{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Additional note on Gaussian Discriminant Analysis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### I) The multivariate Normal Distribution" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Simple illustration of the MVN\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "\n", "\n", "x1 = np.linspace(-5, 5, 100)\n", "x2 = np.linspace(-5, 5, 100)\n", "\n", "xx1, xx2 = np.meshgrid(x1,x2)\n", "\n", "X = np.vstack((xx1.flatten(), xx2.flatten())).T\n", "\n", "\n", "# multivariate Gaussian\n", "\n", "\n", "mean = np.asarray([1,1])\n", "\n", "Sigma = np.eye(2,2)\n", "D = 2\n", "\n", "\n", "MVN = np.zeros(np.shape(X)[0],)\n", "\n", "for i in np.arange(np.shape(X)[0]):\n", " current = X[i,:]\n", " tmpL = np.matmul(current-mean,np.linalg.inv(Sigma))\n", " tmp = np.matmul(tmpL, (current-mean).T)\n", " MVN[i] = 1/((2*np.pi)**(D/2) * np.linalg.det(Sigma)*(1/2))\\\n", " * np.exp(-(1/2)*(tmp)) \n", " \n", " \n", "fig, ax = plt.subplots(subplot_kw={\"projection\": \"3d\"})\n", "ax.plot_surface(xx1, xx2, np.reshape(MVN, np.shape(xx1)), \\\n", " alpha=0.5, cmap=cm.get_cmap('hsv'))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.contour(xx1, xx2, np.reshape(MVN, np.shape(xx1)), cmap=cm.get_cmap('hsv'))\n", "plt.axis('equal')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Simple illustration of the MVN\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "\n", "\n", "x1 = np.linspace(-5, 5, 100)\n", "x2 = np.linspace(-5, 5, 100)\n", "\n", "xx1, xx2 = np.meshgrid(x1,x2)\n", "\n", "X = np.vstack((xx1.flatten(), xx2.flatten())).T\n", "\n", "\n", "# multivariate Gaussian\n", "\n", "\n", "mean = np.asarray([1,1])\n", "\n", "Sigma = np.eye(2,2)\n", "D = 2\n", "\n", "\n", "MVN = np.zeros(np.shape(X)[0],)\n", "\n", "for i in np.arange(np.shape(X)[0]):\n", " current = X[i,:]\n", " tmpL = np.matmul(current-mean,np.linalg.inv(Sigma))\n", " tmp = np.matmul(tmpL, (current-mean).T)\n", " MVN[i] = 1/((2*np.pi)**(D/2) * np.linalg.det(Sigma)*(1/2))\\\n", " * np.exp(-(1/2)*(tmp)) \n", " \n", "\n", " \n", " \n", "# Set up a figure twice as tall as it is wide\n", "fig = plt.figure(figsize=plt.figaspect(.4))\n", "fig.suptitle('Standard Multivariate Normal Distribution')\n", "\n", "# First subplot\n", "ax = fig.add_subplot(1,2, 1)\n", "ax.contour(xx1, xx2, np.reshape(MVN, np.shape(xx1)), cmap=cm.get_cmap('hsv'))\n", "ax.axis('equal')\n", "# Second subplot\n", "ax = fig.add_subplot(1, 2, 2, projection='3d')\n", "\n", "surf = ax.plot_surface(xx1, xx2, np.reshape(MVN, np.shape(xx1)), \\\n", " alpha=0.5, cmap=cm.get_cmap('hsv'))\n", "plt.show()\n", "\n" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Simple illustration of the MVN\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "\n", "\n", "x1 = np.linspace(-5, 5, 100)\n", "x2 = np.linspace(-5, 5, 100)\n", "\n", "xx1, xx2 = np.meshgrid(x1,x2)\n", "\n", "X = np.vstack((xx1.flatten(), xx2.flatten())).T\n", "\n", "\n", "# multivariate Gaussian\n", "\n", "\n", "mean = np.asarray([1,1])\n", "\n", "Sigma = np.eye(2,2)\n", "\n", "\n", "Sigma[0,1] = .5\n", "Sigma[1,0] = .5\n", "\n", "\n", "D = 2\n", "\n", "\n", "MVN = np.zeros(np.shape(X)[0],)\n", "\n", "for i in np.arange(np.shape(X)[0]):\n", " current = X[i,:]\n", " tmpL = np.matmul(current-mean,np.linalg.inv(Sigma))\n", " tmp = np.matmul(tmpL, (current-mean).T)\n", " MVN[i] = 1/((2*np.pi)**(D/2) * np.linalg.det(Sigma)*(1/2))\\\n", " * np.exp(-(1/2)*(tmp)) \n", " \n", "\n", " \n", " \n", "# Set up a figure twice as tall as it is wide\n", "fig = plt.figure(figsize=plt.figaspect(.4))\n", "fig.suptitle('Adding off diagonal entries in Covariance')\n", "\n", "# First subplot\n", "ax = fig.add_subplot(1,2, 1)\n", "ax.contour(xx1, xx2, np.reshape(MVN, np.shape(xx1)), cmap=cm.get_cmap('hsv'))\n", "ax.axis('equal')\n", "# Second subplot\n", "ax = fig.add_subplot(1, 2, 2, projection='3d')\n", "\n", "surf = ax.plot_surface(xx1, xx2, np.reshape(MVN, np.shape(xx1)), \\\n", " alpha=0.5, cmap=cm.get_cmap('hsv'))\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([1.5, 0.5]),\n", " array([[ 0.70710678, -0.70710678],\n", " [ 0.70710678, 0.70710678]]))" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.eig(Sigma)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Simple illustration of the MVN\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "\n", "\n", "x1 = np.linspace(-5, 5, 100)\n", "x2 = np.linspace(-5, 5, 100)\n", "\n", "xx1, xx2 = np.meshgrid(x1,x2)\n", "\n", "X = np.vstack((xx1.flatten(), xx2.flatten())).T\n", "\n", "\n", "# multivariate Gaussian\n", "\n", "\n", "mean = np.asarray([1,1])\n", "\n", "Sigma = np.eye(2,2)\n", "\n", "\n", "Sigma[0,1] = .8\n", "Sigma[1,0] = .8\n", "\n", "\n", "D = 2\n", "\n", "\n", "MVN = np.zeros(np.shape(X)[0],)\n", "\n", "for i in np.arange(np.shape(X)[0]):\n", " current = X[i,:]\n", " tmpL = np.matmul(current-mean,np.linalg.inv(Sigma))\n", " tmp = np.matmul(tmpL, (current-mean).T)\n", " MVN[i] = 1/((2*np.pi)**(D/2) * np.linalg.det(Sigma)*(1/2))\\\n", " * np.exp(-(1/2)*(tmp)) \n", " \n", "\n", " \n", " \n", "# Set up a figure twice as tall as it is wide\n", "fig = plt.figure(figsize=plt.figaspect(.4))\n", "fig.suptitle('Adding off diagonal entries in Covariance')\n", "\n", "# First subplot\n", "ax = fig.add_subplot(1,2, 1)\n", "ax.contour(xx1, xx2, np.reshape(MVN, np.shape(xx1)), cmap=cm.get_cmap('hsv'))\n", "ax.axis('equal')\n", "# Second subplot\n", "ax = fig.add_subplot(1, 2, 2, projection='3d')\n", "\n", "surf = ax.plot_surface(xx1, xx2, np.reshape(MVN, np.shape(xx1)), \\\n", " alpha=0.5, cmap=cm.get_cmap('hsv'))\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([1.8, 0.2]),\n", " array([[ 0.70710678, -0.70710678],\n", " [ 0.70710678, 0.70710678]]))" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.eig(Sigma)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Simple illustration of the MVN\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "\n", "\n", "x1 = np.linspace(-5, 5, 100)\n", "x2 = np.linspace(-5, 5, 100)\n", "\n", "xx1, xx2 = np.meshgrid(x1,x2)\n", "\n", "X = np.vstack((xx1.flatten(), xx2.flatten())).T\n", "\n", "\n", "# multivariate Gaussian\n", "\n", "\n", "mean = np.asarray([1,1])\n", "\n", "Sigma = np.eye(2,2)\n", "\n", "\n", "Sigma[0,1] = -.5\n", "Sigma[1,0] = -.5\n", "\n", "\n", "D = 2\n", "\n", "\n", "MVN = np.zeros(np.shape(X)[0],)\n", "\n", "for i in np.arange(np.shape(X)[0]):\n", " current = X[i,:]\n", " tmpL = np.matmul(current-mean,np.linalg.inv(Sigma))\n", " tmp = np.matmul(tmpL, (current-mean).T)\n", " MVN[i] = 