnUYzqn93vPpEjpMRHOdn4gHltdp1XWM5sSVMWPQJvX1aGnKGnH8mXECj62Olb3ATORrOST\ntOfOXMuy6avp9FZbOrzZOv2KYmO1cbMFCmgTQdni66tNHCWEx9n5BUwyvj465vaqzXO1ij7ct/fC\nXdrN2MYP/1wkIUG6IAshRHYmCa0Q2Vh+StCXOfjib/G4HwE05gUa8HyK/RXqlOXd7wey8PQXPPN2\nO/7+dS9v1BrOiNbj2bvhgFePUbvEEZut0gCxmDnEHzSgC/a0CvmTg8o87lBsF/jXrnLnOZBie8eq\n3Xw16FsadapDv2kvWTkLLYl96y3InRvKloWGDe0LTKeDfv3sKyuEK+Urn6nTDHodU56rxog2FdHr\ntKQ43BzHqOWHeObL7fxz7o4zoxRCCOFFJKEVIpt7nBcZzVoq0AgDfviTA18CKEApXuULXmcuipVW\nkZAS+en36Ut8f3E2r07uwflDFxnZegL9ag5j7TcbMZtc3001gQT2s5YZ9GAibZlH/zQJX3Iq9o+d\nU0nASCDdmYwvAVbL+RJAH75C5+BHpmp3d0r1YdnD248zufsMytUqzchF71gfN3v8OFStCnPmaGNi\nTSZtMihbXYkDAuDVV6FECftfiBCuYm8XeYunKrzRrAw/9WtA8TxJf88HLt+ny5yddJ2zk79O3fLq\nL+SEEEJknJIVP9hr166t7tmzx9NhCJHl3OUq97iGPzkIobTVRNaaGHMsGxf9yfIZqzl/+BLBeYJo\n++oTdHizNSElnL+c1hWOM4HWRHAnafkh9PjgSwUaMoxf8Cc4xTkR3KUvhYkl/a62PvjShrd4KXFy\nqFVM5UfeQ0F5OMb1QVfkN5hHI7o5/HoGEcpljtgsV5TKfMYRdq3ey/gu08hfLC/Ttn5I7pBclk+I\nj4dSpeDy5fQn1fH1TZrx2M9P+9m3L0yfrrXSPsIURdmbuF66yCSn/N88qx7cPJ60/cH9TF3GFBPP\nV1tOM/vPs8TEpfySq3S+QLrVLcazNYuSL8jPkWiFEEK4kL3/N0tCK4TIMFVVObj1KCu+WMuOFf8A\n0KBjHToNaEv1ZlVQHGhleeAO/zGEqkRy12LLpgE/SvIY49mOPtU44c/oxk5+Sre11oCR6RyjACUf\n7gvnDluYz0l2oKCnGi1pTHeMdoyxtcdWFvI1b2JOZxytH4H04UvMC4rz6WtfUeaxkkxcPZrcBXJa\nv/Dq1fDCCxAenn4AAQHQoYPWavvYY1rLbBE7Jpd6BEhC6zhvSmgfuHQnipmbTrF83xXiUo2l1SlQ\nt1Qe2lUtROsqBQnJYX1WeCGEEO4nCa0Q3iIhATZuhM8/h7NnISgIevaEl16CHDncH4+qwq5dWqvc\n4cNaS90zz2gtdQUKZPhyNy7e5Nev1rNm3kbCbodTMrQYnQa0pUWPJvgHZuAG8dQp7Xf0558AHGmq\n8vXbx7hSzvJMxQBGghjIj9SifYr9N7nIMB4jivsWk1o/AmnNm7xoYfIlV4olhvdozEUOWWxBNmCk\nmBpK9Skj+Xbkj9RsWZX3lw0jINjyGOiHunWDJUtsB5Ajh7Y8z+OOjQXOjiShdZw3JrQPXLoTxbxt\nZ1m+7wrhZsufKeVDgmhUNh+Ny+ajbqk8BBsNTqlbCCFE5khCK4Q3uHMHnnwSTp6EiGRrnQYGal08\nV6yAFi3cF4/JBJ07a0mjyaQl2wBGozZ2be5cLdnOBLPJzOYftrPii7Wc+fc8QbkCafliU9r1aUmp\n0OLWT1RVGDECvvgC4uK0GXqBWAMk+MDat2DxR1id/LQKzfiAzWn2X+UUn9CJm1wgBhMqCfgRiEoC\nnRjBc4zNcJdrZzARwRf0Yj9rUIE4zPjgi4JCaHhbdO80Y+P8v2jWrRHD5/fH4GvHTXWrVrBhg+1y\nOXPCd9/B0087/DqyG0loHeeU/5u/qAu3TiRtOymhfSAqJo7fDl7lpz2X2HPhrtUe+ooCZfMHUb1Y\nLqoXy0WNYrkoFxKEn4+NtZ+FEEI4jSS0QnhafLy2FMqxY0njFlMLCICdO6FaNffE1KkTrF+vJbOW\n+PvDL79AaxvLwqRDVVWObD/Oyi/XsX35LmJj4qhYtyxteregWbdGBOZINfnSpEnaI9JyN9zoAFg2\nBlaMslxfTkKYxzWr8ZxmN/tZg5koClGOhnRNM+7WE25ykb/5ibtcIxch5N9Vj9k9l3Dt3A26v9uZ\nF99/Hp2941r79YN587T3XHqCgmDrVqhZ0/EXkM1IQuu4rJDQJncjLJp1R66x9vA1dp+/Q2x8+vdD\nep1CybwBVCgYTLkCwYk/gyiWJwCjQRJdIYRwNklohfC0NWuga9eULbOpKYrWWrZypevjOXIE6tSx\nnsw+EBoKhw45pcr7t8LYuGgba7/ZyPkjlzAG+NHk+fq0eaUFVZtUQjGZIH9+iIpK9zrRgfDqDYix\nMBFxXooym0uZDzIuTvv9f/qp1pJuMEDbtjB4sPa7cLG42DiWfLySheOWkq9IHkZ+9zZVm1TK2EX2\n7YMmTWz+HilZUuv27oQxztmNJLSOy2oJbXJRMXHsPn+XHadvsf3MLY5dDSfezvVrFQUK5jBSPE8A\nxfMEUCJvAMXzBlIstz+Fc/mTL8jv4VJCQggh7Gfv/80+7ghGiEfSjBnpJ7Ogdbddtw7u3YNcVmaw\ndZbZsx92503X2bNw9ChUrsw9rrOP1ZgIIw9FqMlT+FlZ09aSnPly8OzA9jzzTjuO/3Oa37/ZyJYl\nO9iwYCuFyxak1WO5eJIACpB+IqYqUPcX+KtHyv16fP7f3p2HyVWV+x7/vl3V1WOmTmJISEiIJEAA\nhRhREQyEgJHjYVCUwEVQOXBUOKI8XAXhcLkc4CKXK8d7RBQEAQdAUR6iwkHGg1xIIChTEjKQIJnI\n3AmdnmpY94+1K727UtVVne6uofv3eZ56atfaa1e9vXpX7Xprrb02MzPOn+