1/((2*np.pi)**(D/2) * np.linalg.det(Sigma)*(1/2))\\\n", " * np.exp(-(1/2)*(tmp)) \n", " \n", "\n", " \n", " \n", "# Set up a figure twice as tall as it is wide\n", "fig = plt.figure(figsize=plt.figaspect(.4))\n", "fig.suptitle('Adding off diagonal entries in Covariance')\n", "\n", "# First subplot\n", "ax = fig.add_subplot(1,2, 1)\n", "ax.contour(xx1, xx2, np.reshape(MVN, np.shape(xx1)), cmap=cm.get_cmap('hsv'))\n", "ax.axis('equal')\n", "# Second subplot\n", "ax = fig.add_subplot(1, 2, 2, projection='3d')\n", "\n", "surf = ax.plot_surface(xx1, xx2, np.reshape(MVN, np.shape(xx1)), \\\n", " alpha=0.5, cmap=cm.get_cmap('hsv'))\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([1.5, 0.5]),\n", " array([[ 0.70710678, 0.70710678],\n", " [-0.70710678, 0.70710678]]))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.eig(Sigma)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Simple illustration of the MVN\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "\n", "\n", "x1 = np.linspace(-5, 5, 100)\n", "x2 = np.linspace(-5, 5, 100)\n", "\n", "xx1, xx2 = np.meshgrid(x1,x2)\n", "\n", "X = np.vstack((xx1.flatten(), xx2.flatten())).T\n", "\n", "\n", "# multivariate Gaussian\n", "\n", "\n", "mean = np.asarray([1,1])\n", "\n", "Sigma = np.eye(2,2)\n", "\n", "\n", "Sigma[0,1] = -.8\n", "Sigma[1,0] = -.8\n", "\n", "\n", "D = 2\n", "\n", "\n", "MVN = np.zeros(np.shape(X)[0],)\n", "\n", "for i in np.arange(np.shape(X)[0]):\n", " current = X[i,:]\n", " tmpL = np.matmul(current-mean,np.linalg.inv(Sigma))\n", " tmp = np.matmul(tmpL, (current-mean).T)\n", " MVN[i] = 1/((2*np.pi)**(D/2) * np.linalg.det(Sigma)*(1/2))\\\n", " * np.exp(-(1/2)*(tmp)) \n", " \n", "\n", " \n", " \n", "# Set up a figure twice as tall as it is wide\n", "fig = plt.figure(figsize=plt.figaspect(.4))\n", "fig.suptitle('Adding off diagonal entries in Covariance')\n", "\n", "# First subplot\n", "ax = fig.add_subplot(1,2, 1)\n", "ax.contour(xx1, xx2, np.reshape(MVN, np.shape(xx1)), cmap=cm.get_cmap('hsv'))\n", "ax.axis('equal')\n", "# Second subplot\n", "ax = fig.add_subplot(1, 2, 2, projection='3d')\n", "\n", "surf = ax.plot_surface(xx1, xx2, np.reshape(MVN, np.shape(xx1)), \\\n", " alpha=0.5, cmap=cm.get_cmap('hsv'))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Simple illustration of the MVN\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import cm\n", "\n", "\n", "x1 = np.linspace(-5, 5, 100)\n", "x2 = np.linspace(-5, 5, 100)\n", "\n", "xx1, xx2 = np.meshgrid(x1,x2)\n", "\n", "X = np.vstack((xx1.flatten(), xx2.flatten())).T\n", "\n", "\n", "# multivariate Gaussian\n", "\n", "\n", "mean = np.asarray([1,1])\n", "\n", "Sigma = np.eye(2,2)\n", "\n", "\n", "Sigma[0,1] = 0\n", "Sigma[1,0] = 0\n", "\n", "Sigma[0,0]= 3\n", "\n", "\n", "\n", "D = 2\n", "\n", "\n", "MVN = np.zeros(np.shape(X)[0],)\n", "\n", "for i in np.arange(np.shape(X)[0]):\n", " current = X[i,:]\n", " tmpL = np.matmul(current-mean,np.linalg.inv(Sigma))\n", " tmp = np.matmul(tmpL, (current-mean).T)\n", " MVN[i] = 1/((2*np.pi)**(D/2) * np.linalg.det(Sigma)*(1/2))\\\n", " * np.exp(-(1/2)*(tmp)) \n", " \n", "\n", " \n", " \n", "# Set up a figure twice as tall as it is wide\n", "fig = plt.figure(figsize=plt.figaspect(.4))\n", "fig.suptitle('Adding off diagonal entries in Covariance')\n", "\n", "# First subplot\n", "ax = fig.add_subplot(1,2, 