2V5mY/5Hvlyu7/q/vu\ngwcegH/9V7gyR9dwP1j64nL+/Wt3sOaNdznh7E/yzdsupHHkPkxANXMmHH207+3PdZme+nq46SYl\nsyJZ1MeizJ4+ltnT/WztrZ0JlmzYxavvNvPq2mZeX9/M2u3Zfwx0DjbubGfjznYWZbnebaTKSu9f\nwQAAHsRJREFUGDeshv1G1DJ+RF1wX8t+I2oZ21jDmGE1jGmoYXhdtF8m1BMRGWqU0IoMlLffLqxe\nLAYbNgx8QvvWW743Mp/qajrWLOG2GdeymD9QRYQkCaLEAMepfIczubpX55+aGYd+bBqHfmwaX7v1\nyzz/+0U8/vNnuOehJdzLbA5nK8ezluNYzyj2TshqWuEDa/Z+3gjV/APfKjiOvfzjP/qe68wh4cmk\n78m+/np/fdZzztn318hi28Yd3HP1/Tx+z7OM2b+J//nwdzjmtI/27UkfeQROPNH/n8PJeTTqe52v\nvdaPGBCRvOpjUT46pYmPTmnaU7a7I8GqzS2s2PQ+Kza9z/JNLaze0sKG5jZ66sxNphwbdrazYWc7\n0JyzXnXEGN1Qw5hhMX/fWMOYxhhjGmsY3RijqSHGyPoYI+uqGVUfY1htlCr1/IqIKKEVGTD1WcbH\nZpNIFF63L4YVdt6ocynuavgui9lAPJRcJoLlR7iJZjZyIT/epzDqGmo56UuzOelLs9l41Y08efP9\nPJuYwH/YTG5zR3EYWzmO9RzLesYG14NNVkNHRsdljHq+yLXszyH7FAeLF/uhurnObwY/hPd73/OX\nxOmHnpNNf9/Cgzc/wn/e/TQuleLz3/4sX/ofX8g/i3Ehhg+HhQv9UPdbboHly30i+9nPwqWXwiH7\n2E4iRVW+p0E11ET3TBIV1plIsaG5jb9vb+Xdbbv5+7ZW/r69lfU72ti0q51tu3v4jAmJJx3v7Wrn\nvV09X0M7zQxGBMntiLpqRtbvvTyyvprhddUMr40yrLaaYcF9Qyyi3mARGTSU0IoMlPnzYdWq/Oes\njhvnewEH2llnwZNP5r1WaSLVwaKPb+yWzIZ10Mqz3MscvsoH6dsph+PP+zxfuvV6zk28yTtuOH9h\nIn9hf35sR/JjjmS6284n2MgsNrDklAT1REiRopHRnMtNfJL5+/7id94J7QV8cdy2zSe+H/nIPr/U\n26+9w+/+/Y88/avnMYOTzz+e+Vecwfip4/b5ObOKRHyvs2YxFimaWLSKKWMamDKmARi71/r2eJLN\nuzrYuLON93b5ocnv7Wxn4842trzfwbbdnWx9v4PdnXkmdcvgHDS3xmluLeBUkgxVBo01XUnu8D3J\nbvfEN12WXt9QE6Wxxt/XxyLURKuUGItIySmhFRkoF14IN9zQc52GBrjiiuKc13jGGXDxxT1WcXV1\nPP3P0FrbcxIep50/8AO+xa/7FtPBB8NRR2EvvcSBiV0cyFLOYynrXCPPsz8vMoH7bAb3dh7GqE83\nMm3eeGZ+5gjmzTmNhmF97NVes6brskU9iURg48ZeP31HWwfP/XYhf/zpn1n64gpq6mKc+o1P84XL\nT2XsxNH7ELDIEPDBObB1hV/er0izvw+w2uoIB4yu54DRPX9mtXUm2drSleBu293B1pZOtrb4++bW\nTna0dtLcGmdnazzn9XQLkXKwqz3BrvZ9fw6AaJVRH4vQWBOlPkh0G2KR7vc1URpiURpqwo8je5XX\nxyLUVUeIRgqc3V1EJKCEVmSgjB0L99/ve2qz9dLW18O8eT7xLYZYDP70J5g7118iJ3OG87o6kh86\nlF9fvyTvUzlSLOO5/onrt7+FWbNg69Y9k1ZNpIX5LGd+9Wq2jxrPou/8gIXPv83ffv0GL92xkjuj\njzDtI1M54thDOOyThzDjE9MZNa6X5yA3NeWvA76dRowoqGrzlp28/NirLHr0FV7+z1dp3dXGpIMn\n8PUffJm5532K4U2lv1yQSFmbczVsWgLtO+EL95Q6mqKqi0WY1FTPpKbCfqyLJ1PsbPM9tDvbfKK7\nozVOc2snO9viXclvW5z32xO8356+T9AW711vcC6JlOuXxDgsFqmitrqK+liUuiDJrYtFqI9FqK2O\n7El80+u6yqPUxaqoq47uqZ+tnnqVRQYfXbZHZKAtXOjPw3zhBaip8RMOjRzpZ8/9+teh0GuN9pdl\ny+Cqq+Cxx3ySm0r5uC69lO3fOZd/qTmMTvIMkwZGMYE7WN8/MW3eDNdcA7/4hZ/ECPy5xeedB9dd\n538cAOKdcZa+sIJXnniN1/5rKSsXv02803+RGjd5LAfNPJBpR03loKOmMPmwSXzggDG5r+VayGWV\nwP+vNm/256OGOOfYsnYrS15YwdIXlrPkxeWs+usanHM07TeSoz9zFHP+23EcecLh+vJUAXTZnr7T\nsblyxJMpWoLkdld7ZsIbzyjvWm7tTLC7I8nuzgS7OxJ5r91bjqqMINH1CXBttCvRra2OUFtdRU11\nJCjvKquNRqhJPw4vV0eoDbatqe56vvS2SqBF9p2uQysCsHatn0F4xAg/vLWUB5VNm2DdOmhshOnT\nS3/5lO3b4Z13fDJ78MEQjZIkwQWMZXcPM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_regularization_example(X, Y)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Regularyzacja\n", "\n", "* Metoda zapobiegania zjawisku nadmiernego dopasowania (*overfitting*)\n", "* „Kara” za ekstremalne wartości parametrów $\\theta$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Regularyzacja dla regresji liniowej – funkcja kosztu\n", "\n", "$$\n", "J(\\theta) \\, = \\, \\dfrac{1}{2m} \\left( \\displaystyle\\sum_{i=1}^{m} h_\\theta(x^{(i)}) - y^{(i)} \\color{red}{ + \\lambda \\displaystyle\\sum_{j=1}^{n} \\theta^2_j } \\right)\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "* $\\lambda$ – parametr regularyzacji\n", "* jeżeli $\\lambda$ jest zbyt mały, skutkuje to nadmiernym dopasowaniem\n", "* jeżeli $\\lambda$ jest zbyt duży, skutkuje to niedostatecznym dopasowaniem" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Regularyzacja dla regresji liniowej – gradient\n", "\n", "$$\\small\n", "\\begin{array}{llll}\n", "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_0} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_0 & \\textrm{dla $j = 0$ }\\\\\n", "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_j} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_j \\color{red}{+ \\dfrac{\\lambda}{m}\\theta_j} & \\textrm{dla $j = 1, 2, \\ldots, n $} \\\\\n", "\\end{array} \n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Regularyzacja dla regresji logistycznej – funkcja kosztu\n", "\n", "$$\n", "\\begin{array}{rtl}\n", "J(\\theta) & = & -\\dfrac{1}{m} \\left( \\displaystyle\\sum_{i=1}^{m} y^{(i)} \\log h_\\theta(x^{(i)}) + \\left( 1-y^{(i)} \\right) \\log \\left( 1-h_\\theta(x^{(i)}) \\right) \\right) \\\\\n", "& & \\color{red}{ + \\dfrac{\\lambda}{2m} \\displaystyle\\sum_{j=1}^{n} \\theta^2_j } \\\\\n", "\\end{array}\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Regularyzacja dla regresji logistycznej – gradient\n", "\n", "$$\\small\n", "\\begin{array}{llll}\n", "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_0} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_0 & \\textrm{dla $j = 0$ }\\\\\n", "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_j} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_j \\color{red}{+ \\dfrac{\\lambda}{m}\\theta_j} & \\textrm{dla $j = 1, 2, \\ldots, n $} \\\\\n", "\\end{array} \n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "### Implementacja metody regularyzacji" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "def J_(h,theta,X,y,lamb=0):\n", " m = float(len(y))\n", " f = h(theta, X, eps=10**-7)\n", " j = 1.0/m \\\n", " * -np.sum(np.multiply(y, np.log(f)) + \n", " np.multiply(1 - y, np.log(1 - f)), axis=0) \\\n", " + lamb/(2*m) * np.sum(np.power(theta[1:] ,2))\n", " return j\n", "\n", "def dJ_(h,theta,X,y,lamb=0):\n", " m = float(y.shape[0])\n", " g = 1.0/y.shape[0]*(X.T*(h(theta,X)-y))\n", " g[1:] += lamb/m * theta[1:]\n", " return g" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "slider_lambda = widgets.FloatSlider(min=0.0, max=0.5, step=0.005, value=0.01, description=r'$\\lambda$', width=300)\n", "\n", "def slide_regularization_example_2(lamb):\n", " draw_regularization_example(X, Y, lamb=lamb)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "0738c69d0fff4e32ab23d4aa93ca9a71", "version_major": 2, "version_minor": 0 }, "text/html": [ "

Failed to display Jupyter Widget of type interactive.

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\n", " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", " that the widgets JavaScript is still loading. If this message persists, it\n", " likely means that the widgets JavaScript library is either not installed or\n", " not enabled. See the Jupyter\n", " Widgets Documentation for setup instructions.\n", "

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\n", " If you're reading this message in another notebook frontend (for example, a static\n", " rendering on GitHub or NBViewer),\n", " it may mean that your frontend doesn't currently support widgets.\n", "

\n" ], "text/plain": [ "interactive(children=(FloatSlider(value=0.01, description=u'$\\\\lambda$', max=0.5, step=0.005), Button(description=u'Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "widgets.interact_manual(slide_regularization_example_2, lamb=slider_lambda)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def cost_lambda_fun(lamb):\n", " theta = np.matrix(np.zeros(X.shape[1])).reshape(X.shape[1],1)\n", " thetaBest, err = SGD(h, J, dJ, theta, X, Y, alpha=1, adaGrad=True, maxEpochs=2500, batchSize=100, \n", " logError=True, validate=0.25, valStep=1, lamb=lamb)\n", " return err[1][-1], err[3][-1]\n", "\n", "def plot_cost_lambda():\n", " plt.figure(figsize=(16,8))\n", " ax = plt.subplot(111)\n", " Lambda = np.arange(0.0, 1.0, 0.01)\n", " Costs = [cost_lambda_fun(lamb) for lamb in Lambda]\n", " CostTrain = [cost[0] for cost in Costs]\n", " CostCV = [cost[1] for cost in Costs]\n", " plt.plot(Lambda, CostTrain, lw=3, label='training error')\n", " plt.plot(Lambda, CostCV, lw=3, label='validation error')\n", " ax.set_xlabel(r'$\\lambda$')\n", " ax.set_ylabel(u'cost')\n", " plt.legend()\n", " plt.ylim(0.2,0.8)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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a9QfDsUB1voZiYZoYqam8QVJRTmYsTEsLslWWEKpOrDrrZQXZzJ4CmHOIWQAA\nAFcoHFFHf1AtbpC29A65y3ikRtcHR8IpGYM/NzMWo2UF2W6oulGaH98O5GVz114A8xoxCwAA5rxB\ndxa1pXdILb3DaukZSgjWeKCm6jTfAl+GyqIzp+6yLGEZDdeSPB4rAwATRcwCAABPstaqdziklp74\nDGpzz5C7HQ/X1p5h9abgUTPZGWlOkCbGacJ2aUG2yt1Q5RRfAEg+YhYAAMwq8UgdUrMbqs09w2rp\nGVZz71BsVrWlJzWn+gbyskaFaXmBb1Sklhc66wXZ3CQJAGYSMQsAAKbNQDCkk92JkTrkRmp0VtX5\nXrIjNTPdOLOnhT6VuzOm0UgtL4gHaml+Ns9ABQCPIGYBAMA5C4YisTht7hkes4xHa7JP983OSFNF\nNFALnUCNLRP2FedkKi2NWVQAmEuIWQAAcFrWWnUNjOhkz5BO9gypudtduqF6sntILb1DausLJvVz\nczLTVTEmTisKnTitcPeVFfhU6ONUXwCYr4hZAADmqcTZ1JPdwzrRPeis9wwnROuQhkORpH1mVnqa\nyguzVVnoc2ZUC7NVUeiEqhOpzno+16MCAM6CmAUAYA6KXpt6sntIJ9wwja8P6mT3sNr7h2WT9Bia\nNCOV5merssin8gKfKoucOK0o9KmiKB6rxbmZRCoAICmIWQAAPKZvOKQTXYNOmCYEauJ29+BI0j4v\nPztDFYVOqFYU+lRZ6IutR7dL87OUwY2TAADTiJgFAGAWSQzVE93usmtIJ3qGdKJrUCe7h5J2EyXj\nzqZWjYnUxFitLPIpP5tfFwAAsw//dwIAYJoMjYTV5IZqU0KwNnW54dqVvFDNTDeqKPSpqsinyqIc\nVRZmq7IoJxauVUXOY2l4DA0AwKuIWQAAkiAUjqi5d1gnugbVGA3VrkE1dkWDdVCdA8k59Tc7I82N\nVJ+q3ECNR6tPVcU+leRm8SgaAMCcRswCAHAW1lr1DIbU2OVEaVP3oLvuBGtT16BO9gwpkoSbKWVl\npGmBG6oLinKcYC3OUZUbqVVFOfJzEyUAAIhZAACis6qNnU6YNnYNxsO1a1CNnYPqD4bP+XMy0pxT\nfxe4UVpV7ARrVZFPC4qdZUleFqEKAMAEELMAgDlvMBiOBeqoYO10lid7hhROwrRqaX62FkQDtdin\n6uKcWLRWF+eoND9b6Zz6CwBAUhCzAADP6x0aUUOnE6cNnQOjwrWhc1Dt/cFz/oyczHQtKPap2p+r\nBe5MqvMVPx3Yl5mehJ8GAABMBDELAJj1ugdH1NA5oAY3TqPR2uDOrCbjmaql+dmq9ueoJhqoxTmq\ndoO1ujhHxVynCgDArELMAgA+37aIAAAgAElEQVRmXHRm9XhHPFijsXq8c0C9Q+f2uJqMNBM71be6\nOFfV/hxVF/ti61XMqgIA4DnELAAg5YZGwrEwbegY0HE3Vo93OPu6zvGRNVkZaarxOzOoNf7c2Hq1\nP0c1/hyVF/i4VhUAML+FgtJgp/Nl0qSyFTM9onNGzAIAzlk4YnWyZ0jHOwZ0rCMerNHtlt7hc3p/\nX2aaavy5qi7OUW2JM7ta44ZqtT9HpXnZPFMVADA/hEPSUJcTpQMdbqB2nGG7y9kO9sXfo+5q6a7n\nZ+5nSBJiFgAwIT1DIzrWPqDjHQM63ulE6rGO6KnBAxoJT/1uwFkZaaopzlFNiROptf54rNb4c1Wa\nz+NqAABzjLXScO+pITrQ4exLDNPovsFOaaj73D97sOPc32MWIGYBAJLis6vH2gd0rKNfxzoGdNSN\n16Md53YqcJqRqopytLAkV7UlTqDWljjRWluSq7J8ZlYBAB4WHhknRMcuxwnVyLnfwHDCTJqU43e+\nihdN3+emEDELAPPI0EjYidN2J1CPtfe7S+dmS8FwZMrvHcjLUm2JE6e1/mi45qrWn6uqYp8y09OS\n+JMAAJAiI4NObA60x8NzoN2N0fZxQrVTGk7CbOmEGclXJOWWuHHqLmPb7r5c/+jvZxdKaXPr/8XE\nLADMMb1DI06stg/oSHu/jrb3x7ZP9gxN+X2zM9JUW5Krhe5XjRusCwNOsOZl878UAMAsYq00MhCP\n0bFBGotV93sD7vdCg9M3xszchBiNRmhJwnKcfb4iKY078EvELAB4UvfAiA67oXqkbcBZutHa3h+c\n8vsG8rK0MODE6iJ3ZnVRIE+LApwKDACYYSODo0P0lPX2U2dTQ1P/Q9zJMQmzo+ME6en2Z+ZM0/jm\nJmIWAGaproGgDrc5kRoN1sPtznKq16+mGanan6NFJXlaGHCCdVEgVwvd7XxmVwEA0yE8MiZE204f\np9F9IwPTM7a0TCc2cwPx8EyM0MT9zJbOKH5rAYAZ1Dcc0pG2fh1q69cR9+twu7PsnGKwZqWnqbYk\nR4sDeVoUyNPiUnemNZCn6uIcZWXMretlAAAzzFrnDrtjI7Q/MVDbRn8vGXfknYj0bCc+ozOheaVu\ngAZOH6zZBRJ30PcEYhYAUmw4FNax9oFYsB524/VwW79ap/j81eyMNDdWc1VX6syq1gXytKg0T5WF\nPqVzOjAAYKrCIwkx6kZo/5gZ1P620ZEaCaV+XGmZTozG4jQapYHRcZqbsD8zlzCdw4hZAEiCSMTq\nRM+QDrf263Bbnw62RqO1T42dg4pM4RGs0WBdXJqrxaV5Tqy62xUFPq5fBQBMzMig1N+aMFOaEKr9\nbWO226fnzrwmbXSM5rkzpLFYHRuoASkrnzDFKMQsAExC33BIh1udSD3Y0qeDbf062NKnI+39GhqZ\n/GNtMtONE6iBPNUlROtid4aVYAUAnCLY78RnYpD2t8ZjdKBtdJyO9Kd+TFn5CWE6NkgDp37PVzzn\nHhOD6UfMAsAYkYjVyZ4hHWx1g7W1Xwdb+3SotX9Kj7YxRqouzlFdaZ6WlOaprjRPdWX5qgvkaUGx\nTxk8fxUA5rfggBuerU58xsJ07La7nvJHxxh3RrR0dJjmlTr7ojOpuYH4dqYvxWMCTkXMApi3hkNh\nHW7r18EWJ1ajX4da+zUQDE/6/fy5mVpSlu9Ea5kTrkvK8rWwJFe+TO5wCADzRijonrrbGj+9N7qe\nOJManV1N9cxp7FrTUjdCS8dsj9mXU8ydeeEJxGyyRCLSoV9I7QelrmPSjX/NOf3ALNEzNKIDLc4s\n6wF3tvVAS5+OdQxM+lrW6GnB0VBdUpanpWV5WlKaL39eVmp+AADAzIpEpKGu0VE6NlIT14e6Ujue\n9Oz4jGleqZRXdmqo5pXFv59dyO+lmJOI2WQxRnrqbinY62xv/KyUXzajQwLmm47+oPY39+pAa5/2\nNzvBur+lV809k79jsD83U8vK87U0Fqz5WlKWr1p/DqcFA8BcEBqOx2df65hIHbN/oC21d+tNy3Ti\nMy+QEKZlbpSWJmy7scqjYwBJxGzyGCMFlkgndjjb7QeIWSAFrLVq7w9qX3Ov9jc7sRoN1/b+4KTe\nyxipxp+jZWX5sXBd6i5LmGUFAG+xVgr2SX0tboi2JERpy6mRmso79po0d1a0bEyMJgRqdDs3IPmK\niFNgCojZZAosGx2ziy6f2fEAHtfeN6z3E6J1X3Of9jf3qnNgZFLvk5WeprrSPCdYy51wXebOuHIt\nKwDMYtY6p+z2tUr9LWNCtSVhf2vqb4yUXTg6Qkd9BaS88vj3c/xccwpMA2I2mQLL4uvtB2ZuHIDH\n9AyNaH9zr94/2ad9zb16/2Sv9rf0qq1vcjOtvsw0LSvP1/LyAneZr+UVBZwaDACzibXSYKcbpc2j\nAzUWqQkzqeHJ/b9gwky6G5/lztl040VqdH9uKXfrBWYhYjaZEmO24+DMjQOYpYZDYR1o6dP7J51g\nfd8N1xPdk3vcTW5WeixaV1Tka3mFs15dnMNzWQFgJlgrDffEgzQWqdF1N1yj0RqZ3Bk2E5bhS4jT\nxEgdsx6bPeUPOgEvI2aTqWRpfL2dmMX8FYlYNXQOau/JHu11w3XvyR4daR9QeBK3D/ZlpmlFRQHR\nCgAzZWRwdIxGI3Xssr9FCk3+OdwTkpXvzpKWJywTg7U8PpPKjZGAeYWYTabAkvh6+0HnNu78iR/m\nuJ6hESdWT/Roj7t8/2Sv+ifxnNbMdKOlZflaUVGg8yoLnGVFgWr8RCsAJF0k7DwDta9Z6m0+Q6Q2\nO7OtqZBV4MRofsWYQC0/NVazclMzBgCeR8wmU47fuaZioE0KD0s9DVLxwpkeFZAUkYjVsY4B7TnR\noz0nerT7RK/2nOhRY9fkbraxsCRX51UWaGWlE67nVRRocWmeMrmmFQDOTXAgHqG9J90oPRkP1Oi+\n/lbJTvwPHCcsM3dMlFaMidMKAhVAUhGzyRZY5sSs5MzOErPwoMFgWHtP9mh3NFybJj/b6s/N1MrK\nQp1XWaD6qgKdV1mo5eX5ysvmPzsAMGHRmyXFAjVhGZtZdSM1FbOoaRkJURqdRa0YHarR9ax8TvEF\nMK34rTLZAkul42856+0HpKXXzux4gLNo7xvW7hM92tXkROvuEz061NqniV7amplutKy8QPXuTOvK\nqkLVVxaorCBbhl9qAGB8kYjzh9+9J+JBGlueHH0KcHg4+Z+f408I0sqEKHX3FVQ6675iLpkCMGsR\ns8kW4CZQmJ2stWrqHtJ7jd3a1ditXU09eq+pW809E/8lKZCXpfqqQtVXFai+qlCrFhRqaVk+pwgD\nQFQk7JzGG43U3hNumJ4YE6styT/VNz1rdKAWVCQE6pjZ1Izs5H42AMwAYjbZeNYsZoFIxOpox4B+\n29itXU3d2tXohGvXwMQehWCMtKQ0T6sWFKm+qkCrqgq1qqqQ2VYA89eomdSTCcuT8e3oqb82ktzP\nzipww7QyvkycPY0uc/yc5gtgXiFmky3x8Tw8axbTIBKxOtLer982duu9xm4nYBt71DscmtDrfZlp\nWlnpzLKucmdbV1YWKDeL/zwAmAei16T2nogHas+J0dEajdTIxP67OmE5/tGBWlB5aqAWVEpZecn9\nXACYI/htNdlKEh7P03lUCgWljKyZGw/mFGudOwrvbOjWzoYu7Wzo1u6miYdrgS9DaxYUafWCQq2p\ndpZ1pXnK4DRhAHNRcGBMpDa5gdo0ejvZ16TmBqSCKjdGq8aP1fwKKdOX3M8FgHmGmE22rFypsMZ5\nLI8NS11HpdLlMz0qeJC1Vid7hrTjeLd+29jlBmy3ugcndqpwIC9La6qLtKa6UGsWFGlNdZFq/Dmc\nJgzA+6LXpfY0OaEaXcYC9YQzuzrcndzPzfG7cVo5JlYr48v8Cv4QGwCmCTGbCoGlTsxKznWzxCwm\noHtwRL9t6NaOhi69c6xLOxq61No7sdmC0nwnXNdWF8WWVUU+whWA90RnU3sa3dN9m8Ys3WhN5s2T\nsgqcEC2sSojScbaZSQWAWSWlMWuMuVnS1yWlS/qetfbLpznuI5KekXSxtXZrKsc0LQJLpcO/dNa5\nozHGEQxFtOdEj3Y0dOnd487Xodb+Cb22ODdTa6uLdH5NsdbWFGldTZEqCwlXALNc9NrUniZ39rQp\nvh6bTW2UhpI4m5qW6cRoYXT2dIEbrQsStiuk7ILkfSYAYNqkLGaNMemSvinpBkkNkrYYY5631u4e\nc1yBpD+V9HaqxjLtuKMxxmjqGtQ7x7r0zrFOvXO8S79t7FYwdPa7XeZlpWtNdZHOry2OBWxtCacK\nA5hlIhH3tN/GhEBtHB2pPU1SaCh5n5lT4kZpVcIMalV8X0GVc+0qz0gFgDkrlTOzl0g6YK09JEnG\nmB9L+pCk3WOO+/8k/Z2k+1M4lulFzM5rQyNh7Wrq1rajnW7Adulkz9l/gctIM1pZVaDza4p1fm2x\nLqgt1tKyfKWnEa4AZlAk7NzJNxqo3Y1jotWdZU3WnX5Hzaa6cRqL1oRQ5ZRfAJj3Uhmz1ZKOJ2w3\nSLo08QBjzHpJtdbafzPGzM2Y7Tg0c+PAtGjpGdK2o53O17FO7WrsUTB89lnX2pIcXVDr1wW1xbqg\ntkirFxTJl5k+DSMGAFckLPW1uJHaEI/U7obRp/8m6/rUrAI3TqukwupxYrWa2VQAwITN2A2gjDFp\nkh6WdPcEjr1X0r2StHDhwtQOLBmKF0om3fmff0+jFOznGXFzRCRita+lV1uOdGrrkQ5tO9qphs7B\ns74uNytd59cU68KFxbpwoROwZQXZ0zBiAPOWtVJ/m3NDwuhsajRYo9u9J5I3o5pT4sRoLFZr3OWC\neLj6CpPzWQAAKLUx2yipNmG7xt0XVSBpjaRX3ev/KiU9b4zZPPYmUNbaRyU9KkkbNmywKRxzcqRn\nSv7FUod786eOQ1Ll2hkdEqZmOBTWzoZubTnSoa1uwPYMnf0Xv7rSPK1f6Nf6RcVav9CvFRUFnC4M\nILmGup047W6MB2ssVt2Z1WQ9PzW31InSopr4TGph4voCKTMnOZ8FAMAEpTJmt0haboypkxOxH5P0\nn6PftNZ2SyqNbhtjXpX0Z3PibsaSc6pxNGbbDxCzHtE/HNLWo536zeF2/eZwh3Y0nP1GTdkZaTq/\npljrF/l10SK/1i8sViCfWVcA5yAUHDOTetwN14Z4wAZ7k/NZuYF4nBZVx2dSC6ud7YIFXJ8KAJiV\nUhaz1tqQMeYzkl6U82ieH1hrdxljviRpq7X2+VR99qwQWCbtf9FZ5/E8s1b34Ii2HunQ24edr/ca\nuxWOnHnyvzQ/SxsWlWjDYr82LC7RqqpCZWVwfReACbJWGugYE6hjYrWvWVISTkTKLnID1Q3TWLBW\nx2dZmVEFAHhUSq+Ztda+IOmFMfsePM2x16RyLNMusCS+TszOGj1DI/rNoQ79+mC73j7crt0nemTP\n8vtiXWmeNizy6+LFTsDWlebxaBwApxceic+qdkUj9djoWB0ZOPfPycgZHaZFNadGK89PBQDMYTN2\nA6g5j8fzzAr9wyFtOdKhNw+1682D7XqvsVtnmng1RjqvokCXLQnokjonXssLOL0OQILh3oRQPZaw\nftxZ9p7QOc+qmrT43X2joVpUmxCvtVJuifMfLQAA5iliNlWI2RkRDEW0/Vin3jjQpl8fbNeO410K\nnaFe04y0prpIlywu0aVLArp4sV/FuVnTOGIAs4q10mCn1HV0dKB2H4/vG+o698/Jynfj1A3V4tr4\ndvSOwOmZ5/45AADMYcRsqhQscE4BCw1Kgx3O9VG5JTM9qjnHWqt9zX361f5WvX6gTW8f6tDgyOmf\nh2iMtGZBkS5fGtDlSwLasNivAh+/MALzhrVSf6sTpV1Hpa5jbqgec/cdk0b6z/FDjFRQmTCbWuM8\nsi02w1oj+YqZVQUA4BwRs6mSliaVLJFadjnbHYeI2SRp6R3Sa/va9MaBNr1+oE2tvWd+9MTKyoJY\nvF5aF1BRLvEKzFmxWD0Wj9VRX8edP2Q8F+lZCWG6MD6rGl0WVksZnOEBAECqEbOpFFgaj9n2A1LN\nhpkdj0eNhCPafrRTv9zXql/ua9Wupp4zHr+wJFcbl5XqimWlumxJCY/JAeYSa6WB9niodo4TrOca\nq9FTgMdGavEiZz2v3PkDSwAAMKOI2VTiutkpa+oadOL1/Va9caBNvcOh0x5blJOpjcsCumJZma5Y\nVqqFgdxpHCmApBvqdiM1MViPxsP1XE8D9hW5M6rRr1r3NGB3mePnFGAAADyAmE2lwNL4Oo/nOaNw\nxOrd4136xd5m/ceeFu092XvaYzPSjDYs9uvK5WW6cnmpVi8oUnoav3gCnjEy5Fyn2nlU6jriLDuP\nxIP1XG+w5CtyI3VRQrAujAdrTnEyfgoAADDDiNlUYmb2jHqHRvSr/W36jz0tevX9FrX3B097bHVx\njq4+r0xXryjT7ywNcNMmYDaLRKS+ZidQo19dR+PrvSfO7f2zCiR/YqiOiVZiFQCAeYGYTaVRMXvQ\nudZrnp+6dqJ7UC/tata/727W24fbNRIe/7E5WelpunRJia45r1xXryjT0rI8mXn+1w6YVYL97ozq\n4dHR2nnE2R8+843ZzijDNzpS/Yuc9eiS04ABAICI2dTKDTinuw11O9d49Z6UCqtmelTT7lBrn17c\n1ayf7zqpHcdPf/pgaX62Nq0s13X15bpiWanysvnHE5gx1jr/zeo84gRrx5ho7W+Z+nubNKmwJiFS\nF48OVm6wBAAAJoBaSCVjpJKlUtN2Z7vj4LyIWWutdjX16MVdJ/XirpPa19x32mNXLyjUpvoKbVpZ\nrrXVRUrj2ldg+oSGnRsqdRyOz7DG1o+e212Bc/xupC4eHaz+xc51q+lcKgAAAM4NMZtqgWXxmG0/\nIC2+YmbHkyLWWu092auf7mjSv+48oWMdA+Mel5FmdNmSgG5aXaHrV1WoqihnmkcKzDNDPfGZ1Y5D\no2dZuxskjX+q/1mlZbqnAC9O+Fok+eucpa8oaT8CAADAeIjZVJvjN4E61Nqnn+44oZ/ubNKBlvFn\nYLMz0nT1ijLdtLpSm+rLVZybNc2jBOYwa6XBTidUY1+H4+sDbVN/b1+xVFLnBupi56vEXS+sltLS\nk/RDAAAATB4xm2pz8PE8DZ0D+tedJ/TTHU3a1dQz7jEF2RnaVF+um1ZX6urzypSbxT9qwJRZK/W1\njAnWhHAd7p7iGxupqGZ0pPrr4us5/uT9DAAAAElGYaTaHInZ/uGQfvbeST27rUFvHmof95iczHRd\nv6pCH1xXpatWlMmXyawNMGGxYD3oRGq7u+w46ARr8PTXnp9RetaYSE1Y+hdJGdlJ/TEAAACmCzGb\naiUJMdtxSIqEPXNqXiRi9ZsjHXpmW4Ne+O0JDQTDpxyTlZGma88r0++tW6BN9eXMwAJnYq3U3+YE\navvB0ctzCdbMPCdQS5bEl353WbjAM//NAQAAmAzKI9V8hVJ+hdTXLEVGnDuHltTN9KjO6Fj7gJ7d\n3qBntzeoofPUu5mmGemK5WX60PkLdMPqChX6uCspMMpgVzxU2w8618t3HJTaD039lODsQjdWx/nK\nL+e5qwAAYN4hZqdDYJkTs5Lzi+0sjNlwxOoXe1v0xFtH9dq+1nGPWVaer49eVKNbLqxWRaFvmkcI\nzDIjg+7pwAfcr4Px5VRvuhQN1sBSN1SXxrdzAwQrAABAAmJ2OpQskY6+4ax3HJR0/YwOJ1Fr77Ce\n2npcP3r7mBq7Tp2FLfRl6EMXVOujF9VoXU2RDL9MYz6JhKWuowmhmhCu3cen9p5Z+QnBunT0kmAF\nAACYMGJ2Osyyx/NYa7XtaKeeeOuoXvjtCY2ERz9n0hjp6hVluvWiWm2qL+dGTpjbrJUG2p1/N9v2\nS+37nVht2+88kzUcnPx7ZvjipwAHliUE6zJOCQYAAEgSYnY6zJKYHQlH9JN3m/T91w9rz4lTH6nj\nz83U7Rcv1B9culC1JbkzMEIghUJB97Tg/U6oRsO1bb801DX59zPpzt2AA8vdYHXDtWSp+wzWtOT/\nDAAAAIghZqfDqJid/sfzDAbD+qctx/TdXx0e91TiCxcW687LFukDa6uYhYW3RWdZ2/a5wbovHq2d\nRyQbmfx75lc6/w6XLnOj1f0qXiRlZCX9RwAAAMDEELPTwb9YkpFknbsZh4an5dmO3QMjeuKtI3rs\njSNq7x99qqQvM00fOr9ad16+SGuqi1I+FiCpwiEnTtv2jQ7X9v3SYOfk3y8zNx6ppcvd2Vb3tGBf\nYdKHDwAAgHNHzE6HTJ9UXOuErKzzPMnylSn7uJaeIX3/9cP64dvH1DccGvW9krws/dHGxfr4ZYtU\nnMusEma54d6EGdaEcG0/6DzqalKMVFT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cost_lambda()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 2.9. Krzywa uczenia się" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "* Krzywa uczenia pozwala sprawdzić, czy uczenie przebiega poprawnie.\n", "* Krzywa uczenia to wykres zależności między wielkością zbioru treningowego a wartością funkcji kosztu.\n", "* Wraz ze wzrostem wielkości zbioru treningowego wartość funkcji kosztu na zbiorze treningowym rośnie.\n", "* Wraz ze wzrostem wielkości zbioru treningowego wartość funkcji kosztu na zbiorze walidacyjnym maleje." ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "def cost_trainsetsize_fun(m):\n", " theta = np.matrix(np.zeros(X.shape[1])).reshape(X.shape[1],1)\n", " thetaBest, err = SGD(h, J, dJ, theta, X, Y, alpha=1, adaGrad=True, maxEpochs=2500, batchSize=100, \n", " logError=True, validate=0.25, valStep=1, lamb=0.01, trainsetsize=m)\n", " return err[1][-1], err[3][-1]\n", "\n", "def plot_learning_curve():\n", " plt.figure(figsize=(16,8))\n", " ax = plt.subplot(111)\n", " M = np.arange(0.3, 1.0, 0.05)\n", " Costs = [cost_trainsetsize_fun(m) for m in M]\n", " CostTrain = [cost[0] for cost in Costs]\n", " CostCV = [cost[1] for cost in Costs]\n", " plt.plot(M, CostTrain, lw=3, label='training error')\n", " plt.plot(M, CostCV, lw=3, label='validation error')\n", " ax.set_xlabel(u'trainset size')\n", " ax.set_ylabel(u'cost')\n", " plt.legend()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Krzywa uczenia a obciążenie i wariancja\n", "\n", "\n", "\n", "Źródło: http://www.ritchieng.com/machinelearning-learning-curve" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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TvxVvHh263CZw1o8S85u/g51b4ssjSZIkVcEyq5qzan7lo3jn3w/ZOfHl0eHr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\nltNHctdZqo8VCXTWWgr317K2sJJ1RRWsLaxgTWElZdXt2ws3NNgwOjX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_learning_curve()" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## 2.10. Obserwacje odstające" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Funkcja regresji liniowej\n", "\n", "def h_linear(Theta, x):\n", " return x * Theta\n", "\n", "def linear_regression(theta):\n", " return lambda x: h_linear(theta, x)\n", "\n", "# Wykres krzywej regresji (wersja macierzowa)\n", "def plot_regression(fig, fun, theta, X):\n", " ax = fig.axes[0]\n", " x0 = np.min(X[:, 1]) - 1.0\n", " x1 = np.max(X[:, 1]) + 1.0\n", " L = [x0, x1]\n", " LX = np.matrix([1, x0, 1, x1]).reshape(2, 2)\n", " ax.plot(L, fun(theta, LX), linewidth='2',\n", " label=(r'$y={theta0:.2}{op}{theta1:.2}x$'.format(\n", " theta0=float(theta[0][0]),\n", " theta1=(float(theta[1][0]) if theta[1][0] >= 0 else float(-theta[1][0])),\n", " op='+' if theta[1][0] >= 0 else '-')))" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "# Wczytanie danych (mieszkania) przy pomocy biblioteki pandas\n", "\n", "alldata = pandas.read_csv('data_flats_with_outliers.tsv', sep='\\t',\n", " names=['price', 'isNew', 'rooms', 'floor', 'location', 'sqrMetres'])\n", "data = np.matrix(alldata[['price', 'sqrMetres']])\n", "\n", "m, n_plus_1 = data.shape\n", "n = n_plus_1 - 1\n", "Xn = data[:, 0:n]\n", "\n", "Xo = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n + 1)\n", "yo = np.matrix(data[:, -1]).reshape(m, 1)\n", "\n", "Xo /= np.amax(Xo, axis=0)\n", "yo /= np.amax(yo, axis=0)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(Xo, yo, xlabel=u'metraż', ylabel=u'cena')\n", "theta_start = np.matrix([0.0, 0.0]).reshape(2, 1)\n", "theta, logs = gradient_descent(cost, gradient, theta_start, Xo, yo, alpha=0.01)\n", "plot_regression(fig, h_linear, theta, Xo)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [], "source": [ "# Odrzućmy obserwacje odstające\n", "alldata_no_outliers = [\n", " (index, item) for index, item in alldata.iterrows() \n", " if item.price > 100 and item.sqrMetres > 10]\n", "\n", "alldata_no_outliers = alldata.loc[(alldata['price'] > 100) & (alldata['sqrMetres'] > 100)]" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "slideshow": { "slide_type": "notes" } }, "outputs": [], "source": [ "data = np.matrix(alldata_no_outliers[['price', 'sqrMetres']])\n", "\n", "m, n_plus_1 = data.shape\n", "n = n_plus_1 - 1\n", "Xn = data[:, 0:n]\n", "\n", "Xo = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n + 1)\n", "yo = np.matrix(data[:, -1]).reshape(m, 1)\n", "\n", "Xo /= np.amax(Xo, axis=0)\n", "yo /= np.amax(yo, axis=0)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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AEIK0etiul/Q9d18n6Xvx4yRj7n5WfLuocc0DAAAIR1qB7WJJt8f3b5f0Rym1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\nAhsAAEDgCGwAAACBI7ABAAAE7v8D/evd63NrC9gAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plot_data(Xo, yo, xlabel=u'metraż', ylabel=u'cena')\n", "theta_start = np.matrix([0.0, 0.0]).reshape(2, 1)\n", "theta, logs = gradient_descent(cost, gradient, theta_start, Xo, yo, alpha=0.01)\n", "plot_regression(fig, h_linear, theta, Xo)" ] } ], "metadata": { "celltoolbar": "Slideshow", "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.14" }, "livereveal": { "start_slideshow_at": "selected", "theme": "amu" } }, "nbformat": 4, "nbformat_minor": 2 }