1)\n", "ax.contour(xx1, xx2, np.reshape(MVN, np.shape(xx1)), cmap=cm.get_cmap('hsv'))\n", "ax.axis('equal')\n", "# Second subplot\n", "ax = fig.add_subplot(1, 2, 2, projection='3d')\n", "\n", "surf = ax.plot_surface(xx1, xx2, np.reshape(MVN, np.shape(xx1)), \\\n", " alpha=0.5, cmap=cm.get_cmap('hsv'))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### II) LDA as a logistic regression classifier" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Connection between LDA and Logistic regression\n", "\n", "# Generating binary dataset \n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "mu1, sigma1 = -1, 0.5 \n", "x_class1 = np.random.normal(mu1, sigma1, 30)\n", "\n", "mu2, sigma2 = 1, 0.5 \n", "x_class2 = np.random.normal(mu2, sigma2, 30)\n", "\n", "plt.scatter(x_class1, np.zeros(np.shape(x_class1)), c='b')\n", "plt.scatter(x_class2, np.zeros(np.shape(x_class2)), c='r')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pi_1 = len(x_class1)/(len(x_class1) + len(x_class2))\n", "\n", "mu1_recovered = np.mean(x_class1)\n", "mu2_recovered = np.mean(x_class2)\n", "\n", "tmp1 = x_class1 - mu1_recovered\n", "tmp2 = x_class2 - mu2_recovered\n", "\n", "\n", "covariance = (1/(len(x_class1) + len(x_class2)))*\\\n", "(np.sum(tmp1**2)+ np.sum(tmp2**2))\n", "\n", "\n", "x = np.linspace(-3,3,100)\n", "\n", "\n", "gaussian_class1 = (1/np.sqrt(2*np.pi)/np.sqrt(covariance))*\\\n", "np.exp(-(1/2)*(x - mu1_recovered)**2/covariance)\n", "\n", "gaussian_class2 = (1/np.sqrt(2*np.pi)/np.sqrt(covariance))*\\\n", "np.exp(-(1/2)*(x - mu2_recovered)**2/covariance)\n", "\n", "\n", "plt.scatter(x_class1, np.zeros(np.shape(x_class1)), c='b')\n", "plt.scatter(x_class2, np.zeros(np.shape(x_class2)), c='r')\n", "plt.plot(x, gaussian_class1, c='b')\n", "plt.plot(x, gaussian_class2, c='r')\n", "plt.show()\n", "\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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mAH/q0OfO1cnou/tUf3/ZZfoz8AUxEc8SumHuXOjZE844w78Yxo3TdRt27/YvhopsytWEHvYql/374YMP/CudA3TsqMtMWUKPGpbQ49yBA/D++/6VzgPGjdOq2vnz/Y2jvIzcDFo1aEWz+s3Ce+D33oOiIv8/mMsv1wFG0TR5fRyzhB7n0tJ0bnK/88Y550CHDpFX7bIpd5M/9edz5mgL9ZAh4T92WePG6RQAkXamNRWyhB7n5szRroMXXOBvHM5p7li4MLKWtdyU40OXxeJiXQNw7FgduuunAQN0Yp9IO9OaCllCj2PFxfDuuzBmTGhWJqqpcePg4EH48EO/I1GFxYVs278t/A2in38Oe/f6W38ekJCgcSxYEFlnWlMhS+hxbPlyyMryv7ol4NJLdSxLpBQGt+3fRrEUh7+EPmeOlsxHjQrvcSszbhzk5dmo0SgQVEJ3zo12zq13zm10zt1fyTaXOOe+dM5965z7wNswTSjMn68FsEjJGw0bRtZYlmM9XMJdhz53Llx0kfcLQddWaqpO1vXuu35HYqpRbUJ3ziUCTwJjgD7Adc65PuW2aQ48BYwXkTOBEC+PYLzw3nva/9uP0aGVuewyyMjQFdf8FuiDHtYS+o4dOiHXmDHhO2Z1GjXS2R4XLvQ7ElONYErog4GNIpIhIgXADKD8WOQfAf8WkW0AIrLH2zCN13JydEKuSCmdBwTiee89f+MA7bJYL7EepzY5NXwHDbzwSPxg1q7VedJNxAomoXcAtpf5O7P0vrJOB1o455Y651Y5526saEfOucnOuZXOuZVZWVm1i9h4YtEi7Y0WaXmje3fo0SMyCoObcnWWxQQXxqamhQu1V8lZZ4XvmMEYOVJ/RsKZ1lQqmG+qq+C+8jWcScAA4DJgFPAb59xJqwGIyLMiMlBEBrZp06bGwRrvLFyoVbSDBvkdyclGjdLBTn53qgh7H/TiYh0YMHKk9uOMJH376gIbkXCmNZUKJqFnAmVXpu0I7KxgmwUickhEsoEPgXO8CdF4TUT/L1NT/e/mXJGRI+HQIfj0U/9iEJHw90H/4gutC4u0yybQE8zIkXppZ4teRKxgEvoKoKdzrptzLgW4FphdbptZwEXOuSTnXEPgPMCmaItQa9dq21sk5g2AYcP0ROPn1X3W4SwOFR4Kb0IPlH5HjAjfMWti1Cg94UT6qt5xrNqELiJFwJ3AQjRJzxSRb51ztzvnbi/dJh1YAHwFLAeeF5FvQhe2qYtA3ojUhN60KZx/vr9X977Msvjee9C/P0RqdWRqqpbUrdolYgXV2iMi80TkdBHpISJTS++bJiLTymzzqIj0EZG+IvK3EMVrPLBwIfTuDZ06Vb+tX0aN0hoIv9rOw94HPS9PJ8GK1LMs6GKzAwZYQo9gNlI0zuTn69D60aP9jqRqgU4VaWn+HH9TziYcjm7Nu4XngEuW6OyKkZzQQeNbtkyn9zURxxJ6nPnwQzhyJPLzRv/+0KqVf/XoGfsy6NC0A/WS6oXngAsXQuPGWtcUyUaN0kbRJUv8jsRUwBJ6nElLg5QUHVkeyRITtcr2vff8mQZgc+7m8JXOQV/osGH64USyIUOgSROrdolQltDjzKJFcOGFOm9KpBs5Er7/XkfCh9uWfVvo1iJMCT0jQ2+R2rulrORkPfEsXux3JKYCltDjyJ49sGaNlnyjQSDORYvCe9yC4gIy8zLDV0IPJMdoSOigH8zGjbBli9+RmHIsoceRQLVntCT0zp3h9NPDXxjctn8bgtC1edfwHHDRIl2uyc9FXWsi8AWyUnrEsYQeR9LSdLh///5+RxK81FRYuhQKC8N3zC37tgCEp4ReUqKJMdDHOxr06qXTAIT70slUyxJ6nBDRhH7ppdrgGC1SU3UagM8/D98xN+duBghPHfqaNbo6UbRcNoGeeFJT9URUUuJ3NKYMS+hxYuNG2L49uvIGwCWX6CIc4SwMbt63maSEJDo0KT+paAgEXtjw4aE/lpdSU3XU19df+x2JKcMSepwI5I1oS+gtWujgxHAm9C37ttC5WWcSE8JwKbNoEZx5JpwaxjnXvRA4Afk18stUyBJ6nFi0SBsZTzvN70hqLjVVByfm5YXneJv3hakP+pEjuk5ntJ1lQevQ+/SxevQIYwk9DgQG9kVTu1tZqan6Gj78MDzHC9ugos8+07kYojGhg8b94Ydw9KjfkZhSltDjwKpVsG9f9OaNH/wA6tcPTy+5/MJ8dh/aHZ4ui4sWaQv10KGhP1YopKbqCemzz/yOxJSyhB4HAlfFl17qbxy1Vb++TlUQjqv7Y10Ww9HDZdGi40Ppo9HQoXpCsnr0iGEJPQ4sXgxnnw1t2/odSe2lpuoUAN9/H9rjbN5X2mUx1FUuubmwcmX09W4pq2lTGDzYBhhFEEvoMS4/Hz75JLrzBhyvLgr1JH+BEnrIq1yWLtU+3NFaDxaQmgorVth0uhHCEnqM++QTbbOK9rzRrx+0bBn6apfNuZupn1Sfdo3bhfZAixfrDGnnnRfa44Ta8OF6Ylq61O9IDJbQY97ixbo+58UX+x1J3SQkaBvA4sWhnU53877NdG3eFRfq7kCLFmkddKRPl1udIUP0xGTVLhHBEnqMC7S7NW7sdyR1N3y4jnbdsCF0xwgk9JDKzIT166O/HgygXr3wtViballCj2G5udplMRbyBoRnkr8t+7aEvkE08AKivR4sIDUV0tNh506/I4l7ltBj2Pvva/VErOSNHj10tGuoCoN5R/PIyc8JT0Jv3RrOOiu0xwmXQInBql18Zwk9hi1eDI0aac+yWBCY5O/993XkqNcCsyyGtMpFRM9Iw4drw0AsOOccXQDWErrvYuQbZSqyeHFstLuVNXy4ViWtXu39vsMyqGjdOu1MHyuXTXC8xXrRIn8WgDXHWEKPUbHU7lZWKK/uwzKoKFqny61Oairs2AHffed3JHHNEnqMirV2t4C2baFv39DUo2/O3UyTlCa0bNDS+50HLF4M3btDtzCtVxougROU9XbxlSX0GLVoEbRpo8kv1qSmwscf6+yzXtqyf0to+6AXFWkDQKyVzkFPUl27WkL3mSX0GBRod0tNjZ12t7JSUzWZf/KJt/vdlLOJHi17eLvTslau1EndY+2yCU5ssS4q8juauBWD/+7mm29g1y4YMcLvSELj4ot19KuXhUERISM3g+7Nu3u30/LS0jTxxWIJHfQLt3+/nriMLyyhx6DAbKaxmtCbNIHzz4f33vNun7sO7iK/KD+0JfS0NOjfX7v4xaLhw/WEZdPp+sYSegxKS4NevaBjR78jCZ0RI7TrYna2N/vblLsJgO4tQlRCP3BAF4KI1bMs6Imqf39L6D6yhB5jjh6FDz6IzWraskaO1LYCr7ovZuRmANCjRYhK6EuXat1yLCd00Nf32Wd6AjNhF1RCd86Nds6td85tdM7dX8V2g5xzxc65q7wL0dTEp5/qHOixnjcGDoTmzb0rDG7K2USCS6BL8y7e7LC8tDRo0AAuuCA0+48Uqal64vrgA78jiUvVJnTnXCLwJDAG6ANc55zrU8l2jwALvQ7SBC8tTVcFu+QSvyMJrcREHZyYlubN4MSMfRl0atqJlMQQDatNS9PW3Hr1QrP/SHHBBbpmoFW7+CKYEvpgYKOIZIhIATADmFDBdncBbwF7PIzP1FBamk6X27Sp35GE3ogRsG2bN4MTN+VsCl39eWamDvmP9csm0GR+8cWW0H0STELvAGwv83dm6X3HOOc6AFcC06rakXNusnNupXNuZVZWVk1jNdXIydHpcuMhb8Dx1+lF7sjIzQhd/Xmsdzsqb8QInU43M9PvSOJOMAm9omFz5S9y/wbcJyJVzoEnIs+KyEARGdimTZsgQzTBWrJEqx/iJW/06KEDFOua0A8WHGT3od2hK6GnpemcBbEyXW51Al9AGzUadsEk9EygU5m/OwLlZ7IfCMxwzm0BrgKecs5d4UWAJnhpaccXYo8XI0bo4MTCwtrv41gPl1D0QS8pOT5sN9TL2kWKs86CU06xhO6DYBL6CqCnc66bcy4FuBaYXXYDEekmIl1FpCvwL+DnIvKO18GayonAggU6tiMpye9owmfECO0h9/nntd9HIKGHpIT+1VeQlRU/l02g802MGKEjv0pK/I4mrlSb0EWkCLgT7b2SDswUkW+dc7c7524PdYAmOOvWaQPh6NF+RxJel16q+WNhHfpWbcrRQUUhqUOfP19/jhrl/b4j2ejReiILxcT1plJB9UMXkXkicrqI9BCRqaX3TRORkxpBReRmEfmX14Gaqi1YoD/jLW+0aKHTAARef21k5GbQon4LWjRo4V1gAQsWwLnnQrt23u87ko0cqT8DJzQTFjZSNEYsWAC9e0OXEI2LiWSjR+t8UHtq2WF2U26Iuizu369TQsbbZRNoHfqAAXU705oas4QeAw4f1oF5Y8b4HYk/Aq+7tpN1ZeRmhKZBdPFiXfw0nj+Yzz7TNQNNWFhCjwEffKBzuMRjQRC0RuOUU2p3dV9cUsyWfVtCM23uggXa7WjIEO/3HQ1Gjz7ey8eEhSX0GLBggU4TctFFfkfij4QEbTtYuFALxDWxPW87hSWF3pfQRfQMk5oKycne7jtanHeeTrhj1S5hYwk9BsyfD8OG6ajreDVmDOzdqyNlayJkXRbXrtWRkvFa3QLaf3bECE3oXky4Y6plCT3KbdoEGzbEb3VLwMiROm6nptUuIeuyGK/dFcsbPRp27oSvv/Y7krhgCT3KBfpfx3tCb9VKR8jWNKFn5GaQnJBMx6YerwayYAGceSZ06lT9trEs8MW0apewsIQe5ebP1/lMTjvN70j8N2YMLF+uVS/B2pS7ia7Nu5KYkOhdIAcPwkcfxXd1S0D79nD22dYfPUwsoUexw4e1A8G4cfEzTUhVxozRqtqadF/ckLPB+wbRxYuhoMAumwLGjIGPP4Z9+/yOJOZZQo9iixfDkSNw+eV+RxIZBgzQ7otz5gS3fYmUsD57Pb1b9/Y2kDlzoFkznRfcwPjxuoqRVbuEnCX0KDZ7tnZztryhEhP1amXevOBmX9y2fxv5Rfn0at3LuyBKSjShjx4dv90VyzvvPGjdOvgzrak1S+hRqqQE5s7VvJESolXTotH48Tri/qOPqt82PSsdwNsS+vLlOgfB+PHe7TPa1fRMa2rNEnqUWrkSdu2y6pbyUlO1P/7s2dVvm55dmtDbeJjQZ8/WBGYNoicaP17r0D/+2O9IYpol9Cg1Z46OkLS8caJGjTSpz5pV/ViW9Kx0WjdsTeuGrb0LYPZsrQNrEYKZG6PZiBF6KWnVLiFlCT1KzZkDF16o/a/NicaPhy1b4Jtvqt5u3d513la3bNoE335r1S0VadxYV1+ZPdtGjYaQJfQotHUrrFlj1S2VGTdOf1ZX7ZKele5tg2ig9GkfTMXGj9eT3rp1fkcSsyyhR6G5c/WnFQQrduqpOmq0qoSedSiLvfl7vS2hz56to0N7hGAq3lgQ7JnW1Jol9Cg0ezacfrreTMUmTNAOJ99/X/HjnjeI5ubChx/aWbYqHTtC//6W0EPIEnqUycmBJUvgyiv9jiSyBfJqZW1wnndZfPddnbvXqluqNmGCLnpR2ZnW1Ikl9Cjzzjs66O7qq/2OJLIFaj7eeqvix9Oz02mY3JBOzTyaPOvNN6FDBx1EYyp31VXaKPrvf/sdSUyyhB5l3nwTunXTK1dTOedg0iSdHiE7++TH12Wvo1frXiQ4D/4F8vJ0WPvVV2tfUlO5Pn30NnOm35HEJPv2RZGcHJ2M66qrbDKuYEyapLUgb7998mPp2R72cJk9Wyfjssum4EyapEN5rdrFc5bQo8isWVbdUhPnnAM9e55cGDxYcJBt+7d5V3/+5pva4Beva4fW1NVXW7VLiFhCjyL/+hd07QoDB/odSXQIVLssWQJZWcfvX5+9HvCoQXT/fq1uueoqq24JllW7hIx9A6PEvn2QlmbVLTU1aZJOZFa2MOhpl8U5c7S6ZdKkuu8rnli1S0hYQo8Ss2bpRHVW3VIzZ50FZ5xxYmFwXfY6El0ip7X0YJmnmTO1usV6t9SMVbuEhCX0KPHmm9ClCwwa5Hck0SVQ7bJ0KezerfelZ6dzWsvTSEms47zD+/froq7Wu6XmrNolJOxbGAWysjRvTJpk1S21Eah2CfRJ/3bPt970cJk1y3q31EWg2iUz0+9IYoYl9Cjwz39q75abbvI7kuh05pl6mz4d8o7m8d3e7xhw6oC67/jll3WFbuvdUjs//rFWu0yf7nckMcMSehR4+WVdL/PMM/2OJDo5pyfDzz6Dt5etQhAGdahj3dXWrdp95uab7bKptnr0gIsugpdesil1PRJUQnfOjXbOrXfObXTO3V/B49c7574qvX3qnDvH+1Dj01dfwerVVjqvqxtu0IWEXkpbAcDA9nXs+/nKK/rzxhvrGFmcu+kmWL8ePv/c70hiQrUJ3TmXCDwJjAH6ANc55/qU22wzMFREzgb+B3jW60Dj1csv61rD113ndyTRrV07Xd1p2fYVdGverW6rFIloqfLSS7Wl2tTe1VdDgwb6RTd1FkwJfTCwUUQyRKQAmAFMKLuBiHwqIrmlfy4DOnobZnwqKoLXXtNppFt7uEpavLr5ZjjScgWdEupY3fLxx5CRoTs0ddO0KUycCK+/DkeO+B1N1AsmoXcAtpf5O7P0vsr8BJhf0QPOucnOuZXOuZVZZYfumQotXKhd7ay6xRtDhmdB863sS69jQn/pJV1S7Yc/9CSuuHfTTdoFdNYsvyOJesEk9IpafCpswXDODUMT+n0VPS4iz4rIQBEZ2KZNm+CjjFMvv6wlc1sI2htrsrT+fG3aIHJyarmTQ4e07/SkSboitam7YcOgUyc9UZo6CSahZwJlJ43uCOwsv5Fz7mzgeWCCiOz1Jrz4tXu3Fliuv14XSzd1t2LHChyOom39mTGjljt56y04eNCqW7yUmKiNy++9B9u3V7+9qVQwCX0F0NM51805lwJcC5ywhpRzrjPwb+AGEfnO+zDjz7PP6piVKVP8jiR2rNi5gt5tetOvTxOmTatlT7knn9S5BC680PP44tpPf6o/p03zN44oV21CF5Ei4E5gIZAOzBSRb51ztzvnbi/d7LdAK+Ap59yXzrmVIYs4DhQW6vd65EjNHabuRIQVO1cwqP0g7roLvv5apwOokc8/14VK77rL+p57rWtXXb7v2WetcbQOguqHLiLzROR0EekhIlNL75smItNKf/+piLQQkX6lN5vgtQ7efht27tS8YbyxPW87ew7tYVD7QVx3HbRqBX//ew138thj2ivD+p6Hxt136/JSta4PMzZSNAI9/riOKLfGUO+s2KENooM6DKJBA7jtNl1oaPPmIHewc6c2ht56KzRpErpA49mwYToc+rHHbORoLVlCjzBffqndnO+4Q9uKjDdW7FxBckIy57TVQcw//7m+v088EeQOnnlG17O7447QBRnvnNPL0tWr4ZNP/I4mKllCjzBPPAENG8Itt/gdSWxZsXMFZ7c9m3pJ9QDo0EEXC3nhBe20UqWjR7VR47LL4DQP5lA3lfvxj6F5c71MNTVmCT2C7NqlI0N//GNo0cLvaGJHQXEBy3csZ3CHwSfcf889Op6l2lHnb7wBe/ZoHa8JrUaN4Cc/0e6h27b5HU3UsYQeQR59VLsq/uIXfkcSWz7Z9gkHCw4yqseoE+4/7zwYPBj+/GftWVSh4mL4wx+gb19ITQ19sEarXRIS4JFH/I4k6lhCjxB79sDTT+tAop49/Y4mtszbMI+UxBSGdx9+wv3OwW9+ow2jgckTTzJzJqxbBw89ZF0Vw6VLF61zfP55G2hUQ5bQI8T//Z9W1f76135HEnvmbZzH0C5DaZzS+KTHLrtMl/X73//Vq6MTFBfDf/+3Lkxq87aE1wMP6DJTf/yj35FEFUvoESArSwcgXncdnH6639HEli37trA2ay1je46t8HHn4OGHYcuWCqYSeeON46VzWzM0vLp00S6iVkqvEfuWRoA//xny8610HgrzNswDqDShA4weravITZ2qV0nAiaXzK68MQ6TmJFZKrzFL6D7btUu7Kl5zDfTyYN1ic6J5G+bRo0UPerasvGEiUErftg1efLH0ztdf15V0rHTun7KldOvxEhT7pvrs/vu17vbhh/2OJPbkF+azZPMSxvYci6umQXPECLjgAi2U531/SEuH/fpZ6dxvDz6oJ9Rf/tLvSKKCJXQfLVumfaD/8z+t7jwUPtj6AflF+VVWtwQ4B3/9q05b/PkVv9d628cft9K53zp31lLPG2/A++/7HU3Es2+rT0pKtLtt+/ZWdx4q8zbMo0FSA4Z2GRrU9oMGwa+v2cDFy/+P3HE32BS5keKXv4Ru3fQfptIBAwYsofvmxRdh5UodTNT45N50po5EhHc3vMvw7sNpkNwg2Cfx66y7Oerqc/OeP9n8UJGiQQP429/g229rMPlOfLKE7oO9e+FXv4KLLtKuisZ7H279kIzcDH7Yqwb9x2fNImXxAtZOepjZy9sxfXro4jM1dPnlOv3oQw/B99/7HU3EsoQeZiK6OEtenhY2bPBhaDy+/HFaNWjFtX2vDe4JWVm6PNRZZzH4lTsZMkTbNnaetNii8YVzOoF9YaH2fCkp8TuiiGQJPcyeew7eeUenBzn7bL+jiU3b9m/j7XVv89P+Pw2uukVE1wjNzYXp00lISeIf/4DDh+GGG7RLuokAPXvCX/4CCxbonOnmJJbQw2jdOrj3Xu0id++9fkcTu55e8TQAPx/08+Ce8NhjMG+ezr9Qepbt1Us7uSxZYnNERZTbb4cJE+C++3TedHMCJz61/AwcOFBWroyfpUePHoXzz9fxEV99pb1bjPfyC/Pp9NdODO06lLcmvVX9E778UqddHDUKZs06oQ5MBH70I3jzTfjwQ/jBD0IXt6mB7Gw45xxdOWrVKp1yN44451ZVtsynldDDoKREJ49bvVoXVLBkHjqvf/M6e/P3ctfgIBZk3b0bJk7UBUZffPGkBg3ndF2Lzp3h2mutPj1itG4Nr74K331ndWLlWEIPgwce0JHkf/iDXi2a0BARHl/+OGedclb1fc8PHNCpFnft0lW5W7eucLNmzXSthdxcnfNl3z7v4za1cOmlOhLs7be1/tL6mAKW0EPu6ae1DnbKFK32M6Hz8pqX+XLXl/zHkP+oeqh/QYGuP/fllzrf+XnnVbnfc8/VvLFunZ6QjxzxNm5TS/fcA//1X9pd7NFH/Y4mMoiIL7cBAwZIrHv5ZZGEBJFx40QKC/2OJrbtzNspzf/YXC588UIpLimufMOCApHrrhMBkRdeqNExZswQcU7kiitEjh6tY8DGG8XFItdeq5/nM8/4HU1YACulkrxqJfQQENECw003wSWXwIwZkJTkd1SxS0S4Y94d5Bfm8/zlz5PgKvlaHzyoA1QC9V+33lqj41xzjXaIeecdGDtW1yM1PktI0Insx4yB227T2dXiufqlskwf6lusltCLi0X+8z+1wDBpksiRI35HFPtmfjNT+B3yyMePVL7Rrl0iAwaIJCaKPPdcnY73yisiSUkiffuKbNtWp10ZrxQUiNx0k/7jTZ4c05fEVFFCt4TuoR07REaM0Hf1rrs0uZvQ2py7WU559BQZ8MwAKSyu5J946VKRzp1FGjYUmTvXk+OmpYk0aSLSvr3IokWe7NLUVUmJyAMP6D/gsGExe7atKqFblYtH3nlHx6R8/LE2hP797zbzaqhtytnExf+4mMLiQl6+4mWSEsrVax09qjP1DRsGycnwwQfas8UDqan6WTdpor/ffbeOLDU+ck6XnfrHP2D5cv2HfP11v6MKr8oyfahvsVJC/+47kauu0kJB//4i6el+RxQf1mWtk/Z/bi+tHmklq79ffeKDJSUi774rcuaZxy/BDxwISRyHDoncc48epmdPkXfe0cMbn23cKHL++frBjB8vsnat3xF5Biuhe2/HDrjzTujTB+bP1xWHPvvMlpELh/kb5jP0paEUlRSx9Oal9GvX7/iDn36qLdGXXaYLtc6ZA888E7I5ihs21JldFy/Wv6+4QkeUvv9+fLfN+a5HDx3e+8c/6ofRty/87Gexv+B0ZZk+1LdoLKGXlIgsXiwycaK2rSUmikyZIvL9935HFh+2798uE9+YKPwO6fVEL1m7p7TUdeCAyLPPaqMniLRtK/Lkk2HvW1hQoGF06KBh9Osn8tRTIvv2hTUMU96ePXoZlZys/YgnTBCZPz9qG7moooRuc7lU48gRrXqdPVtvmZk6UvzWW3WeoO7d/Y4wtokIq75fxYurX+SVNa9QLMX85uLf8IvTbiRl4SItgS9cCIcOaSnsttt05kQfVw3Jz9elBZ95RscuNWwII0fCuHHa3fHUU30LLb5t3apzObzwgk6X3L69dmO9/HIdedogyIVQfFbVXC5BlaaB0cB6YCNwfwWPO+Cx0se/AvpXt89ILKEfPiyyerXIP/+pXQ/PP18kJUVLWw0bilx5pcj06SL5+aE5/vTpIl266OCVLl3077KPtWqlsYD+Pn36ic9p1UpvZZ9ffp9TpuhP0CsMOHnbwDHK3gLbVnaMsrEFbvXqHb+/queXfw869twrnDFbmk78pXT6/VnC75D6/50iP/7jYHmz/0RJ54xjB9lOB/lHvdtkwW8/kemvllT5/lX2mBcf1kdTph/7865W0+VAqy5SgpMVzYbLz+s9L53Yeux96cl6uYGX5QnukA+5UPa4U6SkYaOqP7iq7qvozS97C7zp5T+IRo1O/kIF84Use3/gHyRw69On+ufU9AOo7MtfW0eP6iixiROPvwfJySKDB2tJ/tVXRVatEjl4sPbHCCHqUkJ3ziUC3wEjgExgBXCdiKwts81Y4C5gLHAe8HcRqXI8dahK6CI6V8/Ro1pSOnxYfx44oItK5OXpikHZ2XqS3rFDq9UCt8DbUa+erjF5/vkwdGjoT+CvvQaTJ5/YU6JhQ3j2Wf39lltOXk4xKUkb9itbZjE5WR8vKKj++DXZtvzzRKCoqIqNEgohKZ+k5DzqJeeQUi9bbw12U7/5Di5I/Z6UNjtY9f12NhTuIq9pnr6+YseAzERu+aqIa76F5kdgD21YxhCWMYQFjGY15wKuwvei7PtX2Xt7/fU1e71AhR/WIRryM/RgzzGZRpzY5UWAb+jLPMbyGeezjCHspt2xx1uQQzc205FMOibspK3bQ+vi3bRiLy3IpUnSEZqSR6OifTQgnwbkUz+pmGQpwBVX9ebXQEqKTlJ2/fWVfyFvukkvP4Lt0lPZc4L9AF57reIvf9lY6+LoUVi6VOdJXrYMVqzQhBHQqdPxW4cO0KaNzvvTqpVO9NOkid4aNdIE0aCBJo/ExJCtXlNVCT2YhH4+8DsRGVX6968AROQPZbZ5BlgqIq+X/r0euEREKl0rqrYJ/e8PT+WJrP8B9J/kxF9qzrnKb+FUUFBxI1ogjqo+JnHeVJtJmdcsZd7UE+53pY85fdtLnCAOShyUJAjFTihJgMIEoSgRChJPfH5lWh+C03KgZw50ya5P922n0nxHT/YUdWVPi1785rVe9BjXm4ySLugFYXC6dNGfW7dW/NiWLUHv6riuXSvc4Rb0YF2p4GDlCLCdTqylD+voxXrOYCtdyNSUTi4tgw4nmQJSKCCJIhIpJokiEighgRISKcYhJFCCQ066ASf8TlIy7rQesHEjFBUevz9INdo+ORl6nl71Nhu+q7rEUt3zayhJCul6dD3dC9bR/Wg6nQs20K4wk3ZF2zmlcAcNJL/6nQAlOIpcMkUkU+SSKHZJFJNIiUukhAQ2jLyTi969v1YxVpXQgxmQ3gEo2zSciZbCq9umA3BCQnfOTQYmA3Tu3DmIQ5+sTZs2dNlSZmY8d/zf27njf1eUoBMSSn8mQmJCZC3/lrmnrnuo/Ys58XxQLnuXv1f0TXalNW2uJAEXuK8kAScJUJKIK0kkoTgJV5xMQnEyrrA+FNXHFTaAo82Qo00pyW9F0aGOHD3UiU9Xt+LUs9uwipYUknJifPvgN2Mgoxarjm3bVrvHarPTzgS/Qwd0Zjud2c5oFp70eAHJ5NCSvbRiH805QBPyaMohGpWWzxtwhPoUHkvnKRSTSBFJFJFECQkUk0gxicfSdwkJJ6Rz4ITfAaTIwdk9YN2qE+4PRk23pxDoU01CXrumbs+vsWSgL5n0JbOCR1OKDtOkYC9NjmbToOgADQrzaFiUR0pxPinFh0kpzieppIDkkgKSSgpIKCkiSQpJkCISpLj0VkLSaad5HHepyupiAjfgauD5Mn/fADxebpt3gQvL/L0YGFDVfiOxDt1PldVdd+lS+WOxcuvSpfr3QOR49W9N913dfr36sDbTRTYT5R9WdR9GbT6Eyp4TzAdQ1Ze/1h9gdKOO/dAzgU5l/u4IlJ/qP5htTBWmTtVqxbIaNtT7p07Vq8vykpIqvj8gOVmrGoNRk23LP68uE48FXiNU/R6AVulWpqL3ouz7V9V+a6yCHR6iIQ8wlQeYyiEaVvLEIFX0YaSknPwC6/rml5eSUv2HMXnyyfdXpbLnBPsBVPblLxurOa6yTB+4odUyGUA3IAVYA5xZbpvLgPnoleQQYHl1+7US+smsl0v1nSGmTNGuxGWPU9F7EQm9XE74UED/Lht44O+EBO1tYb1cKn+vvezlEuWoaz/00l4sfwMSgRdFZKpz7vbSE8I0p6sJPIF2bzwM3CIiVbZ4Rks/dGOMiSR1bRRFROYB88rdN63M7wLcUZcgjTHG1I3N5WKMMTHCEroxxsQIS+jGGBMjLKEbY0yM8G22RedcFgQxRrpirYFsD8Pxk72WyBQrryVWXgfYawnoIiJtKnrAt4ReF865lZV124k29loiU6y8llh5HWCvJRhW5WKMMTHCEroxxsSIaE3oz/odgIfstUSmWHktsfI6wF5LtaKyDt0YY8zJorWEbowxphxL6MYYEyOiNqE75/7HOfeVc+5L59x7zrn2fsdUW865R51z60pfz9vOueZ+x1RbzrmrnXPfOudKnHNR18XMOTfaObfeObfROVe7NcIigHPuRefcHufcN37HUlfOuU7Oufedc+ml3617/I6pNpxz9Z1zy51za0pfx8OeHyNa69Cdc01FJK/097uBPiJyu89h1YpzbiSwRESKnHOPAIjIfT6HVSvOud5ACfAM8IvqplGOJMEsiB4tnHMXAweBV0Skr9/x1IVz7lTgVBH5wjnXBFgFXBFtn0vpNOONROSgcy4Z+Bi4R0SWeXWMqC2hB5J5qUZQl6Wi/SUi74lIYOn2ZeiKT1FJRNJFZL3fcdTSYGCjiGSISAEwA5jgc0y1IiIfAjl+x+EFEfleRL4o/f0AkI6uWRxVStenOFj6Z3LpzdO8FbUJHcA5N9U5tx24Hvit3/F45FZ09ScTfpUtdm4ihHOuK3Au8LnPodSKcy7ROfclsAdIExFPX0dEJ3Tn3CLn3DcV3CYAiMiDItIJeA24099oq1bdaynd5kGgCH09ESuY1xKlKlq2Pmqv/GKNc64x8BZwb7kr9KghIsUi0g+9Ch/snPO0OszDFWa9JyKpQW76T+Bd4KEQhlMn1b0W59xNwDhguER4w0YNPpdoY4udR6jSOue3gNdE5N9+x1NXIrLPObcUXbbTs4briC6hV8U517PMn+OBdX7FUlfOudHAfcB4ETnsdzxxbAXQ0znXzTmXAlwLzPY5prhX2pj4ApAuIn/xO57acs61CfRgc841AFLxOG9Fcy+Xt4Az0B4VW4HbRWSHv1HVjnNuI1AP2Ft617Io7rFzJfA40AbYB3wpIqN8DaoGKloQ3d+Iasc59zpwCTpN627gIRF5wdegask5dyHwEfA1+v8O8EDpWsdRwzl3NvAy+t1KAGaKyH97eoxoTejGGGNOFLVVLsYYY05kCd0YY2KEJXRjjIkRltCNMSZGWEI3xpgYYQndGGNihCV0Y4yJEf8fA30tvl7Y/4sAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# p(t = 1|x) = (p(x|t = 1)p(t=1)) / (p(x|t=1)p(t=1) + p(x|t=2)p(t=2))\n", "\n", "posterior = np.divide(gaussian_class1*pi_1, \\\n", " gaussian_class1*pi_1 + gaussian_class2*(1-pi_1)) \n", "\n", "plt.scatter(x_class1, np.zeros(np.shape(x_class1)), c='b')\n", "plt.scatter(x_class2, np.zeros(np.shape(x_class2)), c='r')\n", "plt.plot(x, gaussian_class1, c='b')\n", "plt.plot(x, gaussian_class2, c='r')\n", "plt.plot(x, 1-posterior, c='g')\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }