Naive_Bayes_Classifier.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "72290924",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import warnings\n",
    "from sklearn.model_selection import train_test_split\n",
    "warnings.filterwarnings('ignore')\n",
    "plt.style.use('seaborn')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d633078",
   "metadata": {},
   "source": [
    "### What are Generative Classifiers?\n",
    "\n",
    "Say we have a feature x and a target variable y.\n",
    "\n",
    "Generative Classifiers learn the joint probability distribution P(x,y) with the focus on how the features and the target variable occur together.\n",
    "\n",
    "So, the aim is to be able to model how the data gets generated hence the name Generative Classifiers. Once the model understands the data generation process (i.e. the underlying data distribution), it can take new data points in and make predictions on them\n",
    "\n",
    "In order to make predictions, generative classifiers transforms the joint probability P(x,y) to a conditional probability P(y|x) using Bayes Rule."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62efb7a2",
   "metadata": {},
   "source": [
    "### Introduction to Naive Bayes Classifier\n",
    "\n",
    "Naive Bayes Classifier is a Generative Classifier which makes strong (naive) conditional independence assumption between features given a label.\n",
    "Therefore Likelihood can be expressed as\n",
    "\n",
    "$$\n",
    "p(\\textbf x|y) = P(x_{1},x_{2},...,x_{m}, |\\ y) = P(x_{1}|\\ y)P(x_{2}|\\ y)...P(x_{m}|\\ y) = \\prod \\limits_{j = 1}^{m} P(x_{i}|\\ y)\n",
    "$$\n",
    "\n",
    "#### Bayes Theorem\n",
    "$$\n",
    "p(y=y_{c}|\\textbf x) = \\cfrac{p(\\textbf x,y)}{p(\\textbf x)} = \\cfrac{p(\\textbf x|y_{c})p(y_{c})}{p(\\textbf x)}\n",
    "$$\n",
    "\n",
    "Here,\n",
    "\n",
    "$p(y=y_{c}|\\textbf x)$ is the Posterior Probability\n",
    "\n",
    "$p(\\textbf x|y_{c}))$ is the Class Conditional Density\n",
    "\n",
    "$p(y_{c})$ is the Class Prior\n",
    "\n",
    "$p(\\textbf x)$ is the Evidence\n",
    "\n",
    "$$\n",
    "Posterior = \\cfrac{Prior\\times Likelihood}{Evidence}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adfca85a",
   "metadata": {},
   "source": [
    "After using Bayes Theorem and the Conditional Independence Assumption we get,\n",
    "$$\n",
    "p(y=y_{c}|\\textbf x) = \\cfrac{p(y_{c}) \\prod \\limits_{j = 1}^{m} P(x_{i}|\\ y_{c})}{\\sum \\limits_{r = 1}^{k} p(y_{r})\\prod \\limits_{j = 1}^{m} P(x_{i}|\\ y_{r})}\n",
    "$$\n",
    "\n",
    "Here,\n",
    "\n",
    "$ \\sum \\limits_{r = 1}^{k} p(y_{r}) $ corresponds to the $k$ prior probabilities\n",
    "\n",
    "$ \\prod \\limits_{j = 1}^{m} P(x_{i}|\\ y_{r}) $ corresponds to the $ k\\times m$ class conditional densities\n",
    "\n",
    "The number of parameters for each conditional density vary and depends on its mathematical form."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b93d2f9",
   "metadata": {},
   "source": [
    "#### Example \n",
    "\n",
    "A setting where the Naive Bayes classifier is often used is spam filtering. Here, the data is emails and the label is spam or not-spam. The Naive Bayes assumption implies that the words in an email are conditionally independent, given that you know that an email is spam or not. Clearly this is not true. Neither the words of spam or not-spam emails are drawn independently at random. However, the resulting classifiers can work well in practice even if this assumption is violated."
   ]
  },
  {
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G8KfzoUOHHj58mJ6ejps4mUymlZWVv7+/rKzs9OnTycUePnzoZGUlyWC0SnER0lFX3zZ37h9TpgTfuuU8bFjvPn3Wb9o0ZMiQVtrcrwuiUwAAaA4JCYnqpt9KKiMlhbtSw6Kjd/v7r1uzZtWaNb/PmyfMQzhxdBoUFGRiYtLowtnZ2d26daubnpWVRV6Ms7KysrOz8QRCysrKvIHivXv3oqKinj9//uHDh0aj0+TkZJxnaGiolJTU6NGjcXp6enpSUtKqVasaWtHDw8PDw6PRfWkqDw8PdXX1+/fvS0pK1v1USUkJ5qgAAIDO48yZMzNnzuS90UNLS+vVq1f29vaWlpZk4rs3b3rr6rZ2YWSlpb0nTfIaN+6v8PDZU6daWln5BwQ0+5afDglmRQIAgOag0+k1LZjoyNnKiu3vf3XDBnZoaHdd3WNHjwqeNqmqqurFixdqamrChKYIoeLiYr7eVGzKlCnkHbNPnz5FDcwAPGjQoM2bN3t5eQmzrb59+/bt2xchdP78+REjRpCPGBUww3Dr2bt3b35+fmRkpKKiYr0LyMrK8vbuAgAA6Ni+fPnCG4UihOTk5FJTU9euXcub+PH9+35GRm1TJIaExO8uLvEnT/ZgMs1MTXdu2wZzJpEgOm0v4HmnALR/VMr/c3d3vxYRQbGz4/2j8kzMI4z+JiYhmzff2779YnBwzx49bt68SRBEvUtGR0dXVFQIf7eksrJyozEYm81WVFT87bff6n6koKAgJSUl5Law9+/fJyUl8Xa0stlsdXV1Y2PjJuXTEpcuXXry5Mnff/8t4EnoJSUlysrKbVYk0K7A804B6DCEP50HDRqUlJREvs3MzHz//r2qqqqMjExFRQWZ/vPnT1Xh7h8RFYaEhO+cOW+Cg6PDw81MTZ89e9aWW2+3YGRve9HenndKpVDqryMjhBCiIMRtoA7dDtXU1Pj7+0dHR+fl5UlJSY0ZM2bhwoXC3+wHAIlASPD/ff2T9jSmj4FBhL///Vev1qxatXv79uATJ8zMzPiWwf2QwkenampqhYWFgpd59OjR4MGDqdT/NlMmJiZqaWkJM8a4XjExMQgh3mfYsNlswR2nmzZtOnXqlDCZS0pKxsTENNQdikVERISFhYWEhJAzBm/ZsmXt2rV843uLiorU1NSE2SjoeDZv3gy3ngLQMQh/OgcHB3t6eu7atUtTU7OwsFBGRubKlSv29vbHjh2rqalZtGgRXiwrO7trC9ouqXZ2jdScIyPr/UhXXf3Gli3hMTGuo0Zt3rJliXCjljowiE5B/QTXwptXBReLmpqaUaNGeXl5eXt70+n0yMjIcePG/fXXX48fP25q1xAArWpE//7DLSzOhofb29gsW7bsjw0beB+p2tRRspqamh8+fKibfvbsWQMDg4EDByYlJcXHx8+cOZP8aMeOHcePH292+ZOTkxUUFMi5c9PS0pKSklavXi1glS1btgg56SLurxawwLt370JDQ0+ePMnb8JSYmMgXmpaVlRUVFcEdPgAA0Hno6endvXuXL/HNmzd8KWXl5dL1zVYgpBbWnIdbWr7688+xGzfGRkcHHT/emeuoMLIXdHABAQHjx493cXHBFX07O7t58+a9evVq/fr14i4aAPyoVOqsESPeBQc/Cwvrb25Ohpc/f/58/vy5goKCqampkFk5OTm9e/eO717WFy9ezJw588yZMwihvXv3amtrk8HbrVu3RowY0ZIxBQYGBhwOp7q6Gr/FYWej4TRVOIJD02/fvo0aNSo+Pn7EiBGOjo6Ojo729vYWFhYFBQV8S75580ZRURHupAAAAMCHy+VSBV5rWpuehsbLQ4cqfvywtrIqKioSY0nEC/pO2wt43mkruX37dnp6+oABA8ihki4uLn5+ftevX9+3b594ywZAvTRVVcN27ToVFuZoLJEYMgAAIABJREFUZ7dy9eqnz54lJydLSkrW1tY6OjpaWlru3Lmz0UwsLCyUlJS+fPmCHx6DaWtrm5qaDho0yMvLy9raevbs2evWrVNXV8/MzFRRUZk1a1ZLij19+vS7d+/OmTNn7NixMTExsbGxGhoaPXr0aEmeQpo2bVpGRkZGRgZfure3N1/Kq1evRo8eDQP7Oy143ikAHUZrnM5ivzrISEld2rhx/fHjCgoKOTk59T4ZrsOD6LS9gOedtpLKysqkpKSkpCQyOh0wYABCKDU1tbq6mpy8FID2Zo6z83ALi1H/+c/YiROvXbtW78NRBKBQKG5ubteuXeONTjU1NePi4uLj40eNGoXnDXr06FF8fPyECRNafi4wGIyQkJCioqKMjAw3N7fTp09PmTKlhXkKSfiZJG7fvr1ixYpWLQxoz+CmUwA6DJGfzkwZmeKyMtnmTr4gQjt+/72wtHTwwIHPXr7shNP4wche0Bbi4uLWr1/v6en5/Plz3vT9+/e/evWqVTd99erVu3fvjhkzhkxJS0tDCGlra0NoCto5TVXV5wcPJkRHjx45UvDzZuo1Y8aMEydO8K1IoVBMTU3JKW3x24bOhZqaGiG3e+fOHWdn59LSUnl5eVNT08uXL+fn53t6eja1zK3q48ePSUlJTk5O4i4IAACAdkdBXr6wtFTcpfivP5cvHzdgwIypUxuayb8Dg75T0OpKSkrOnj27Y8eOPXv2eHt7v3jxAqcnJSWtXLny5MmT/fv3r7sWl8t9/fp1TU2NMJvo3r17Q5NwamlpaWlp8aZcu3YNIbRgwYKm7QYA4iAtKXlxwwaKnZ2psXHc589NalKxtLS0tbUNCQnhfcqLkO7fvx8eHv78+XMajTZr1iwVFZWNGzcqNDzV/q5duxITE/HdocXFxRs2bDhw4IChoWFTt9uqDhw4sGvXrs481QQAAICGKCkqFpWVibsU/2/L7NnWy5YF7N+/fOVKcZelTUF02l6Ym5vXnT2sY7h165anpyeNRouOjuZ9xIXgOUjz8vL8/f2FjE7Hjx8v5BjCrKysffv2WVlZ1b0hDYB2ixsR4bJ+/azp089fuiR4fiA+/v7+Tk5O1tbWTZ2ldsSIESNGjBB+eTc3N2NjYyaT+f79+2XLlnl7e7e3jtO7d+8WFBRMnTpV3AUB4uTr6wuDewHoGER+Omt07fo9K2sgz+0w4kWn0UJ8fPouWDBpyhQNDQ1xF6ftUDphf3H7RKG0r++C0tjzToUv7b1790aOHFlaWtqlS5cVK1Zs27YNp8+YMePJkyffvn1rcWGbwMXFJT09nc1mC35wIgD1EnxeIHxqNPBAsxbicrk23t6uU6d6C3xGS13v3r3z9fW9du2aaCd7CA0NZbPZBw8exG9ramoePXoUGxurqqo6cuRIvgELYpeWljZv3rxr167JysqKuyxAnNrbpRYA0GwiP51Xe3urlJSsbW4jJqWx5502r3qw4vBhbpcuAYcONa9UvyL4mW4v2tslU4TRKfbXX3/NmjXrw4cP5OxE2tra9vb2p0+fbkExm2bv3r2hoaF37twhb7oDoEmoQkSnDT1uu+X+ycgY6OUV8+aNrq5uk1asrq4mCILBYIiwMDU1NdXV1dLtYPYIYVRUVEhJSTWp2xl0SO3tUgsAaDaRn86HDx+Oe/gwaPnyZpandaLTotJS3alTk1NTO0+3CozsBW0kNDTU2NiYDE2TkpLS0tIafRaiCF26dOnJkyePHj36VerToB3i8lwIU1JS9PX1W6mntF4GmppLxo7dsXXr0RMnmrRia0wARqfT8TOEfwlw1gMAABBMX1//Tna2uEvBT15WdmCvXg8fPmzGFBK/KJizt71ob887pTT211QxMTEODg7kW3zTqZ2dXUPLZ2VlGRoa6gonICBA8NYfPXoUFhYWEhJCVlI3b97cjElQASDR6XQWk9nGG105YcK1a9dyc3PbeLsAdAzwvFMAOgyRn85mZmZvv35t9uoirzmT3IcOvXHtWgsy+MX8Mi3fHV57e94pV6SDJSoqKjIzM42NjckUNputq6uro6PT0CpdunT58uULl8ttNHMKhSK4D+fdu3c3btw4efIk7313ycnJYn/mMvjl1B3ZS/l3C0urjuxFCLGYzAG9ekVFRY0bN671tgJARwVTIgHQYYj8dNbS0qqsrs4pLFRteIJ6AVrv6q+nrp4RFdVKmbdD0HcK2oK0tHTXrl2Li4vx27i4uJCQkEaH9dJoNAkhCA5Nv337NmrUqC9fvowcOdLJycnJyWnYsGEWFhbl5eUi2z3QaRBC/LU2+99+e/70aetvBwAgAoWFhTt27BB5tosXL66srBR5tq2hsLBw165dcLsv+CX07tXrfVKSuEvBT1lePi8vT9ylaDvQdwpEr6GZYzZs2LBhwwaE0Ny5cysqKgQM6xWhqVOnZmRkZGRk8KU7Ozu3wdYBEDlpBqOiPT2QDYDOIDMzk81m1w2x6HS6np6eiYmJnJxc3bXKy8vHjRt37NgxkZfnyZMnpaWlkpKSIs9Z5BQUFIyNjZcvX97oPTgAiF0fc/MPSUnD+vVr4+1SBc6o1NlA32l7YW5uLu4iiEyjPUumpqbS0tKjRo1qg8I8f/6cqM/WrVvbYOsAiByXIKgwKB2AZvH19W3einiegtDQ0OnTp+/bt6+2thaP3ElISPDx8dHW1t66dWvd2HXevHlLlizp3r17S8vd7kVHR7u5uY0ZM6Zfv37jx4+PjY3l/dTV1ZVOp7flFP2gM2j26SzAAGvrp58/izzbRol9WFa7AtFpe/H27VtxF6HtBAUFTZ8+HR7rAkAzxHz92tfCQtylAG2qNUaHxsbGBgUFiTbP1iOq0aHNnkalW7duU6dOxTNErFixYubMme7u7pMmTdq0aVNYWNimTZs2bdq0b98+3lUePnyYl5c3fvz4Fpa5/bt27drRo0ePHTt269atV69eqaqqWllZHTlyhHcZHx+fLVu2dKrRiaC1tcYkZ4MGDXoeFyfybEGTwIO/2ouO9BC2Rp+Vampq+uLFCxaL1XZlAkAUBP9voxY80ExIVdXVOlOnPouO1tfXb72tgFbS7NGho0aNOnbsmGi74EJCQthsdmBgoAjzbFU3btyIjIxs4ejQFl5q7e3tIyMj09PTNTU1edPfv3/fp08fExOTzzy9Ln369Nm+fbuLi0vzi9swMzMzNputrKzcGpk3SWlpqYuLy/3798kp8SsqKpSVlblcblxcnIGBAbnkmjVrEEJ79uwRT0FBh9NKNWdNdfWn+/fraWiIPGcBBD8rFeHaRUcJExoFfadADMLDwyE0BaAZrj1+3Lt3bwhNf1EwOrRRHA5n7dq13t7edT8S++jQysrKFy9eGBgY8IWmCKHk5GT07wcLx8fHFxUVjRw5sk2LKA4xMTFPnz718vIiU6Slpe3s7CorK8PDw3mX9PDwuHr1apsXEICmGWxtDd2n4gWzIrUX7e15p62q7qUdANCootLSVcHBV65fF3dBQDPh0aH//PNPaGjoihUrpk+fzvvp/v37V65cKSMjwxubdZ7RoStXrszJyeFwONeuXfPw8Kh3GR8fnz59+owePbrZfYYtGQoYHR3N4XDqnW3+6dOnCKHRo0eTKTdu3LC1taVQWvKMw18Dl8vlcrl8N5r279//3r17OGgn9ejRo7y8/O3bt3379m3bMoKOqZUeX2w7bNjD27enOTq2RuZAGNB32l60t+edAgDam9VHj44aM2bw4MHiLghoETabjRCqO2m5vb09QujEiRO8iatXr+btlerAvLy8jh07dvLkSQHLsFisCRMm7N69u9lbackDEh8/fowQqhud/vz589SpU1ZWVuvWrSMTb9y40b9//3rziY+P37Vr1+bNm+fOnZuRkZGYmOjt7b1z587Vq1dXVFQ0r2zv3r37448/Fi5cGBERwZu+d+9e/P/WehwcHCIjI+/cucOb+O3bN4SQoaEh38JDhgy5Du1rQERa6fHFjo6OD//d2gLaGPSdgv9q6DEwGAUhbqcZ7w5AOzRz5864Hz+iLlwQd0FAi8Do0Ibo6ekhhKqrqwUv5uHhMWLECLHcu4jDPL7o9MaNG2vXrrW3tw8ODmYymTixqqoqJiam3ltkP3/+fOnSJV9fXwqFsnPnzqlTp5qZmQUEBAQGBu7du9fZ2Rk3UjRJbm7upUuXdu7c6efnt2rVqjdv3uD0tLS01atXBwUF1dvfy+Vynz9/XlNTI8wmunfv3q1bt4Y+5cu/srLy9u3bKioq7u7ufEuampo+efJEmC0CIC4GBgZ0BuPL9+/G2tqClxT8GBgKQtzWnIeiA4PoFPyX4BmrO/7gJACEI5ZzYfu5c2fDw/Py8mRlZcWxfSAyMDq0hcQ1OrSqqurFixfS0tLk5MmlpaUIIXl5+XPnzllaWvIunJ2dTRCEiopK3Xz8/PyOHz+Ov1MFBYWoqKgdO3bQaDQ6nT5mzBhra2tyySdPnnz69KlLly729vby8vICynb48GFPT08KhfLixYuSkhIyvaHOXiw/P//YsWNCRqdOTk4zZ84UZkmE0M6dOwsKCq5cuaKoqMj3kZKSUlZWlpD5ACAuuPu00egUas6tBKLT9sLc3Jxs7wQAtFuNzqoncn8cOxb68mVBwf+xd+fxUK3/A8CfMTN2WVLZIpIsoUW2Vi0ilEqWtEilbqW0b4hK0aqk0kaStF3VTUkLrYpkyZ4la7TJzpjl98d8r58bY52ZMzM+79d93RfnnHmez8Rjzuec5zyfKgkJCRY0D9iqp7NDnZyc2jdCo9HOnj3b3Nyck5MzduxYFxeXgICAyspKCoUyZcoUMzOz3sWWkpISERHx+/dvW1vbtnfwjh49qqenxyjJYT/67NDeZafe3t69mw34/v37xsZGW1vbwMDALg/+9u0bQqh9SllXV2dpaYn/t15xWlqapKSkkZERQmj9+vXr16+nb29ubl65cqWVldXEiROfPHmirq5+4cKFTiqEKygoKCgo1NXVPXnyZMOGDa3b4+LiZGRk1NXVO3yVtLT0lStXunwvPRUfH+/j4xMUFNThw9JSUlL0fxwA+q7Xw7lLpubm106fdp0/nxWNgy5BdsopeKneKa7Tc3S4mARAN1XX1R2+det1fv67xERITXkDU2aHenp62tvba2lpkUgkaWnppKQkBweH5cuXa2hovHnzpnfZKeazQ7uvL7NDvby8enc6S//BTZkypTsH19TUIISEhYX/2C4qKto2Z3v9+vXkyZP5+P5cASQgIMDAwIA+LXbUqFHJyckODg4VFRWtvxt/oC8iFRkZWV9fb2dn1zbmbgbMLN+/f3dycrp06RKjG62ioqJt7+4C0Be9Hs5dmjlz5orly0ktLfxtHrUAbAPZKWA+eEIVgL57lZbmePCgxZw5z168EBAQwDocwARMmR36/PlzFRUVLS0thBA/P7+QkFBBQcHUqVN//vw5YsSIdevWtR5ZW1v77NmzysrKkSNHTpkypfMZwpw2O7QTmMwO7fCyAiP0JYVra2sZ5ZMIoR8/fmRkZDg7O7ffVVpaevv27dZbqVZWVlevXk1LS6PfZWXk77//VlNTa11hsbS0ND8/f+vWrd0JmCnq6+ttbW39/f3Nzc0ZHVNbW8sJNVoB6JykpKTOqFEvUlNn6umxp8fO7+ugfnZrB7JTAADgLPWNjQeuXQuJibl85Uon53mA6zBldmhlZWVrKZrKyspv375ZWFgghAYOHNh2vdbk5OSAgIBly5bJyckdP3588+bN0dHRgwcPZtQdR80O7Rz7Z4fSLysMGjRIU1OzO8fT/52rq6tlZGQYHfP8+XMajdb23mZaWpqOjg5CaP/+/Zs3b267nY+PT7GrR+ASExPbPrTMaGnoVpWVlcbGxiQSqev3g9Dq1avd3d07OYBMJjs7Ox84cKD10dm6urqAgIC2M9URQtXV1Z38EgLAOcwtLB4lJLAtO21dP+nu69duQUEpnz715wlTkJ1yin5V7xQAwMiN5883nzs3febM1PR0OI3jMUyZHerg4ND6NX0hpQ5v6G3fvv3MmTP0kh5XrlwZMmSIq6vrjRs3GHXHObNDu9SX2aG9K5BIv6xAvwrQHdLS0gICAsXFxSNHjmy7vaCg4O7duxs3bsTj8f/884+wsPDo0aPpu96+fduanYqJiYmJidG3NzY2RkREbNy4sfM64c3NzWVlZW0vIsTGxsrKyv4RQFtDhgzJy8ujdW+uU/vpx3/YunXrli1b2hbReffuXfuYy8vLoeA5YBYW1Tulm21puSg4+DjrOuhI4devq44ffxQT059TUwTZKeeAeqcA9HPphYUbz5z50dBw6+5dY2NjrMMBzMf02aFxcXGSkpL0lOYPmZmZZ86cOXHiBEJIQEDA1NT0zZs3XXaK+ezQ7ujL7NDePaV2584dhFDbBXU7h8fjp0+fnpSUNHPmzLbb//rrrydPntjb25NIpA8fPvDz89O3NzU1Xb169dSpU3+0Q6PR1qxZY25ufuzYsc57FBAQGDp0KP2KBkIoOzv7xo0bbW+ldgiHwzFlRehdu3b9888/GRkZrWG3tLRkZ2f/UQQVIZSYmDhnzpy+9wgAYlm9U7qxY8dW19d/qagYxngGBHORWlps9u3z9PLSY9cNW44F2SkAAGDsV02NR0jIzbi4fQcOrF6zpsvbFIAbsWJ26LNnzyZOnNj6C/P582cFBQUhISGE0Js3bwYNGtR6ZFpaGr2gaOewnR3aTeycHXr48OGnT58mJSWJi4ufPn06Li7Oy8ur9YZnJ+bNm/f48eM/NhoZGQ0YMCAmJiY2NvbNmzdbt27dsWOHgYHB+/fvvb29if9df4VGo23YsGH06NGbNm3qTqiBgYE+Pj6DBg1qbm7OyMior6/v5AfHRE+ePPH19UX/FuxtS0NDo+23NBotKSnp0qVLbIgKgL4zMzOLio9fN28ee7rbdv68uq6ua5sHK/otyE4BAKC7mL5uAY1Gu/Dgwe7Llx0WLcrNz29fHhDwDGbNDr169aqqqqqRkVF+fn5WVlbbdYYOHjx48eJF+tfDhg1r3R4fH19YWHju3LnOe8R8dmg3sXN26Pbt27dv396LF86dO3fbtm11dXVtaxR7eXlVVVWVl5cvW7YMh8Ndvnz5x48fjY2NNjY2f7ycRqNt377dysrK1NQUIfTo0SN5efkOb5K3srKysrKyyszMlJWVDQsL4+fnnzt3bi8i76mZM2d28xfgxYsXysrKbX8zAeBks62sQvz92ZOdpublXX/+PCs3lw19cT64Qs8pxo4di20AuK7+AwBQaf+hICf39vRpWmxs63+tCxt0R0F5+bStW0Nev3755k1AYCCkpryt17ND226Mj49funQpfSGio0ePKioqtq7nfP/+fTMzs9Zamq2+ffu2YsWK+/fvdzmjuMPZoV0+dIrD4fi6pzvvury8vPX/jCQmJtJztl7w9vbu3Qt7atCgQRMmTAgPD/9ju6SkpJaWVut8Wmlp6fZVdqhUqouLi4CAwO/fv2/evBkeHn7ixAklJSVGfbW0tCxatOjChQsIIU1NTTExsTNnztjb2w8ZMoSp76mvTp8+TX+8GQCmYPVwNjU1fZmS0tS9uSF9QaPRXPz9fQ8fhhWt6frpvdPGxkb63CfOgXm9UygDA0BPlZaXt3SvlkZ7pyMj94WF7dq9223zZqY8+gU4lq2t7e/fv5kyO1RRUVFTU9PY2NjV1XXChAlOTk67du2SkZEpLy+XlpZetmzZHy1UVlbSs9k/ytUwgtXsUITQunXrKioqcnJyJCQk3r9/P2vWLHFxcScnp9mzZ7c9rI+zQ1lXILG9Y8eOOTo6Ojs7Ewg9O9fy9PRsvQdOJy8v33715lYvXry4fv166zXuwMBACoVCf+SYcxQWFubm5kZERGAdCOAdrB7O4uLi48aMeZGSMqvNcl9tdX7zpvuf67fi4ggiIs5w7eZfuG7Ox+AZFRUVO3fubG5uvn79Otax/AcO1+9+FgBwOxwO9+zYsWk9nPjwq6Zm1fHjX37/vh0Z2Z1HAUG/9f37dzU1tZKSkrazQ2k0WlZWloyMjJSUVOu3I0aMILarGv/169edO3f6+fnRn1z19fXduXNn6947d+7ExcUFBAS077d1dujWrVuLi4s56hZcXFzcpk2ben09l80ftb6+vjU1Na3lbZlIW1s7Li6Ofqelvr5+6dKlERERjY2Nly5devDgwaVLlzhqAi2ZTJ41a9bBgwcNDAywjgXwDjYMZz9f39LExABXV5b2Mn7dOveDB9kzFZ8r9KOZvfb29vPnz/fy8rpy5Uo3S4cDAEDnyBRKj47PKS4ev26d/KhR8QkJkJqCznU4OxSHw2lqatJT09Zv26em5eXldnZ2JiYmL1++vHHjRmhoaGpqaid9wexQVti5c2dlZeWTJ0+Y3nLb5XZFREROnDhx6dKlgIAATU3Np0+fclRqihDy8PBwdnaG1BRwndkWFg8TEljaxbOkpPqWFljLuq1+NLM3LCyMQCBQqdSgoCCsY+kA1DsFgOuMUFHp0czeLxUVY1xcLl2+7LBoEeuiAryk17NDTUxMcnNzX7161brFzc2tk+P7yexQlhZI7NClS5coPbyG1R3JycltnzFWVFRcs2YN03thFh8fH1iKHDAdG4aztrY2iULJKS4eqajIoi7Cnj933bQJHvBpqx9lpz39aGczqHcKANfRUFfv/r3TuJQUk02b/v7773nsWp4e8ICRI0fa2Nh4enr2dHZoTk5Oj443MjKaP3/+xo0ba2pq6LNDY2JiWu/QcgIymbxy5coLFy705dOcbQ+dttV+qSrObJN1IDVlLhqNVlZWVlxcXFRUVFJS8uVLSXFxaXl5WXJyoqKiipCQkLCwsJjYAAkJcSkpKWlpKVnZITIyMrKyskOHDlVSUmo/1YJLsWc4W1paPkpIYFF2SqVS/3n7dl9XC6r3NxydsAEAACcjEAjdzE4Ts7MX7tv35MmTGTNmsDoqwGN27ty5YsWKJ0+ezJw5k4nNtp0aitrMDv3586eenp6bmxunXcuH2aGgH2poaMjPz8/Ly8vPz8/JycvPLywsLCgrK5aQGCgvryItrTB48DBp6ZGGhjMGDZIXFZVACEcmkxoaapua6mtqftXW/qqt/V1UVPL7d2JVVeXXr18qK0sHDRqirKyioaGura2pqamppaUlJyeH9RvlXLOtrPz373drV/aJKd5mZAxVUGi/cHc/x77lAahUKn3p54yMjJCQkNY1Hj5//uzh4RESEiIoKMieMPB4vI2Nza1bt9jQHQCAh9nb2FhratpPm9b5YT+qq8etWRMUHGxmZsaewADvqa+vFxERYWKDZDK5paWF05avZ4RKpTY3N3NLtAD0Ao1GKykpyczMzMnJyczMycrK+fw55/fvKjm5YfLyqjIyw+XkVBUURgwerCgjo8TP38tzZgqF8v17aUXFly9fMoqLM0tKMr98yeLjw+nrGxgZ6RsY6BsZGQkLCzP3rXG1hoYGmcGDS2/cGMDUv8B0/rdvF+HxJ06eZHrLXI199079/PyWLFkyfPjwgQMH3r5928nJib793Llz9+/fZzTrIysrKzMzszvt4/H4GTNmtF3YkLuMHTv248ePWEcBAOiBzOxsy5EjuzzM+ejRpc7OkJqCvmBuaooQIhAIHP7AS1t8fHxMSU29vb0xmdwLQHtfv3799OlTenp6amp6enpGVlaGuLiUouJIefmRCgoaVlbWQ4eOlJFhWOe2d/B4vIyMkoyM0ujR/1/KuKKiKCvrfVpawt9/78/M/KCnp29ubjprlunYHq5Iz2bsGc7CwsITjY1jPnyw6ar4cy/kV1aqTpzI9Ga5HZs+mchk8s+fP1VVVTMyMqqqqqhUauuuFy9eGBsb8/Pzd/jCtLS0ly9fdqcLPB6vq6vLvdkp5vVOAQA99Skjg2xp2fkxrz99Svvy5fazZ+wJCQDQCXbWOwWgLRqNlpeX9/Hjx48fU5KSklNSkqlUqpraGAUFjWHDjJYvX6msPEpEZAAmsdHzVRMTW4RQY2N9Skrcx48xFy44NjfXOzjYL1niyJlro7BtOFtaWz+MimJFdlrw9aupigrTm+V2bMpOSSQSvUr4nTt3iESitbU1fXt1dXVycjJ9xm+H7Ozs7Ozs2BMkAAD0VJfPnfqEh/v4+jK6AAcAAIBXff/+/f379/Hx796+ff/hQ4Kk5KDhw3WVlUdPn75+9eoxgwbJYx1gB4SERIyMLIyMLBBCRUVZT5+GmZvPFRUVXrVqxZo1LmJiYlgHiAFLS8u9e/ZQqVSmr+9V+v07p9V/4gRsyk6FhYW1tbURQmFhYTNnzmxdBvDVq1dUKtXExIQ9YQAAAHN1XlGmuq7uXUbGHVikFwAA+of8/Py4uLhnz+Levo3/9eunlpa+mprhrFmb3NwMxMUHYh1dzygpaaxY4bNihU9GRvyDB2d9fIa5uKzauNFVXp4T82rWUVRUlJOTe5eZaTxqFHNbFhUSqqmpYW6bPICtz5xkZGR8/vx5z549rVvi4uKEhYX19fXZGQZngnqnAHAdfT29zu+dZhUXj1BVhRUmAOAQ7K93CvqD0tLSJ0+ePH0aGxsbS6HQxoyZqq099cABT3l5VU5b+7p3tLSMtLSMKiqK7tw5rqWls3z58gMHvJn+MHxPsXM4W82dG/X+PdOzUxEhofr6eua2yQPYmp1++PABIdT2TmlcXJyxsXEnlZe8vLzOda8KEJFIjIqK0tHR6XucmODMOf0AgE4YGxuTO713WvHr11AFBbbFAwDoHPc+dNrY2JiUlJSUlPS1rOzXz59EIlFy4EBDIyMjIyNJSUkoKMp+NBrt/fv39+8/uH//QWlpiaHh7FGjJh854ikvr4p1aKwiI6O0bt3JZcu8AwPdRoxQDwwMsLaei2H6zc7hbDV37gpHR58VK5jbrLCAQENDA3Pb5AGy7OgkAAAgAElEQVRszU4LCgqEhIRaq/r8/v07JSVl3759nbzEy8sLrnQCADgTkUhsaWrq5AARQcHfv3+zLR4AAI9pamq6fv367YiIV2/eqA8bZqiuLispOUJKqolE+llefmrfvkUZGdIDBzo5O2/eupV7F4bkIjQaLS4u7sqVsPv370tJyRgYWK5eHailZdR/LhCIikrs2BGSmvpy8+bV798neXjsxPwmKhvo6+v/qK4uKC9XYWptWKVBgwoLC5nYIG9ga3Y6YsQIEonU0NBA/z329vamUChTp05lZwxlZWWt/wcAgL4gEImdz+ydrKNj4+3948cPaWlptkUFAOABTU1NQWfP+vn6GmpoLJ406c6WLYIdLa5Go9FyS0oOXLumoqR0yNd38dKlAgIC7I+2P8jOzg4ODr169aqYmLSp6fIzZzyZXu6Fi+jqTr5wIe3cuS2GhhNjYh7KyspiHRFr4XC4OXPm3HvzZtPChUxsdrya2j9v3qBNm5jYJg/A0Wg0tnVGJpOXLFlCoVAWLlz44cOHuLg4eoGZTmb2MpGrq2tZWdnnz59LS0txONyYMWMkJSUXLFjg4ODAht67BPVOAeB8fDhc538xcQhRY2PbbrE9cMBs0SJnZ2eWBgYA6A6uqHfa0tLif/z48WPHDNXV9y5dOlq1WzNFMwoL94aG/iST7z54IC4uzuog+w8ajXbv3r0DB3yLiopnzFhsarpUWZnJDx9ytfBw3wcPAhMS4hXY/hgLm4fzw4cPj3h6xh49ysQ2P5eWzty160tJCRPb5AFszU7pamtri4qKNDQ01NTUjIyMwsLC2BwAZ8LhMPhZAAB6BNeN7JT23+z0cUKCa1BQanq6kJAQS2MDAHSJ8z9qMzMzlzg4KElK7l28WLd7eWlbGwIC4rKyEj5+FBQUZEV4/QqJRLp2LfzgQT8iUdTR0cPIyLL/TN/tkaioi0ePrqqqqpKQkGBnv2wezs3NzYOlpfPDwqSZevVHcs6cnLy8wYMHM7FNbse+YRYdHT179uzq6moxMbFRo0ZFR0cXFBRs2LCBbQEA1uHDdYaPJxasA6B3ZunrG6ipue/ejXUgAACORqFQThw7NmXChL9MTf/28upFaooQOuXqOgCPFxISqq2tZXqE/UpkZOTw4Wpnz15bs+b0mTOJEybMgdSUEQuLldOm2c+da0OlUrGOhYUEBATMTE2j4uOZ0hqfiQnOxARnYvK7tnbIkCFw5twW+646TJkyJS0t7cuXL+Li4k1NTXp6egsWLPD29mZP75yP8y/odqLzG0o4hLj3rQHQVi/unSKEyr5/N1i//lJo6KxZs1gXGwCgSxz7Ufv9+/cF1ta0+vrQHTuU+/wI34ojR+oEBW/cucOU2Pqb8vLyFStccnMLN226MGqUMdbhcAcqlbpt2wxz84kHDnS21ilzsX84X79+/Vpg4IMDB/reFM7EBM6cGWHfdSArK6vQ0FBxcfH8/Py5c+cuXLgQFuNtC+qdAsCr5AcNivLxWTBv3v3797GOBYB+jTNPPLKzs/XHjTPX0npx/HjfU1OE0JmNG7PT0s53ryAfaCsnJ2fs2PGDB485fz4VUtPu4+Pj8/K6c/p04NevX9nWKfuHs6Wl5Yvk5FqoAcNi7F4ViX7Tn0AgwAQJjtL5Wi84hKid/p7AvVPQT/Tu3ild4devKosWPXr0yMzMjBWxAQC4UWxsrJ2NzbHVq5eYmjKx2aKKinF//fUxNVVRUZGJzfK2wsJCFRWVnTuvzJq1FOtYuNKxYy7jxil6ebljHQgLzbWwsBszZtGMGXxd3fykMjgZ+N8BcO+UMbamiAQCgZ+fn5+fH1JTTkPr6j8AQB8py8q+PHlyqaPj3chIrGMBAHCEh1FRdgsW3PLwYG5qihBSkpFxNjM72GlJedBWVVXV5MkmO3aEQGraa/Pnbzh79gyZTMY6EBaysbe/8fIlgjNnVoIsEQAA2GSSjs7Tw4fXr1kTcPIk1rEAADB2/do1C0vLp0eOTBk9mhXt71q06M6dO7m5uaxonPecOnV69OiZZmbLsA6Eiykrj1JWHhUVFYV1ICxkbW0dB5N7WQyyU04xduxYrEMAALCczvDhb0+dOnvy5OfMTN5e3hAADsQ5azEGX7q0bfPmpKAgneHDWdSFpJjY7kWLPGDB8G6gUqmhoWELFmzCOhCup6qq9/EjmxZSwWQ4i4mJTTcxuf3iBfu77j/6e3ba3NxcV1eXmZmJ+fTu5ORkbAMAALCH4pAh8adOTZ0yZamjI+Z/eQDoVzhkVaTQkBD3Xbtijx0bq6bG0o5WWlg8fvyYnQvVcCkajVZcXDh06EisA+F6I0aM/fQpgz19YTWcFzs5XYfslJX6dXYaEnJVUVFTUnKIoeECQUHxyZNnV1RUYB0UAICj4Tr9r5vERUULw8OvRURYzZ7NwlgBAJwn/Nq13Tt2vPL3H6GgwOq+xISFF8+ceTYwkNUdcTscDsfPL0Amk7AOhNM1NTWcPbvT1dXa2lp5w4b558+7k0hNbQ8QEhL7/bsaq/DYw8LC4mNODtZR8LL+m53q609Zvdr327f7ZHJNbW0WiVT0+rWpnNzQuro6rEMDAHAu+moHLQgVIXQboZcIff3vKgiTN23zDA6OTU5uJnV2osNPJDbHxBTl5h5iRuU0AABXePXq1UZX18e+vipycuzpcb21ddC5cy0tLezpjkvx8fGpqqrl5UFtv84UFmbY2WlFRjakpy+urn726ZP9nTs/7O112iaoAgJCpE4/+3iAgIDA4sWLsY6Cl/XT7PTgwROJiS9JpBSEtBDCI4QQkqTR3Gi0QDk5td+/f7M/JK6ud9r53aTu31ACgCskIzQciY5EEsvRDHM0ahgSXIREWz+NLR0O5LfIbLwQLjFn7tQt2/2uX0/Ny+uwHX4i8c2pU/4nTmRnZ7MteAD6M2xn9ubk5NjMmxexZ4+WsjLbOlVXVNRWUXnw4AHbeuRSVlYWz55dwzoKzlVd/dPZeVRNzeGWllMI2SCkgpAtiXSuqspj/nzVurr/3S+trCySl5dnT0gYDueVq1f3sQU4c+4EW+uddhOVSuXj4yOTyQQCgRXtV1RUKCtrNDXlITSw/V4i0cPR8XtwcP+qYQ0FSwHoDhwO9w/CzUGIhm4iZPPvZjIeLddC0YnohwBCsbH/GyyNjXWpqS8T3z/4kBjd0FBjZWRkM2nC9LFjBfj527bp6Os7097eycmJvW8FAMBW379/N9DT83RwcGJ7xeNLUVGPPn++ffcum/vlLj9+/Bg+XO3y5YyBA2WxjoUTbdlinZw8ikbrYLIPH99uQ8MvPj7hCKHwcF8xsapjx/zYHiC7dX3m3Gm9U0bO3b9/IzEx9tWrXgfGAzju3umtW7dHjzYREpISEZEaOdL44MEjTF/WMi8vD48f2WFqihBqaZmakJDF3B4BADzDCtFo6HWb1BQhRKCgq2nIWAANaHukkJCooeFs141nroQVBJxJEhpm4h5+X3reggXeB6Li4ykUCkLoZ3V1+OPHaixeGQUAgK3m5mar2bOdZ85kf2qKELKZMiXm6dOamhr2d81FpKWlbWxsbt06inUgPUYiNd++fdLHZ/26deZnz+6Nj2d+QRcajZaW9oxG29rhXip1/cePT+lf//xZpqjIpnunPGmVhcWvioo7d+5gHQiWOCg7pdFo5uYLlyxx//TJvakpm0T6mpvru2/fU0vLVcztKDk5mUYbx3j/uIICLp5kCwBgndWrXQkET4SMO9r5t5DQkLNnEzp8oYyM0sKFm4+fehsWXqg8zm5XWOQQG9uF3vsHz5t3+NAhY+MOGwQA8IiN69fLi4i4Y/Ssmrio6Ixx4+7cvo1J71zkxImj797du3fvLNaB9EB+fpqDg+6lSx+ePlXNzHS9eZO6f/9uT09n5vZSVJRFJA5FSILBfjmEhL9+LUQIZWXFjxnDkvq9/QQejz+5bt3WTZuampq6PppHcVB26uKy6enT7ObmVIRmIjQYIRGEJjc3P46OTjM2ZuaylmPGjMHhkhjvT1JRwWBcYVvvFKa/A9AdSUl5ZDKja1t4Mlm3rKzjR0xbiYtLW1quOhWY4B/wjl/OQFRM4s27D69fv2Z6qAB0ori4+Pnz53fv3g0JCfH39/fy8jpx4sTly5fv3Lnz9OnToqIirANkFUwKJIYEB8fGxFzZsYP9XbdynDbt2pUrGAbAFQYMGPDPP5H+/mtzcjo5S+Qgv35Vrlyp++uXR1PTVYTcEJqN0P7GxoTXr2OOHvVkYkeSkkNIpDLG+8ktLd8lJAaXlOT++FE2adIkJnbdCWzLF7PuzHnq6NHjhg8/feoU02LlNpzy3GlaWpqRkVlDQ2ZHF2aoYmImgYErlyxZwpS+unru1N3R8Qf7nzvF4TjlZwEAYERWVq2i4h+EOq6Jx8fnvmyZwNKlHt1vsKmp4eHDS5GR/vr6eqdP+8vKwvNOgCUqKyujo6Pj4xNSUtIyMtIEBUVUVDQFBERFRCRERSVERCTq66sbGqobGqqbmuoKCjLq62s0NEbp6mpPnjzBzMxs8ODBWL8D5mD/R+3Hjx9nzZjxyt9fXVGRnf3+oZlEkrGxyczJgT8yXYqNjZs7d97p0+8UFTm6/CmNRlu9etrnzxMR2t9uJ5lINNyw4S9LyxVM6YtEalqwYERd3UuEOlzQK11Scv6NG+nh4b4iIr9On/ZnSqddwvzMmUKh6Gpp7Xd0nMfshDyrqGjypk0FRUViYmLMbZkrcEpGFBoaumpVNIkUzmD/MSen4uDgk8zq7uDBE97eV0mk9wgR/7vnMUJmVVVVEhKMZi+wCuZjDADQJXPzxdHRMxDqeAUjAYHp+/Zt19ef1dNmKRRySIjXw4fnr1+/Zmo6s89hAvA/r1+//uefqKio6KKiQgODWerqxsOH66io6IiLd7zyQqva2qrCwvQvXzJTUp4kJj5VURk+e7bZkiWOmpqa7ImcRdj8UVtVVTVWV9ffxWXuxIls65SRFUePapmYbN6yBetAuEBw8JXt23cFBLyVkRmGdSwM/f793dZWo6XlB4P9j9TUTgYFRTOruxs3Tl28GE4mx7e7L0hBiLBp04XZs5c5O2uGhwdPZNdvOyecOcfExLg4OaVduDBARIS5LS/z81MeP95r3z7mNssVsP+50rm4rL9wQQ2hDQz2v9HU3JaR8ZZZ3dFoNB0d/fT0DwilI6SOEB6hKhzuCoHg/vZtnJ6eHrM66j5OGGMAgM6dPHnKze0OQi862llCIOhcv54hLd3LMobZ2Yl//aV/8+athQttuj4aAMaKi4tDQkKDg0OIRBFDwznjx5tpahri8fjetUahkDMy4j98ePzo0WUlJcXVq1fY2tqKi4szN2b2YPNHrc28eUOJxBNr17Ktx048//hxx9WricnJWAfCHUJDw7Zt27l//301NSwfvOrE+/ePvL39GxsfM9j/TVBw1MOHlTgc0x7PsraWr64uR6gOodZMrIZAsJKQKLl1q+DyZc+GhtzbtyOY1V2XOOTM2X3XLh9f38bHjwX/uyB/H32pqBi7Zs3n/PyBA7u4mMh7OOW501Gj1Pn4Mhnvz1RVZeb8ChwO9+lTYnBw6ODBc/D4AWJiGvz8ShMnxhQW5mCSmiIur3cKQD9Bo9FwuDyE3NvtqUJIkUbr019UdfXx584lrl79148fjK6FA9CFx48fm5jM1NEZk5LydceO6+fPpzo779fWntDr1BQhhMcTdHQmOTsfuHGj1MbGMzw8WklJZevW7ZWVlUyMnD3YWSDx0sWLnzMyfFeuZFuPnZs6enRZaSlUV+6mpUsXBwSc2Llz1osXHLp6KoFApNGaGe9vxuHwTExNEUKRkaXW1jsFBEbw81vw8Xnw85sLCKjNn28SEfG5vLzg/v3AkyePMbG7LmFbvrjVgUOHHGxtrdzdv1VVMbHZYTIydlOn9s+nTzniqgNC6PHjx3Z2HtXV7zpMmIWFV+/apeTuvpvp/TY3N7e0tBQXF2toaDB3DAMAeI+5+eLoaCOE1iM0BSF3hPQR+oZQGkLrEHIQEEjt3czettat07t06bShoSGzYgb9AZlMjoiIOHToCIlEs7ffNXnyAiKRmVfx//DrV0V4+MGYmKtLlizZs2ennFwv5wvwsNzcXGMDg1f+/hpKSljH8v+2nz9PUFQ86OuLdSBcIyUlxcJijqXlOgcHLBe16tCvXxX29qMYz+x9oK5++syZR0w/uS0qyiopyc3PTx0xYszQoSOHDlWjUMjbt8+cO3e6p2f7S7f9xfatWy9furTDzm65ubk0k6aW5BQXT968uai0VFBQkCkNcgtOyU4RQhMnWsbHj6JS2//RvImQXX19vbCwMAZhAQDAv/5dFWkEQr4IxSCUipA4QhoI7UFoIg7n7uTUs1WR/pCXl7Jq1Zhv374NGjSIiWEDHkalUsPDw/fs8Rw8WHnhwm36+uwrp1lV9e3OnRMPHpzfsmXztm1b+tv5UyfIZLKBnt6aGTNWWVpiHct/fCoosPDwKCothcvx3VdRUWFlZS0oOGTHjiuiouxelKRzmzZZp6RoInSw3Z5mhAS9vG5PmbKA1THQaDQvrwWyssIREWGs7ovD5ebm+vr4RN69qz18uMX48VN1dcerq/Px9WlSleWePdZOTitXMbm4JofjlJm9CKG7d0OoVD8+vpkItfy7jYbQMYTsU1NTITUFAGBOQUEVoRyE+BDajVAcQlUIfUHoEUITEUIEQo68vGqvG3/+PGLVqjGJiYmQmoJuevTokbb2mMOHz2zffu3IkWfsTE0RQpKSg1euPHTuXNLz58kjRqhHRkays3dOtt/bW15MjNNSU4SQtoqKpIgIlLDqERkZmTdvXo4ereziMjon5wPW4fyHh0cQQocQ8vvv5hoCwVxRcTQbUlOEkJ+fE4XyKzT0Mhv64nBqamqXr1wpr6jYffBgpZCQS2Cg9Lx5C/ftC370qKq2tndtbl248ExAAHPj5HwclJ1KS0s3NjYuWKDIzy8tIjJOTGwagTBg3LiogoJ8HR0drKNjOWzrnQIAumPcOFUCgVEdPAqBkNq77PT9+0fbtk2/cWNfYmIiVo++A+6Sk5Mzfbrp2rWbHRz2nTr1VkvLCKtIZGSG7d17e8uWK1u27FmwwJbDn5pmQ4HElJSUs4GBQW5urO6od1zMzQP82VTwg2fw8/MHBPgHBp7Ytcv83r0zWIfz/6Skhty5UyEpGSQiYorQToSC8XgXQUHd2bP1Ll9meSJNoZCXLh358uXtp0+j+Zm6IFA3YVvvlBEhISEzM7Pj/v6pGRk5eXmWy5Y9zs8ftmiRlbv7jefPSS0tXTfRxmQdnbKysvz8fBZFy5k4aGZvq6qqqtzc3NraWj09PfZXdsEKh6w8BgDoxPfv34cN02pouIdQ+2RgtKGh1qFD17rfWmFhemzsjZcvb0pIiLm5rXd0dCQSiV2/DPRv9fX1+/f7BAWdX7LE09p6fR+njTERmdxy+bJ7TEzIuXOBNjYcuu40qz9qW1paxo0evd3aevFMDi0NVdvQMNTOLvvzZxkZGaxj4T4FBQW2tg4CAoO2bQuWkOCUSS5UKjUu7lZh4efi4s+6ugYaGnoaGvqs7rS5udHDY+7AgQL37t3BJDVFXHXmXFdXd+/eveALF1LT0paZmq6aPXtktwsguwUGDtbV3e3ej57p5ZqfK8/jojEGQH8WFfXI0nI2QhEI2f27rYWPz4VKDYmJae5yKZqqqm/p6W8SEx99+BBDIOBsbRfa29vC/VLQTU+ePFmxwkVd3XjNmmNSUpyYXWRlJfj5LZk1a/qpUycEBASwDudPrP6o3evhkfbyZSRH3tJp9Ze/v+zo0Z6csd4p12lpaXF39wwODt2x48q4cTOwDgcbeXkpPj4OpqYmZ84E9GU98D7ixjPngoKCC0FBwZcvjxw6dPXs2fMnT+6yDs2dFy+uJiTcjYpiT4ScgPt+rryKG8cYAP1Tdnb2rFk2FRXfSSQdQcE6CiVn0qSFW7ceExIS7fD4srK8lJS4jIzX6elvqqt/GBlNMDObOWuWqYaGBpsjB9yrtrZ206atUVGPduwIHT16KtbhdKapqeHIkeXfvuX8/fetESNGYB3Of7D0ozYrK2uikVHG5csyUlIs6oIp0gsLZ+3aVVhcjNUtLx4QGxvr6Lh08mS7FSsOsnR9bA5069bx8PCDp0+fcnRchG0k3HvmTCaT79+/fyko6N3794umT181e7bO8OGMDs4vKzPdvTu/qIidEWKLW3+uvCc1NVVXVxfrKAAA3UImk2NjY+fPt/HxeaCgMKL9XayWFlJCQvTLlzdTUmLxeL6pU6dOnTppwoQJmpqasFom6KkXL14sWeKkqzvjr7+OCwuLYR1Ot9y/fy4szDs8/OqMGRx0f8nb23vv3r2saJlGo000MlpibLxmzhxWtM9cdgcOjJ0+fceuXVgHwsWqqqqcnFZkZRXs2XNdSalfXGosLs4JDHRFqO7mzetKHFAqiXXDmW1KSkouX7x46eLFIRISLubm8ydNGtiuGk1afr7jkSOf+lOlYshOAQCgN7Kzs83NrYOD//zAKC39fPv2sefPb+jo6C5b5jh9+nQVFRVMIgQ8gEql7t3rfe7c+R07QvX0OPRRRkY+fXrj7b1gz55dmzZtxDoWlrtw/vylgID4U6e44vJTdnHxJDe3gqIiMTHuuNjBsS5cuLh9+04np/1z5/6FdSws1NTUEBZ2ICrqvKenx4YN6zGczcuTqFTqkydPQi5efBgdPVFHZ+aYMeb6+sPl5Ql4PJVKnbV9+0Bl5Yhbt7AOk30gOwUAgN7Iy8ubNs0sNDSvdcu3byWBgRvS099s2ODq4rJSVlYWw/AADygpKbGzW0QmC+7cGSYlNQTrcHqjouKLh8ccKyvT48ePYh0LC3379k1bUzP26FHNYcOwjqW7Fvn4aEyc6MHlt544wefPn+3sHEVEZLdtCx4wgKMndffO69d3AwM3Tp488eTJY7CYFks1NDQ8evQo5tGjZ0+fln79Kjto0JeyMn4iser3735VWROyUwAA6I0vX75MmDD12rUv9G/v3Dl59eq+PXt2r1v3V7/6FAEs8vz5czu7RTY2W21tt3DF7ThGGhvrduyYNWPGBD8/H15dlXqFk5NkU9PRNWuwDqQHyn/8GLN69cOYmHHjxmEdC9cjk8nbt+8MD7+xZ891be2JWIfDNBUVX06dWvfjR+H582emTuXox915T3Nzc2VlJT8/fz+8IsApK9EDqHcKAHchEonV1b/oXwcHu1+7tj8x8d22bVsgNQV95+t72NZ20Z49EXZ2W7k6NUUICQmJHj36LCnps7X1AjKZjG0wrCiQmJCQ8Cgqau/SpUxvmaXkpKVPrlu32MGhubkZ61i4HoFAOH78aEjIBW/vBVeueFOpVKwj6isSqenKFa+1a8fPmTMlIyOVM1NTzqx3yiwCAgKKior9MDVFcO+Uc3DvymMA9E+VlZUyMjKxsbSIiCORkcfz8nLhCS7Qd01NTU5OKzIyCjw9bw8aJI91OExDpVKXLVNXVpaPi3uGYY1Wpn/U0mi08WPHus2ezbEFTjtBpVIX7tunPGbM0RMnsI6FR1RUVDg4LG5owO/Zc517Z/m+fn33zBk3Y2ODkyePy8tz7l8hOHPmVfBz5RQwxgDgLj9//pSWlj537oOnp1Vq6sf+eYETMFdlZaWFxRwJCeUdO0LpZSp+/CgvKPiUnZ0gL68qL6+qrj6+k5enp78tLc399atSU9NAVXWMqOifaz+2at9sdnZiWVleWVmeurq+ioo2Qqj7/XautS9ZWeWICD81NaX79yOxmuLL9I/aKyEhF/z9X/v7M7FNdvpdV2eyZYvZvHmHfH2xjoVHUKnUHTt2hYVFeHn9PXIkl82aLinJPXNmQ1VVydmzp01MTLAOpwtw5syr4OfKKWCMAcBdampqxMXFzc2XTZyovnv3TqzDAVwvKyvLzMxi5kznxYvd6Vvu3Am6cMEdIR0SyYhAyCEQUnV1x+/bF9y+vmJlZbGnp3Np6XcSSZtKleXnj+fjy/f2vqanN619R+2aTREQIDY1tVAoo8nkkfz88WRyMg5Hw+PHdtlvl9r3JSTEZ2ZmePVqMCZ3UJn7UdvQ0KA2fPgdDw8DTc2uu+7JuT4OIWpsbNstfCYm3Yy7/Ws796umZurWrQPl5GLj4rr/KtC5yMjIlStXOzsfsrBYgXUs3dLQUHvtms/Dhxc9PPZs2OBKIBCwjqhrcObMq7jgl6+fSElJwToEAEAPEAgEPJ7w5s39sLDjWMcCuN6rV6/mzbNZs+bEjBn/K3C/b9/yV69ekckfERqKEGppQS0tlIQE1zVrZp8797BtolhfX2Nvr4TQfoT+l9Y2NSGEkrZt0zt5MkFH5z+3PTtstrFxLUJ5CF1DiL+5eTlCXxCKI5O76LdLHfbV3Lw+MjJ6zZp158+f7cu/WO94eXkxsbUjfn6TtbW7k5rStZ5H49p83aH2jxrTuv3ynj6mLDVgQMLp00KzZpmZmoaGhQ0ePLiHDYAOzJs3T1NT09JybkVFvrOzD4c/PZ6YGHP8+Mrp002yszOGDOGa5cGZO5wB54BVkTiFrq4u1iEAhlxcXKSkpC5evFhbW4t1LIBTEAgECoU8cKC0lBS3PlzE2/j5+S0sLB49esT5K5Q8ePDA2nrBrl3hranpp0+vY2NDyOREel73LzyVeubLF3FfX9e2L9+8eT5Cy1tT03+NQyhj61azsrL81k2MmkUoCCEJhFwReo1QCEIfutNv5xi/hbPNzWMiIqL8/I50vzVm2cu8Airfvn07HRDgt3IlsxrEkCA/P+nJk7EyMloaGrewK6sYFxeHw+EOHDhQXl6OVQxMNHLkyMTEd7m5cQcPOpLJLViH07GGhtqTJ9f6+6+8efNaWNgVLkpNEVOHM2C6vgxnyE4B6FpaWlpVVZWbm9ugQayIcTkAACAASURBVIPmzZv39OlTmEwC6A/OCQgIYB0I6FhLS8vDhw/t7OykpKQ2bdqUnZ2NdUQdCw+/vnz5Kl/fx+PGTW/dGBTkg9AdhCTbH0+l3nj16uavXxX0b9PT35aWfkfockdta5LJu65e/f9Co500i9ANhG4i5NnNfrvU6Vu42dhY4+vrh2Ei1HcHvL0dp08fyit3GokEwkFn5yd+fgfd3VWUlPbs3p2RkcHmGOLi4hBCPj4+KioqxsbG169fb2pqYnMMzCUhIfHyZWxW1it7e6WWFhLW4fzpy5fMNWvGioo2ZGWlT5o0CetwAE/py3CGmb0AdFd9fT1C6N69e8+ePSMSiStXrly3bp2ioiLWcQFs0GdqQTEGDkef7xAYGBgUFKSkpOTq6rp48eIBAwZgHdf/vHz5avXqv06efEVfiKhVcXEWQjoMXkTA49VLSz9LSclQKOQvXzJIpFGM2qfRtNPTb6elvaJQyBQKuaAgtZNmEVJHKLOTA6jUYT4+DmJikhRKC71BMrml9f9/fPHtWw1CAYyaIpMVSaRCf/9TCxcuZBQ8JyspKbl+/Xp2cDDWgTDZaFXV96dPf8jJuf3mzfQpU/AEgpaWFg6PHz1mjLy8fFlZGYVCGTFiRElJyYEDB1gUA/0UNj4+Pj09fcWKFTY2NmvXrjU0NGRRd6wmICBQUlK8aNHijRsnHD78RFRUAuuI/ic+PurIEaegoLMLF9pgHQvgWb0czjQazczMrPXbx48f0/4F22E7bKdTV1dH7QgKCiKEaBhpGwlsx3Z7Y2MjR8UD2zshIiIiLi5Ow0LbR6S8vLxoNNqNGzcQQgoKqq3b5eSGjRkzSUfHCIcTQqj634cN2/83g348DofD4/EIuTE+MpWP7/9nnuNwgp02Ox8h4e706+Dg8PDhw5iYmNjY2OXLl7e2v3bt2pycnPz8/OLiYjxepMum6P8OjP59OH+7++LFDdHRNVFRVf/8s83evnX7xgULPoeFZV25khEcvGbOnNbtrW8eMf53aft8qamenp+Li8+KFfuWL+/+yxFCZkZGKm0KgcgNGqSnqamjpqapojJQ/P9XchYREpKWlBwgKiosKIhvs0gVkUAQExGRkpBACOHxePRfA6Wk0H8f+WPWv+eUKVNQO/TleXoz5FipL29z2TKv2Fga/b9ly7DZPnnyAqb/+GA7bGfWcIbVrjgFrDzGyQwNDd+/f0//GofDiYqKEonEVatWrV27Fu6d9mc4HE5Hx9jX193c3BzrWMCf2i5DQiQSCQTCsGHDXF1dHR0dOefeaVhYmKCgID08AoHQ+sWSJW4FBQdbs8E/CAjIZmS8VlFRweFwcXFxlpbu9fWvGfRw3tr6XWTk/+b9jho1NSPDnVGzCMkhpIjQAUYHCArK5eS86+Yfvc776lFTTMSsj1r6bxc/kUgkEHA4HD8/Pw4hIpGIw+EIBAJ9I/0H2rolITm5R6siubm68uHxeDyeQCTi8fgDPj7dXxXp4cOHBAIBj8cT2mj9lkgkMvoaw1K0CCEvLy9vb+/Wb8XExMhk8sKFC9euXWtgYIBhYMyybp3ry5cf/PxihIWxLI59//7ZEyfWFhQUKCsrYxhG38GZMyfry3CGmb0AdJeIiAiZTJ49e/a6deumTZvG4UvwAfYYP97i3r0HkJ1yLDExMT4+PmdnZxcXlw4nQWBr8eLFHW5futTa1/d0U1OHqd2NIUMGKikp0f8EjRkzho8vH6EkhNpXViQJCBy2s/v/GZgLF5rm5zNsFiEphCwQOs0gpbwxeLCUnJxc1++qG331qCkO1Itz4p5+ZJw4darttwd8fLr/Wq7+iyQoKEij0caOHbthwwZra2v6NCXeEBgYsG7dhitX3FevPoHVhYDnzyOuXz+Qk5PD7akp4Aq9G85w1YFTwBUgTrZq1apXr15t27bN1tZWTAzLS56Ao+BwuJs3S5ydtcrKSjjndhyg4+fnNzU1Xb9+/cyZM9vPTuRwFApFXV0/P9+MRvsjJ4lHyDgzM1NDQ6N1099/37O1XUKhfEBIrc2RJAJhpbT0i69fi7rZLEKZCKkhpI+QGUJd98vEt8A2GH7U4nC4Ht07/SPO7r+8/Wu5RVxcnLW19bZt25ycnOTbzEzmJWQyeeLEKaNGmS1e7MH+3tPT33p7z09KSuCNaV9w5szJ+jKc4d4pp4B6p5zswoULWIcAOJGwsAgeT9DXNwsKurBt2xaswwH/QSJx3AqZ3YfH45OSYsXFxYWE4hsblyJkhFAOgZDEz3/25s2Hf+R18+fP9fPz2bp1JB/fYSpVByFZhOKFhS8YGSlFReV22Swen0ihHOfjW0SlfkaID6GVCK3F4WJpNJfO+2XiW2AbKJDIyaZOnfr792+so2AtAoFw797furpjVVXHGRrOZmfXFAolMND1yBFf3khNEQxnztaX4QxXHQAAoJfk5Ib6+79taSGtX2+Qk5MJVewB0508eSo6OiElJUFBQXXcONX9+z0GDRrU4ZH5+fk+PseSknJ+//4+btx4OztTOzu7bja7ceNfJ0+eTUrKKy3NGz1a38xMn0ajPX6c2J1+mfgWeFuPZvbiEKL+9/SMr829056+FnCa1NRUE5OZ58+nSEuzb377zZtHs7KiY2Ofsq1HAHoHslMAAOiloUOVDx9+LiurHBS0RUys/vz5c1hHBAAAgAu4um4sK2vZsOEMe7prampYtEgpNfXj0KFD2dMjAL2G5eJsAADA1QgEAoVCRgg5OnrcufM3+4vXAwAA4Eb79nm9fHm7sDCdPd29f/9IR0cHUlPAFSA75RRjx47FOgQAQM/U1Pwmk1sQQqKiEkuXeq1YsZpKpWIdFACAobYVDgDAkKSk5MGDPmfPurGnu+fPQ5cvX8qevtgGhjOvgpm9nAJWHgOA6+BwuIsXU4cP16F/u3PnLDOzCV5enthGBQBgBD5qAecgk8mDBg0JCkoZPJi1tzRbWkhz5kj+/v1LQECApR2xGQxnXgX3TgEAoPfoM3vptm0LCQg4/eHDBwzjAQAAwBUIBML8+fNfvLjJ6o5qan6KiYnxWGoKeBhkpwAA0Hv0mb10AwfKbthwxs5uUWNjI4YhAQAA4AoODnYvXtxgdS+VlcVDh/JIFRnQH0B2yimg3ikAXEdObmjbe6cIoSlTbEaONHZ2XoVVSACATkCBRMBRpk+f/vXrl58/v7K0l8rKomHDlFnaBSZgOPMqyE45ha6uLtYhAAB6RklJ+Y/sFCHk5nbuw4dPAQGBmIQEAOjE3r17sQ4BgP+Hw+FUVUeUleWxtBdBQeG6ujqWdoEJGM68isDqDmg0WkxMTG7u55KSMmNjAz09PQUFBVZ3CgAAbNBaUaYtfn7Bffvurl07Xl9fz8DAAJPAAAAAcAVVVdXKyiKEJrXdSCI1Nzc35OenqamN5ecXJBCIfelCWlq+vLysb2ECwD6szU6/fPkyZ87SoqKWujpdKnWokNBFPr7VZ86cWrrUjqX9AgAAGxCJRAqlpf12WVnl7dtDFiywTUlJkpaWZn9gAAAAuAIej29pIbXd8vr1P0eOrK+vrxIS0m1sTJaUlPf0vKytPaHXXQwcKPf1a3mfIwWATVg4s7e6ulpZWfnTJ6uamngq9RxCexobH9TXv122zD4y8gnr+uVSUO8UAK5TVFTQ/t4pnZGR5YwZTnPmzGtp6SB9BQBgAgokAk7T3NzMzy/Y+q2Pj4u395qamvsUSnVd3SsKpfrHj6BNm2ZnZ2f0ugtxcemWFvK3b9+YES8HgeHMq1iYnc6caYOQC0Lb/rt5OEJl9vaLYBGgPyQnJ2MdAgCgZ/LzPzPKThFCy5Z54fGS69dvZGdIAIBOwDIqgNOkpaUOG6ZF//r163+ePr1AJucipIsQDiGEEB6hqRRK1tq1Y3JyknrXBR6PnzZtYUhICJNC5hQwnHkVq7LTlJSUrKxihII62ilHIu3fv/8Ei7oGAACWolAo3t4HR42aipCAj8/a9evN09JetT8Mh8Pt2nXt8ePnFy5cZH+QAAAAOByZTC4oyFNUVEcIkUjNR46sRygFIZF2B8rRaHcOHVpLpVJ719HUqY6hodf6FiwAbMKq7DQrK4tM1mG8XyclJYtFXQMAAOvU1NSoq+v7+iZkZLgj9K2p6WVGxqqtW+1iY2PaHywsLObjE7Vz5574+Hj2hwoAAICT5efnDx4sT1/0qLm5ob6+CiFGJ88Ty8qycDhc7zoaNcqYREI3brC8tioAfceq7LS6uppGG8h4v1RDQzWLuuZSMNUZAK4gLi6en2/W1HQXoRkIDUBIFaH5LS0Z+/bNiozs4B6pvPzw7dtD5s2zqaioYH+0AIC2YCog4Cj+/qemTVvEx8eHEMrPTxMSap3Q254kgSBZWVnUu47weML27VfWrl1fVsY7i/fCcOZVrMpO9fT0CIR3jPe/Hz1aj0VdcymodwoA5zt58pSQkAmN5tNujyRCxUFBu3786GBdRAMDcwuLNdbWNrBCEgDYggKJgHNUVVWFh4fPnbuO/q2a2tjGxmSEKAwOr6RS62RkhvW6O1XV0QsWbFZQUPj9+3evG+EoMJx5FauyUy0tLWHhWoQed7SzhUh0X7bMikVdAwAAi0RHJzQ2LmWwcyhCOgUFnzrct3ixO5E4cMOGTayLDQAAABc5d+68vr6ZlJQM/Vt+fkFJSXmEOljFACGE0ONhw0b1scdFi3YtWbJr8mSTmpqaPjYFAOuwKjsVEhK6fTsEodkIJfx3TzOBsHTgQD57e/uetkmj0UJDQ93c9piYzNm50zsyMpJZ0QIAQHekpCQgZMRoL4lklJ2d0OEuHA63e3d4dPSzsDBYlwIAAPq7169fHz16bNWqw61bCASip+dlPH4uQu3n4GQgtMzT81IvOmpsrC8szHj0KDg9/e2vXxXOzgfHjrXS0tKJjo7uQ/gAsBALK8pMnjzpxo2bCBkQiXsQuolQPELHRUQMTU1xX77k9rS1iooKXd0prq7XTp7kj4tb4edHcnLynT59Qa+XL+M0UO8UAM6noKCKUA6jvQRCjry8KqO9QkIi7u43XF035ufnsyY6AEAXoEAi4AQVFRWTJk3avv3K4MFD227X1p7g5OSJkDxC/yBUhRBCqBKhK3i8kbf3vU4+Xxh5/fofGxuVv/6aHxDwYts2N3t79TNnPJct83Zzu7hixV8uLn9x9WOoMJx5FY5Go7G0g8rKSj+/4x8+fP72rdzQUH/OnKnz58/vaSONjY3CwsI43AEabU+bzWQ8fsO0afXR0cH0B8q5Gg7H8p8FAKCP1qzZcOmSJJnc4SciRUhI4/jxa+rq4ztpITLy9IsXIYmJ8UQikUVBAgAYgY9agLnv37+PHatnarpiyRLPDg/IyUk6dGhtWVkWgSBBpdYrK2t7eFzsRWoaFOR561YghRKHkPa/2+oJhHmTJ49ydz/W1FQfHOz5+HGIo6Ojh8duWVnZPrwnbMBw5lXc8XO1t19569Z3KvVe+11E4vRdu6Z5e+9pv4u7wBgDgPN9//592DCthoa/EXqJUAxCqQiJI6SB0G6EXA0NtQ4d6nrirrv7HAODkceOHWFDwACAtuCjFmCrrKxs4sQpU6YscnLa18lhVCoVh8NVVhbLyCj1rqPc3I+rV49DqByhP9NOPj5dO7sFLi6eCKHfv7/fuHH40aPLRkZGLi4rrKysCARC73pkPxjOvIoLfq4UCkVYWIpEKkVIrKP96XJydqWl6b2uAcUhYIwBwBVu3bpja7scockIuSGkj9A3hNIQWo1QS0zMNyKRv8sW6uqqly9Xf/ToHz09WLocALaCj1qAoSdPnixb5rxokYelpQtLO6LRaOvXz8rMXImQbUf7a4jEobdvFw4YIEX/vrm5MS7uVkzMpeLi7GXLlq1evWrEiBEsjZApYDjzKi6YEJubm0skyjBITRFCGt++FTU1NbE1JhaAeqcAcAVbWxscbj1CD9rWO0UoF6HqBw9Cu9OCqKj4ihW+Li5reeaxeQC4BRRIBJior693dl65dOmKjRvPszo1RQjhcLji4hyExjHYPwCPV2xbOlVAQGjWrKXHjr04ceL11698xsaTDQ0nXr4cXF9fz+pQ+wKGM6/iguyUj4+PRiMz3k+j0RjVhuImUO8UAM73b73Tg+32dFbvtD0zs2UUCn9Q0AWmRwgA6AQUSARsRqPRrl+/rqExqqqKePlypoGBORs6JZGampp+ITSU0QF8fKrl5QXttysojFi1yjciotTKantw8F1ZWXknp5Xx8fGceYsShjOv4oLsdPjw4RTKD4QYlWbKlpEZLiAgwNaYAAD9Uq/rnba3bVuwu7tHdXU1s2IDAADAUaKiokaN0j148OTmzSEbN54VEhJlT7/8/IIDB6ohlMzogJaWeE1NA0Z78Xj8hAlz9u+/FxKSIyCg5uDgNHKkZkjIFTK5k3tFADANF2SnBAJh4cJFeLxbh3vx+Dlr1izlgTV7AQCcr9f1TttTUBgxZsy0Cxd6U78OAAAAx2pubg4NDdXTM9y4cceiRQcCAt6NHj2FzTGMHWtIIFxnsDNWVFREQmJwl41ISQ1xcNgeEpLj6nrx9OkrqqojQ0OvMjdOANrjjqTu7NkjAgKRONxOhNpOLSATCM4USuGePdswi4x5oN4pAJyvL/VO21u4cOu5c+eZERcAoFugQCJgqZKSkl27dsvLDz137vqCBe7nz6dNmDAHk0hcXQ8LC99FqP1qCLkITdu/P6w7a/i10taecPTo8y1brvj6njQzs8jNzWViqL0Gw5lXcUd2KioqWlZWKCt7a8CAaQjtQegmDrd1wAD9mTOb6urquH21XrrkZIYTMAAAHGLcOFUCIYnBTgqBkNqj7HTkSL2WFmpqaipTYgMAdAmWUQEs8vz587lz52trjy4oaDx58u3Bg4+MjCwxnNknJCRy4cIrhJYRCKsRikWoHqFkhM4TiUbbt1/V0mI4CagT2toTAwLey8kZTJgw+f3790yPuadgOPMqLluLOSIiIiUlJyUl3chonJ6etoWFBdYRMQ2siw0A5/u33um9jub3ju5mvdO2/PyWLlw41dnZmSnhvX37tqWlZcoUJkwhO3z48PLlywcNGtT3ppgrPz8/KSnJ1rbDMgkAdAE+agFz/fjx48qV0AsXLlMoOCur9TNnLhYSEsE6qP/X1NRw7tye5OQPX7+miosrKSuP2LjxcI+uonYoPf3t3r3W0dFR48ePZ0qcvQPDmVfBz5VTwBgDgCtERT2ytJyNUARCdv9ua+Hjc6FSQ2Jimns0VwohFBq6X1GR0uEF4LS0tJs3b/7xZ4FIJA4bNmzKlCnKysp/HJ+SknL8+PHQ0G5VtemSo6Ojl5cX5iXv6uvr8Xi8oKBg241HjhxRVla2sbHBKirAveCjFjAFlUp9+vTpuXMXnzyJmTTJ2tx8pbb2RKyDYquEhOgdO8yrqqokJCSwigGGM6/ijpm9/QHUOwWAK1hYmGdlZSkq7hcQkCUQzPH4MUTikKlT+R8+rO1paooQIpNJjKZ+aWtrr1mzJi4u7siRI3PnznV1dXV1dTU1Na2oqNDQ0Dhy5EjbgxsbG93c3AICAnr5rjhPY2NjZGSkrq5udHT0H7u2bt0aFhZWWFiISWCAq8FUQNBHJSUle/d6Kyoqu7ntHjZsWkRE8fbtIf0tNUUI6eubGRpaLF3KnIk/vQPDmVcRsA4A/A/UOwWAW6irq+fnp3z9+vXYsWNv3pB27XokJSXTu6YyMl4uWrSrw104HE5BQeHr16+Ghob6+vr0jTIyMsbGxsnJyTt27Jg1a5aOjg59++HDh+fPny8uLt67MDjN8ePHS0pKRo4cmZ+f3/7SOA6H27Jly6ZNm+7evYtJeIB7QYFE0GsvXrw4cuTE27dvTEzsvbzuq6r299O2AwfurVunFxUVhdVzdjCceRXcOwUAgB4jEAhDhw6dMGHCgAFSvU5N3717WFv7bcaMGYwOKC4uLiwsnDp16h/bR44cSaPR0tLS6N+SyeTg4GAnJ6fehcGBNm/efOLEienTpzM6YNKkSaWlpSUlJeyMCgDQD9FotIiICB2dsU5Oa9TUzCMiSl1dAyA1RQjh8XgTE8e7dx9gHQjgNZCdAgBALxEIBAqll9XJy8ryDx92On/+LIHAcA5LXFwcQqh9dpqQkIAQmjRpEv3bV69ejRkzZsCAAb2LhEuZmprCvVMAAEs9fPhw1KjRhw4FODr6XL6cOWfOan5+AayD4iATJ1rfv38PHv4EzAXZKaeAeqcAcJ1bt26RyS29eGFdXfWePRYHDx5on3m2FRcXx8/Pb2T0n/WBExMTY2JiNm3apKSkRN9y9+5dAwOD9i+vrq4+ceKEn5/f+fPn6a0FBQX5+/vX19f3NOBXr14dO3YsKCiodQuVSr148WIvmmKWSZMm/f3331j1DrgUFEgE3VRcXDxlynRX120ODvtOnnxjYGDOG/ULmUteXlVYeEB2djYmvcNw5lW9ee60vLw8ISHh7dsEOTkZdXU1U1NTDAs68QyodwoA17l+/bqh4ayevopCoXh5zbe0NFuzxqXzI1+8eGFgYCAkJNS6JTIy0t3dfffu3fv37297mJ+f3x+vraurO3z48M6dO8XExIyMjN69e2dvbz9hwoSJEyfKysra2dmhbvv06VNeXt7mzZvFxcUnT56soaGBEIqPj1+1atXs2bNFRP4sn1BbW5uYmNjl1fShQ4eqqal1P4w/aGtrv379mkajwSkj6D4vLy94Vg106ezZc3v2eDg47Nq7141Zp7hkckt5eT6NRlNQUMPj8UxpkxPw8ws1NTVh0jUMZ17V4+z03LnLW7fuplL1GhuN+fiyRUVvyMvve/MmSlJSkunBffv2raCgICMjQ09Pb9iwYTyz4AcAgGf0Ymavh4e1iAjt5MljnR9WUlJSUFAgIyPj4eGBEGpubqZQKDIyMo8fP1ZQUGh7ZGVlpbS09B8vP3XqlJubm5iYGEJo2LBhOTk5pqamOTk5dnZ2s2b9J6MuLy+Xk5PrJJJr164dOnQoMzOztraWRCLRN8bFxamqqnb4wsrKymfPnnWZnerq6vYlOx04cCCZTG5oaGifHgMAQK9t2bL9wYMnR48+V1HRZkqDjY11J05si4u7zscnjcMRyOTSCRNsd+48LSgozJT226uu/iEuLk2lUtlw90j4/9q777imzjUO4G8CGVAjEGQ4iDgYKiqKBUdFcNZrlaJXrShVWq/cOnDWUatVpG4Rx3VVsTixRdzWOmpcqCiYy1IkKGKs7BEJEALJ/SO9uVxGCBA8Sfx9//BDznlz3oePnwd4ct7zPqacd+/etfQs8EFpXHW6ZMnKnTsPy2S3CXEkhMjlRCwmYnFYhw6Or1+ncrlcbYUll8uDg7ds3LjB2Lgrnd6rqiqUkKw9e3ZNn+6nrSkAAJqvqqpxK3v371+alfVMKExt8I8G5UOnS5cu9fHxUTNMoVDk5ubW/vBu1KhRVlZWyq/j4+OnTp1KCHFyclKtzi0pKYmKinr8+HF4eHhpaamaKcaPH0+j0aKjo52cnFS7i/P5/PqWJXft2vXHH39U/901n4mJCZvNlkgkqE4BQFuWL18ZHX1x//54JpPd8GgNlJQUT5zYqaLic7n8NSEc5bE7d759+nTQ0aP3tTWLUmFhzubNc1JS4svLi+h0o/btnb79druTUz8tTlEbh2OO6hS0qxGfqSQmJm7btl4mi1WWptUsKC2dPXToeC0+Fc3jdd2w4ZxU+koiefzuXXhpaXJp6aN//GP5r79e19YUugb9TgH0zldffdWoe6f79y9NTLz6+PFDTT7P5vP5NBrN09NT/TCFQqFQKGpf0M3NTflFdnb28+fPa1eSDAbD09MzKCioqqpK/RTKfjaRkZGTJk1SHpHJZDExMeofmn0PjIyMsBsHNAoaJIIaP/10aN++/bt2xWixaAwI6CeVzpTLw/9bmhJCWsnle3Ny3AMDh2vxJ9jz5/FTpnSPjf1YLL5cUZFfXi5IT18yd+7oxMR/a2uKOhUWZltaWrboFPVBOhuqRtw7Xb9+ByE7CelQ18m1L164PHr0SNWUrzlCQ3e/efOSEOH/F8+dZbJEP7/Olpa/Dh06tPmz6Br0OwXQI5mZmdHR0SkpKa9eCc+f3z9uXGCDb9mzZ1Fq6q07d25q+BwEn8/v1atXg4PpdLqlpWVxcXF9A27evMlms2tvm8RisTp37pyWlqZJMBkZGSkpKceOHVO+jI2NLS0t9fb2rnOwSCQ6d67hXRydnZ3VdNNpUGVlJW6cQmPhKTWoT3Fx8YoV323a9HurVubauubNm7+UlrZVKGruC0AIIWR/Ts7o33+P+PRTLTQDKy7OCwx0I+Q6IapGXO0I8amsdA8Kardp01V39xHNn6VO+flZtrZNbKvWTEhnQ9WIe6dPnjwlpFd9Z6XSXlrZs0sikaxevZYQUV2xmVVW/vLNN8sqK5vYwgEAoPmWLl3ZsWP3hQuPPngwoKho6Pbtmz/91C43V1Tf+MpK2Y4ds4XCO7du3dCwNFU+dDpkyBBNBtvY2OTl5dU4mJGRofxRee3aNXd3dxbrry4ITdvkMCkpycjIqEePHsqXfD7fwcGhvqdVmUxmaw00s7AsKCig0+moTgFAK1at+mH4cH8nJzctXjM9PbW0dBAhde/cVlo68PnzVK1MtGVLEJ0eXK00VWlLyKOQkK8qKlpq46K8PMqqUzBUjbh3KpGICan3yVKFgqvmw3vN5efnV1YyCGlfz3m3ly+fGdJeZwCgX8aOnXjx4iVC7hDyvz9ipNJ1kyb1+OWXZCurmqtLiovz166d0LatGZ9/Q/OWpJcvXyaEaFidDhw4UCAQjBjxv4/G+Xy+t7f35cuX3dzcLl26pLrJ+euvv1YfpjkzMzMGg6FcP1xWVnbs2DE1y3qtra39/f2bMEsNYrFY9W9t//73v93d3bFhLwBoxc2bMAtJZAAAF4ZJREFUt7/5Zo92rykUJhEyvv7zvdPTD2hlopSUJ3L5inpO9isvlxUX59X+9dR8hYU5HI4Zm63Np2cBGnHv1M2tHyEP6jvLZD7s108LD16np6ebmKjZxdHcyIhd+y6BAUC/UwDd98cff1y8GEWIoHppSgghZBUhs/z9B9QYLxKlzZ798fDhAy5dOqdhaSqVSmfMmLF+/XoOh7Nr166lS5c2+BZfX9+4uLjqR7p06dKnTx+JRLJ27dqYmJiCgoKTJ09u3LjR2Nh44MCBmoRRw6BBg8aPH7906dKzZ88GBwc/e/asvmW9WhEREREYGDh37tzWrVtv3rx51qxZ69evrzEmNjZW/X5RALWhQSLUqbS0NC3tmYODlv8S697djUZ7WP/52O7dtfCXc2npu3fv/iSkR30DWKz+z549av5Etb14kditW/eWuLImkM6Giqb5A9lnzpyZOnV1WdljQli1Tl61tAx89Sqp+YusSkpKLCxsKivFhNR5gzSNyx2Zn/+ymbPoIBqtEf8XAEAJBwdXoXAKIcvqOd9l4cKlqmdQr1yJOHhwaVhY6LRpU1s0qoqKCgcHh6dPn5qamlY/+PLlSwcHB+UNz4yMjPbt2zMYjBrvTUtLc3FxkUqlNY5PnTp1zZo1Dg4O1Q8WFRWJxeLExMTJkye/efOG2i5fHh4eERERzs7OFMYAege/aqFODx48CAxcuGPHfe1e9uHD34KDvystjSWk5s9eQqpMTPovW7Z8yJAJzZ9o7NiOJSV/ENKlzrMsVpcDBy7zeE7Nn6iG06d3ymSp+/b9S+tX1gTS2VA14t6pr6+vt7cLgzGVkBqL1+MIGXXlSpRWnv8xMTGxt3ci5GydZ42Mfh48uObdCQCA90MkKiLEtf7zH6emPiKESCTi4OBJ585tvXHjakuXpoQQJpPp6+sbGRlZ46CTk5NqL197e/vapSn575a/6q+flJTUtWvXpKQkc3NzHo+3ZcuWWbNmUVuaPnr0iMPhoDQFAK2wtbXNzX2r9ct6eIzu1asHnf6P2qdotEAOR6yV0lShUHTs6FT/8sa3hBS2aaOuqXWTZWYm9+7t0hJXhg9Z47r0nj17xNExg8VyIGQLIXcJOcVgfGdi8umxYyf79dPOc+RGRkbR0RF0+lRC4mvPX1W1Pjx8t1YmAgBoLJlMQkjb+s+3y819ExNzYeZMFxeX9gLB4/e2F/eaNWsiIiLUty2tQSqVhoSEBAcHs9nsBQsW7Nixo76RsbGxjo6OnTt3JoQo26Vu3Lix+TE3x8aNG8PCwqiNAQAMhrW1dUFBTktc+YcfDsjlEXS6PSEJhMgIqSIkydh4lLX1g4iIJ1qZgkajLVkSxmAEEfKi1slKQtrNnPmjqSmnjnc2W3z89QbbngE0ViN2RSKEMBiMpKTHFy9ePHv2xv37y6ysbPv1c1yyJFG7u3X17Nnz1KmTEye60elhcvkAQlwIecxkXjY1PR4Tk8Ll1rszk15Dv1MA3Wdt3f7t2/v1717Oz82tCA9fcvz4z++58ZW5ufnatWsXLVq0b98+Dd/CYrG+//57TUZ+8cUXb968OXr0aEZGBofDuXbtWp23Yd+bXbt2jRgxwsUFH9hDo6FBItSJzWa3asXJzs60seFp+8qmf/whP35867lzfgUFL2g0urk5b8yYqV9+uczIqHF/hKthb9993rxtoaFdCLlJyJD/7hIsMjb+G4/n/ve/f6OtiarLynpVVlai2sv9/UM6GyrdXbEtEonmzFkiEDzPykrr2LHnJ5/0DgvbpPmOlwAAWjd//vydO68T8oQQZq2TcYR4Llo0e8OGH5nM2mffB4FAwGaztbLe9fTp08OHD6++fFehUOjCBrm5ubmJiYkG2fUaACg0f/7iggLTr79e10LXl8vlMpmUEMJkslvoZ2lSUswPP0wXi3PZ7P4VFUl0enlg4PrPP5/VEnMRQq5ciRAKf4uKimx4KEBj6G51CgCgg7hch8LCjwn5+f8L1OeEOC1fvmrDhmDKIgMAgKZKSkoaOfKzEycyqA6kWSorZRKJODX1EY/nbGbWxsSkVcvNtWzZiCVLZk2cOLHlpoAPE6pTAIBGEIvFFhY2crklIasIGUDIW0IEhKwbN27MuXOnqI4OAACayMtruJPTyClTGu7jBfn5bwMCuuXmZrNYtRt5ADRL43ZFgpaDfqcAeqF169ZVVWVBQRPatt1Lo3mz2bO6dj1548Z5lKYAug8NEkGNiIhDp05tev36OdWB6IE//oj8/HNfaktTpLOhwr1TXYGuTQB6B2kLoF+Qs6Dehg2bIiPPh4be0uKWRYanokI6dWqn69d/e2/70tcJ6WyocO8UAAAAAICsWLHs449dvv12eEVFOdWx6K4rVw67ufWltjQFA4bqFAAAAACAEEJ++mmfg0P7UaNMpNIyqmPRRZWVslOnNq1cuYzqQMBgoTrVFeh3CqB30GwNQL8gZ6FBNBrt1Knjfn7+QUEDs7JeUR2Ozvn559WDBvUfPHgw1YEgnQ0WVmwDAAAAAPyf0NCwkJD1a9ee6dlzENWx6IqXL5MWL/Z++jTJxsaG6ljAYKE6BQAAAACo6fbt23//++QhQyZ/9VVIi/YO1QsVFdJ58zwWLZodGDiL6ljAkGFlLwAAAABATZ6enomJAhMT8YwZ3WJiLlAdDsXWr/cbNOhjlKbQ0lCd6gr0OwXQO2i2BqBfkLPQWDY2NkeOhP/yy7FDhxavXu0jFH6gu4Rs3/5NSYlo375/UR3I/yCdDRVW9uoKdG0C0DtIWwD9gpyFJpNKpQcOHAwJ+bF790EBASE8nhPVEb0/O3fOPXPmX1KplMlkUh3L/yCdDRXunQIAAAAAqMNisebNm5ORkT56tMfixUOCgycmJNyhOqgWJ5fLz5/f8/z5nby8PJ0qTcGA4VMHXYFPgAD0DtIWQL8gZ0ErJBLJ4cM/b9++08iI7eMTNHKkP4NhgJWbWFzw449T6HTJpUvnuVwu1eHUhHQ2VEZoFqQjfH19bW1tqY4CABqBRqN5eXlRHQUAaAo5C1rBZDLd3d3nz5/n7Nz13LmIsLBFb94ITUxa29h0pNFoVEenHYmJ95YtGzlu3IgjRw5zOByqw6kD0tlQ4VMHAAAAAIAmEolEx4+fPHr0eF5e/rBhU728Jjs49KE6qKYrLs7bv3+JQHBj375/jRs3jupw4IOD6hQAAAAAoLmSk5OPHDkWHX22qKhowICxHh6f9es3gsUyoTouTUkk4vPn90ZFhQYETF+zZnWrVh96i1egBKpTAAAAAACtEQqF589fOHfu4qNHD11dB3fvPrh3b09nZ3edfTy1sDDn11+3Xrp0cMyYMatXr3R2dqY6IvhwYc9eXYF+pwB6B83WAPQLchbej65duy5atPDWrRtZWX+uWDGbw8kPD1/o48P99tuhR44E37t3Pi/vT6pjJIQQiUT822+Hly0bOWOGk6VlRWKi4MSJo/pSmiKdDRXuneoK7DwGoHeQtgD6BTkLFHr37t3du3fv3r0XGxsXF/eYTjdycurr4ODO43Xj8Zzs7JzezxrgqqrK1NTHAgE/MZGfnPzAy2uov/+UMWPGmJqavofZtQjpbKjw/6orkGMAegdpC6BfkLOgO16/fh0fHx8XF5+QkJyamvriRZqlpQ2P52Rn143LbW9l1cHKqoO1tZ2VVQdjY0ZzJhKLC168SMzISM7MTBGJnqakPOrUqcvQoV5Dh3oNHTpUN/fj1QTS2VDh/1VXIMcA9A7SFkC/IGdBZ8nl8oyMjNTUVKFQmJGRmZkpEolEItHrnJwsNtvUzIzL4VhwOBYcDpfDsTQyYhgbM42NmUZGDAaDaWzMKC8vlcmkMplUJiuvqqrIz/+zsDA7Pz8rLy+Lw2nt6NjNxaVHz57dXVx6uLm5WVhYUP3tagHS2VAZUx0A/EUgEFAdAgA0DvpFA+gX5CzoLDqd3rlz586dO9c+VVBQUFBQUFhYWFhYWFBQUFRUVF5eXvEXmVQqlsvlbdqwWCxTNtuCzWabmJhYW1vb2NjY2tra2toymTq6FVMzIZ0NFT51AAAAAAAAAOphz14AAAAAAACgHqpTAAAAAAAAoB6qU12BfqcAegfN1gD0C3IWwGAgnQ0VnjvVFdh5DEDvIG0B9AtyFsBgIJ0NFe6dAgAAAAAAAPVQnQIAAAAAAAD1jNAsSEf4+vra2tpSHQUANAKNRvPy8qI6CgDQFHIWwGAgnQ0VVmwDAAAAwIdOKpWy2WytXIfJZDb/OgAfJqzsBQAAAIAPHYvFSkxMjIiIsLe3Vx6h0Wg5ah04cED19rFjx16/fj09PR2lKUBzGFMdAAAAAAAA9VxcXFxcXHg8nre3t/KIlZWVmvGtW7dWfmFnZxcdHW1sjL+rAZoL9051BfqdAugdNFsD0C/IWdBE9+7dG/sWR0fHFipNtf4Ini4/09eo2JDOhgrVqa548uQJ1SEAQONgVzkA/YKcBU3Q6X/9eUyj0Rr7Fu0Si8Xz58+vqKjQ4jUXLlz47NkzLV5Qi7Zt2yYQCDQcjHQ2VFiBAAAAAADQslJTU9evX5+Tk0MIYTAYlpaWhJCioiJra+v+/fv7+/vXuPtaVVUVEBAQEhKi3QdZS0pKysrKtHjBJrt79+4nn3xS/ciCBQsmT568fft2Ho9HVVRAOVSnAAAAAAAty8nJKSIiYtq0aSdOnHj58mXHjh0JIVKpNC4ubtq0abt3775z546pqalq/NatW0eNGtWtWzfqQtY+mUwmEokSEhL279//5MmTt2/fVj9rbGwcFhb29ddfX716laoIgXJY2asrNF/JAAA6AsuKAPQLchYoJxAIXFxclKUpIYTFYg0cOHD58uXx8fF79uxRDcvOzg4PDw8ICKAozJaSnZ19/PhxNpvdrl27OgfY2dnZ2dmdOnWqwUshnQ0VqlNd0bt3b6pDAIDG+eGHH6gOAQAaATkL1MrNzU1JSfHy8qpxXLn3r0gkUh05fvy4n58fg8F4r/G1vA4dOnz//fejRo1S01p27ty5hw4davBSSGdDheoUAAAAAKDF3b59W6FQ1K5O7969SwgZMWKE6sjZs2f/9re/vdfgdIarq2tCQkJRURHVgQA18NwpAAAAAECL4/P5NBrN09Oz+sFXr14dPHjQz89PVY7m5ubGxcXVXlWXnZ29f/9+FouVl5e3bt26mzdvvnr16s2bN19++aWDg0PTQjp37lxaWlpWVtbmzZtVOw9v3LhxwoQJTb5mM9FoNA8Pj4sXL06bNo2SAIBaqE5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    }
   },
   "cell_type": "markdown",
   "id": "e2af9b72",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)\n",
    "Illustration behind the Naive Bayes algorithm. We estimate $P(x_{α})|y)$ independently in each dimension (middle two images) and then obtain an estimate of the full data distribution by assuming conditional independence $P(\\mathbf{x}|y)=\\prod_\\alpha P(x_\\alpha|y)$ (very right image)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d834102c",
   "metadata": {},
   "source": [
    "### Modeling conditional densities: $p(x_{i}∣y)$\n",
    "#### 1. Binary feature - Bernoulli Distribution\n",
    "e.g. word is present or not\n",
    "$$\n",
    "p(x_{j}∣y_{c}) ∼ Bernoulli(μ_{jc})\n",
    "$$\n",
    "When $x_{j}$ is a binary feature, we use Bernoulli distribution to\n",
    "model the class conditional density:$ p(x_{j}|y_{c}) $\n",
    "Lets take the parameter for the bernoulli Distribution as $μ_{jc}$\n",
    "$$\n",
    "p(x_{j}=1|y_{c})=μ_{jc}\n",
    "p(x_{j}=0|y_{c})=1-μ_{jc}\n",
    "$$\n",
    "Combining the two equations we get:\n",
    "$$\n",
    "p(x_{j}|y{c};μ_{jc})=μ_{jc}^{x_{j}}(1-μ_{jc})^{(1-x_{j})}\n",
    "$$\n",
    "For $s\\le m$ binary features and classes, we will have $k \\times s$\n",
    "parameters for $s$ Bernoulli distributions."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46600279",
   "metadata": {},
   "source": [
    "### Inference\n",
    "Once we learn parameters of different conditional densities, we use them to infer class label for new example.\n",
    "We assign a class label to a new example that maximizes\n",
    "the posterior probability.\n",
    "$$\n",
    "y = \\underset{y_{c}}{\\operatorname{argmax}}p(y_{c}∣\\mathbf x;\\mathbf w)\n",
    "$$\n",
    "Using the definition of posterior probability, we get,\n",
    "$$\n",
    "y = \\underset{y_{c}}{\\operatorname{argmax}} \\cfrac {p(\\mathbf x|y_{c};\\mathbf w)\\ p(y_{c};\\mathbf w)}{p(\\mathbf x,\\mathbf w)}\n",
    "$$\n",
    "Since is independent of , we ignore denominator from this computation\n",
    "$$\n",
    "y = \\underset{y_{c}}{\\operatorname{argmax}} p(\\mathbf x|y_{c};\\mathbf w)\\ p(y_{c};\\mathbf w)\n",
    "$$\n",
    "Expanding p(x∣y ; w) with naive Bayes assumption, we get\n",
    "$$\n",
    "y = \\underset{y_{c}}{\\operatorname{argmax}} \\left( \\prod_{j=1}^{m}p(\\mathbf x_{j}|y_{c};\\mathbf w)\\right)\\ p(y_{c};\\mathbf w)\n",
    "$$\n",
    "This equation involves multiplication of small numbers,there is a risk of underflow in this calculation. Hence we calculat the maximum in the log-space\n",
    "$$\n",
    "y = \\underset{y_{c}}{\\operatorname{argmax}} \\left( \\sum_{j=1}^{m}log \\ p(\\mathbf x_{j}|y_{c};\\mathbf w)\\right)\\ log \\ p(y_{c};\\mathbf w)\n",
    "$$\n",
    "For a new example, , we assign a class label that yields max value among all $y$ = {$y_{1},...,y_{k}$}.\n",
    "This equation is useful for getting the class label. however it does not return the probability of an example belonging to class y_{c}. In case, we want the probability, we should use the following\n",
    "equation and that calculation should also be performed in log space.\n",
    "$$\n",
    "y=\\cfrac {p(\\mathbf x|y_{c};\\mathbf w)\\ p(y_{c};\\mathbf w)}{p(\\mathbf x,\\mathbf w)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d14b39d8",
   "metadata": {},
   "source": [
    "#### Loss function\n",
    "Likelihood describes joint probability of observed data $D$ given the parameter $\\mathbf w$ for the chosen statistical model.\n",
    "$$\n",
    "L(\\mathbf w) = p(D;\\mathbf w) = p(\\mathbf X,\\mathbf y;\\mathbf w)\n",
    "$$\n",
    "Since training examples are i.i.d., we can express this as a product of probability of individual samples:\n",
    "$$\n",
    "L(\\mathbf w) = \\prod_{i=1}^{n} p(\\mathbf x^{(i)},y^{(i)};\\mathbf w)\n",
    "$$\n",
    "For mathematical and computational convenience, we calculate log likelihood by taking log on both the sides:\n",
    "$$\n",
    "l(\\mathbf w) = \\sum_{i=1}^{n} log\\ p(\\mathbf x^{(i)},y^{(i)};\\mathbf w)\n",
    "$$\n",
    "Our job is to find the parameter vector $\\mathbf w$ such that the $l(\\mathbf w)$ is maximized.\n",
    "\n",
    "Equivalently we can minimize the negative log likelihood (NLL) to maintain uniformity with other algorithms:\n",
    "$$\n",
    "J(\\mathbf w) = -l(\\mathbf w) = -\\sum_{i=1}^{n} log\\ p(\\mathbf x^{(i)},y^{(i)};\\mathbf w)\n",
    "$$\n",
    "Simplifying and rearranging with Naive Bayes Assumptions of Conditional Independence of features given label, we get,\n",
    "$$\n",
    "J(\\mathbf w) = -(\\sum_{i=1}^{n} log\\ p(y^{(i)}) +  \\sum_{i=1}^{n} \\sum_{j=1}^{m} log\\ p(x_{j}^{(i)}|y^{(i)}))\n",
    "$$\n",
    "The calculation of depends on the probability distribution of the features."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60cf6173",
   "metadata": {},
   "source": [
    "### Optimization for Parameter Estimation\n",
    "The parameter estimation by maximizing the log likelihood\n",
    "function is carried out with the following three steps:\n",
    "1. Calculate partial derivation of log likelihood function w.r.t. each parameter.\n",
    "2. Set the partial derivative to 0, which is the condition at maxima.\n",
    "3. Solve the resulting equation to obtain the parameter value."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ead2ac3",
   "metadata": {},
   "source": [
    "#### Estimating prior probability: $p(y)$\n",
    "The total number of parameters to be estimated is equal to the number of class labels k - one prior per label.\n",
    "$$\n",
    "p(y=y_{c})=\\cfrac{\\sum_{i=1}^{n}\\ 1(y^{(i)}=y_{c})}{n}\n",
    "$$\n",
    "\n",
    "Note that $1(y^{(i)}=y_{c}) = 1$ when $y^{(i)}=y_{c}$ else $0$.\n",
    "\n",
    "The prior probability for class $y_{c}$ is equal to the ratio of the number of examples with label $y_{c}$ to the total number of examples in the training set $n$.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8d89dc02",
   "metadata": {},
   "source": [
    "### Estimating Class Conditional Densities\n",
    "#### Bernoulli Distribution\n",
    "Let us now take the example of Bernoulli Distribution and estimate its Class Conditional Density\n",
    "We know that the log likelihood function is given by\n",
    "$$\n",
    "l(\\mathbf w) = \\sum_{i=1}^{n} log\\ p(y^{(i)}) +  \\sum_{i=1}^{n} \\sum_{j=1}^{m} log\\ p(x_{j}^{(i)}|y^{(i)})\n",
    "$$\n",
    "For Bernoulli Distribution,\n",
    "$$\n",
    "p(x_{j}|y_{c};w_{jc})=w_{jc}^{x_{j}}(1-w_{jc})^{(1-x_{j})}\n",
    "$$\n",
    "Substituting this in $l(w)$, calculating partial derivation of log likelihood function w.r.t. each parameter, setting it to $0$ and solving the resulting equation, we get,\n",
    "$$\n",
    "w_{jy_{r}} = \\cfrac{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r}) x_{j}^{(i)} }{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r}) } = \\cfrac{\\text{# of examples with label $y_{r}$ and ($x_{j}=1$)}}{\\text{# of examples with label $y_{r}$}}\n",
    "$$\n",
    "Here,\n",
    "\n",
    "Parameters for label $y_{r}: \\mathbf w = w_{1r} , w_{2r} ,..., w_{mr}$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2eacb524",
   "metadata": {},
   "source": [
    "#### The Zero frequency problem\n",
    "If you recall,\n",
    "$$\n",
    "p(y=y_{c}|\\textbf x) = \\cfrac{p(y_{c}) \\prod \\limits_{j = 1}^{m} P(x_{i}|\\ y_{c})}{\\sum \\limits_{r = 1}^{k} p(y_{r})\\prod \\limits_{j = 1}^{m} P(x_{i}|\\ y_{r})}\n",
    "$$\n",
    "Here,\n",
    "$p(y=y_{c}|\\textbf x)$ is dependent on the product of $P(x_{i}|\\ y_{c})$ i.e. The class conditional densities.\n",
    "We also know that $P(x_{i}|\\ y_{c})$ is estimated for Bernoulli Distribution using the following equation,\n",
    "$$\n",
    "w_{jy_{r}} = \\cfrac{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r}) x_{j}^{(i)} }{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r})  }\n",
    "$$\n",
    "So, if any individual class label is missing in the training set, then the numerator of this equation becomes zero which will lead to the product of $P(x_{i}|\\ y_{c})$ to become zero. That would mean that $p(y=y_{r}|\\textbf x)$ becomes zero. \n",
    "So to take a concrete example, in our spam classifier, lets say that the word 'office' is missing from our list of words(created using training data) which are considered spam, whenever we see a new email that consists of the word 'office' it will always be considered a not spam, no matter how ‘spammy’ the other words are because the $p(y=y_{r}|\\textbf x)$ becomes zero.\n",
    "\n",
    "To fix this problem we use a method called Laplace Smoothing. We can correct it by adding +1 to\n",
    "numerator and +2 to denominator (1 for each value of feature: $x_{j} \\in \\ ${0,1}). \n",
    "$$\n",
    "w_{jy_{r}} = \\cfrac{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r}) x_{j}^{(i)}+1 }{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r})+2  }\n",
    "$$\n",
    "In general, we can add to numerator and to denominator. is a hyperparameter that helps control overfitting.\n",
    "$$\n",
    "w_{jy_{r}} = \\cfrac{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r}) x_{j}^{(i)}+c }{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r})+2c  }\n",
    "$$\n",
    "However too high value of c leads to underfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec4defb8",
   "metadata": {},
   "source": [
    "#### 2. Categorical feature - Categorical Distribution\n",
    "e.g. {red, green, blue} or roll of dice\n",
    "It is generalization of binary. When $x_{j}$ is a categorical feature i.e. it takes one of the $e>2$ discrete values, we use categorical distribution to model the class conditional density $p(x_{j}|y_{c})$.\n",
    "$$\n",
    "p(x_{j}∣y_{c}) ∼ Cat(e,μ_{j1c},μ_{j2c},...,μ_{jec})\n",
    "$$\n",
    "Let $v={v_{1},v_{2},...,v_{e}}$ be the set of $e$ discrete values.\n",
    "For discrete set v, $p(x_{j}|y_{c})$ is parameterized by the $|v|$ (i.e. the number of events in $v$) and probability of each event $μ_{j1c},μ_{j2c},...,μ_{jec}$ such that \n",
    "$$\n",
    "\\sum _{q=1}^{e}μ_{jqc}=1\n",
    "$$\n",
    "For $x_{j}=v_{q}$ such that $v_{q} \\in v$:\n",
    "$$\n",
    "p(x_{j}=v_{q}|y_{c};e,μ_{j1c},μ_{j2c},...,μ_{jec})=μ_{jqc}\n",
    "$$\n",
    "Let $μ_{\\textbf jc}=[μ_{j1c},μ_{j2c},...,μ_{jec}]$ be the parameter vector for $p(x_{j}|y_{c})$\n",
    "$$\n",
    "p(x_{j}=v_{q}|y_{c};e,μ_{\\textbf jc})=μ_{j1c}^{1(x_{j}=v_{1})} μ_{j2c}^{1(x_{j}=v_{2})} ... μ_{jec}^{1(x_{j}=v_{e})}\n",
    "$$\n",
    "where, $1(x_{j}=v_{q})=1$ if $x_{j}=v_{q}$ else $0$ <br>\n",
    "Total Parameters = $k \\times \\sum _{j=1}^{m} |v_{j}|$\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8bf6429",
   "metadata": {},
   "source": [
    "#### Categorical distribution\n",
    "Similar to Bernoulli Distribution, we can estimate the Class Conditional Density for Categorical distribution. After performing the 3 steps of Optimization for Parameter Estimation we get,\n",
    "$$\n",
    "w_{jvy_{r}} = \\cfrac{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r}) 1(x_{j}^{(i)}=v)}{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r})}=\\frac{\\text{# of samples with label $y_{r}$ that have feature $x_{j}$}\\text{ with value $v$ }}{\\text{# of samples with label $y_{r}$}}\n",
    "$$\n",
    "Here, $v={v_{1},v_{2},...,v_{e}}$ be the set of $e$ discrete categories.\n",
    "\n",
    "Parameters for $\\mathbf w = \\{w_{111},..., w_{1e1} ,..., w_{m11},...,w_{me1},...,w_{mek}\\}$\n",
    "Incorporating smoothing, we obtain\n",
    "$$\n",
    "w_{jvy_{r}} = \\cfrac{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r}) 1(x_{j}^{(i)}=v)+c}{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r})+ce }\n",
    "$$\n",
    "Smoothing factor is a hyperparameter and leads to Laplace smoothing."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a905f1ea",
   "metadata": {},
   "source": [
    "#### Bernoulli Naive Bayes "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "523893c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "class BernoulliNB(object):\n",
    "    def __init__(self,alpha=1.0):\n",
    "        self.alpha=alpha\n",
    "    \n",
    "    def fit(self,X,y):\n",
    "        n_samples,n_features=X.shape\n",
    "        class_count=np.unique(y)\n",
    "        n_classes=len(class_count)\n",
    "        \n",
    "        self.w=np.zeros((n_classes,n_features),dtype=np.float64)\n",
    "        self.w_priors=np.zeros(n_classes,dtype=np.float64)\n",
    "        \n",
    "        for c in range(n_classes):\n",
    "            X_c=X[y==c]\n",
    "            self.w[c,:]=(np.sum(X_c,axis=0)+self.alpha)/(X_c.shape[0]+2*self.alpha)\n",
    "            self.w_priors[c]=(X_c.shape[0]+self.alpha)/(float(n_samples)+n_classes*self.alpha)\n",
    "            \n",
    "        print(\"Class Conditional Density : \",self.w)\n",
    "        print(\"Prior : \",self.w_priors)\n",
    "        \n",
    "    def log_likelihood_prior_prod(self,X):\n",
    "        return X@(np.log(self.w).T)+(1-X)@np.log((1-self.w).T)+np.log(self.w_priors)\n",
    "    \n",
    "    def predict_prob(self,X):\n",
    "        q=self.log_likelihood_prior_prod(X)\n",
    "        return np.exp(q)/np.expand_dims(np.sum(np.exp(q),axis=1),axis=1)\n",
    "    \n",
    "    def predict(self,X):\n",
    "        return np.argmax(self.log_likelihood_prior_prod(X),axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "af698f31",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Class Conditional Density :  [[0.25 0.75]\n",
      " [0.75 0.25]\n",
      " [0.75 0.75]]\n",
      "Prior :  [0.33333333 0.33333333 0.33333333]\n"
     ]
    }
   ],
   "source": [
    "X=np.array([[1,0],[0,1],[0,1],[1,0],[1,1],[1,1]])\n",
    "y=np.array([1,0,0,1,2,2])\n",
    "bernoulli_nb=BernoulliNB()\n",
    "bernoulli_nb.fit(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "872f9880",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 1, 2, 2], dtype=int64)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bernoulli_nb.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "61c9ba97",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-3.87120101, -1.67397643, -2.77258872],\n",
       "       [-1.67397643, -3.87120101, -2.77258872],\n",
       "       [-1.67397643, -3.87120101, -2.77258872],\n",
       "       [-3.87120101, -1.67397643, -2.77258872],\n",
       "       [-2.77258872, -2.77258872, -1.67397643],\n",
       "       [-2.77258872, -2.77258872, -1.67397643]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bernoulli_nb.log_likelihood_prior_prod(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c44de92e",
   "metadata": {},
   "source": [
    "#### 3. Multinomial feature - Multinomial Distribution\n",
    "If feature values represent counts instead of categories we use Multinomial Distribution.\n",
    "Let us consider the example of spam filtering. Imagine a word that is indicative towards spam. Then if that word occurs 3 times in an email, lets say that this email is likely spam. And another email with that word 6 times should be even more likely to be spam as the spammy word appears twice as often. This kind of information is incorporated in multinomial distribution models.\n",
    "\n",
    "When is $\\textbf x$ count vector i.e. each component $x_{j}$ is a count of\n",
    "appearance in the object it represents and $\\sum x_{j}=l$, which is\n",
    "the length of the object, we use multinomial distribution to\n",
    "model $p(\\textbf x|y_{c})$.\n",
    "$$\n",
    "p(\\textbf x∣y_{c}) ∼ Multinomial(l,μ_{1c},μ_{2c},...,μ_{mc})\n",
    "$$\n",
    "This model is parameterized by the length of object l and probability of features $(x_{1},...,x_{m}):(μ_{1c},...,μ_{mc})$\n",
    "\n",
    "The probability of $p(\\textbf x|y_{c})$ such that $\\sum x_{j}=l$ is given by: \n",
    "$$\n",
    "P(\\mathbf{x}|y_{c};l,μ_{1c},μ_{2c},...,μ_{mc}) = \\frac{l!}{x_1! \\cdot x_2! \\cdot \\dots \\cdot x_m!} \\prod_{j=1}^{m} μ_{jc}^{x_{j}}\n",
    "$$\n",
    "Total Parameters = $k \\times m$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0eb28ce9",
   "metadata": {},
   "source": [
    "#### Multinomial distribution\n",
    "After performing the 3 steps of Optimization for Parameter Estimation and incorporating smoothing, we obtain,\n",
    "$$\n",
    "w_{jy_{r}} = \\cfrac{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r}) x_{j}^{(i)}+c }{ \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r})\\sum_{j=1}^{m}x_{j}^{(i)}+cm }=\\frac{\\text{# of samples with label $y_{r}$ that have feature $x_{j}$}}{\\text{$\\sum$ of feature values in training examples with label $y_{r}$}}\n",
    "$$\n",
    "This is the ratio of number of training examples where $x_{j}$ appears with label $y_{r}$ to the sum of feature values in training examples with label $y_{r}$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ad544c81",
   "metadata": {},
   "source": [
    "#### Gaussian/Normal distribution\n",
    "Let n be the number of examples of class r yr\n",
    "$$\n",
    "n_{r}=\\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r})\n",
    "$$\n",
    "There are two parameters per feature $\\{\\mu_{j} , \\sigma_{j}^2 \\}$ per label.\n",
    "$$\n",
    "  \\mu_{jr} = \\cfrac{1}{n_{r}} \\sum \\limits_{i = 1}^{n} 1(y^{(i)} =y_{r}) x_{j}^{(i)} \n",
    "$$\n",
    "\n",
    "$$\n",
    "  \\sigma_{jr}^{2} = \\cfrac{1}{n_{r}} \\sum \\limits_{i = 1}^{n} 1(y^{(i)} = y_{r}) (x_{j}^{(i)} - \\mu_{jr})^2\n",
    "$$\n"
   ]
  },
  {
   "attachments": {
    "NBGaussian.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "4b3e1a91",
   "metadata": {},
   "source": [
    "#### 4. Continuous feature - Gaussian Distribution\n",
    "\n",
    "![NBGaussian.png](attachment:NBGaussian.png)\n",
    "\n",
    "When is a continuous feature i.e. it takes a real value, we\n",
    "use gaussian (or normal) distribution to model the class\n",
    "conditional density e.g. area of an apartment in sq. feet.\n",
    "\n",
    "$$\n",
    "p(x_{j}∣y_{c}) ∼ N(μ_{jc},σ_{jc})\n",
    "$$\n",
    "i.e. We assume that each feature given label is drawn from a Gaussian Distribution.\n",
    "\n",
    "It is parameterised by the mean $μ_{jc}$ and variance $σ_{jc}$\n",
    "$$\n",
    "P(x_{j}|y_{c};μ_{jc},σ_{jc}^2) = \\cfrac{1}{\\sqrt{2 \\pi} \\sigma_{jc}} \\exp \\left[- \\cfrac{1}{2} \\left(\\cfrac{x_{j} - \\mu_{jc}}{ \\sigma_{jc}} \\right)^2 \\right]\n",
    "$$\n",
    "where,\n",
    "\n",
    "$x_{j}$ is the value of the $j$-th feature,\n",
    "\n",
    "$μ_{jc}$ is the mean of $x_{j}$ for class $y_{c}$\n",
    "\n",
    "$\\sigma_{jc}$ is the standard deviation of $x_{j}$ for class $y_{c}$\n",
    "\n",
    "This is 1-D gaussian distribution. It models class conditional\n",
    "density for a single feature."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "41cc9dc9",
   "metadata": {},
   "source": [
    "#### Multivariate Gaussian Distribution\n",
    "Alternately, we can use multivariate gaussian distribution to represent $p(x|y)$ with parameters mean vector $\\mu_{m \\times 1}$ and covariance matrix $\\Sigma_{m \\times m}$.\n",
    "\n",
    "In Naive Bias setting, since the features are conditionally independent of one another, all entries of $ \\Sigma $ except diagonal entries are zero.\n",
    "$$\n",
    "\\sum_{jr}=0 \\\\ where j \\neq r\\\\\n",
    "$$\n",
    "The diagonal entries represent variance of that feature i.e. \n",
    "\n",
    "$$\\Sigma_{jj} = \\sigma_{j}\\\\$$\n",
    "$$\n",
    "p(\\mathbf x|y;\\mu,\\Sigma)=\\cfrac{1}{\\sqrt{(2\\pi)^m|\\Sigma|}}exp(-\\cfrac{1}{2}(\\mathbf x-\\mu)^T\\Sigma^{-1}(\\mathbf x-\\mu))\n",
    "$$\n",
    "There are $m \\times k$ Gaussian Distributions - one for each feature and label\n",
    "Each Gaussian Distribution has 2 parameters to estimate. Hence \n",
    "Total # of Parameters = $k \\times 2m$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c8e5ba3e",
   "metadata": {},
   "outputs": [],
   "source": [
    "class GaussianNB(object):\n",
    "    def fit(self,X,y):\n",
    "        n_samples,n_features = X.shape\n",
    "        self._classes = np.unique(y)\n",
    "        n_classes = len(self._classes)\n",
    "        \n",
    "        self._mean = np.zeros((n_classes, n_features), dtype=np.float64)\n",
    "        self._var = np.zeros((n_classes, n_features), dtype=np.float64)\n",
    "        self._priors = np.zeros(n_classes, dtype=np.float64)\n",
    "        \n",
    "        for idx, c in enumerate(self._classes):\n",
    "            # Get examples with label c\n",
    "            X_c=X[y==c]\n",
    "            \n",
    "            #estimate mean and varience from the training examples of class c\n",
    "            self._mean[idx,:] = X_c.mean(axis=0)\n",
    "            self._var[idx,:] = X_c.var(axis=0)\n",
    "            \n",
    "            #estimate the priors\n",
    "            self._priors[idx] = X_c.shape[0]/float(n_samples)\n",
    "            \n",
    "        print(\"Mean : \",self._mean)\n",
    "        print(\"Varience : \",self._var)\n",
    "        print(\"Priors : \",self._priors)\n",
    "        \n",
    "    def _calc_pdf(self, class_idx, X):\n",
    "            '''calculates probability density for samples for class label class_idx'''\n",
    "            mean = self._mean[class_idx]\n",
    "            var = np.diag(self._var[class_idx])\n",
    "            z = np.power(2 * np.pi, X.shape[0]/2) * np.power(np.linalg.det(var), 0.5)\n",
    "            return (1/z) * np.exp(-(1/2)*(X-mean).T@(np.linalg.inv(var))@(X-mean))\n",
    "        \n",
    "    def _calc_prod_likelihood_prior(self, X):\n",
    "            '''Calculates product of likelihood and priors'''\n",
    "            self._prod_likelihood_prior = np.zeros((X.shape[0], len(self._classes)), dtype=np.float64)\n",
    "            for x_idx, x in enumerate(X):\n",
    "                for idx, c in enumerate(self._classes):\n",
    "                    self._prod_likelihood_prior[x_idx,c] = (\n",
    "                        np.log(self._calc_pdf(idx,x)) + np.log(self._priors[idx]))\n",
    "    def predict(self,X):\n",
    "            '''Predicts class labels for each example'''\n",
    "            self._calc_prod_likelihood_prior(X)\n",
    "            return np.argmax(self._prod_likelihood_prior, axis=1)\n",
    "        \n",
    "    def predict_prob(self, X):\n",
    "            '''Calculates probability of each sample belonging to different classes'''\n",
    "            self._calc_prod_likelihood_prior(X)\n",
    "            return np.exp(self._prod_likelihood_prior)/np.expand_dims(\n",
    "                np.sum(np.exp(self._prod_likelihood_prior),axis=1),axis=1)\n",
    "                "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c9c709f",
   "metadata": {},
   "source": [
    "##### Lets Generate training data with two multivariate Gaussian Distribution, one with mean [5,5], std=1.5 and 2nd one with mean [10,10], std=1.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "215e8fcd",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_classification, make_blobs\n",
    "X,y = make_blobs(n_samples=100, n_features=2, centers=[[5,5],[10,10]], cluster_std=1.5)\n",
    "X_train,X_test, y_train,y_test = train_test_split(X, y, test_size=0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fe8da9c",
   "metadata": {},
   "source": [
    "Lets Train the Gaussian Naive Bias Classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "e7a33c89",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean :  [[ 4.82799425  4.77211094]\n",
      " [10.26079622 10.52593866]]\n",
      "Varience :  [[2.45944395 1.91415842]\n",
      " [2.6910336  1.91335149]]\n",
      "Priors :  [0.475 0.525]\n"
     ]
    }
   ],
   "source": [
    "gaussian_nb = GaussianNB()\n",
    "gaussian_nb.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d9004c6",
   "metadata": {},
   "source": [
    "Let us now plot the Gaussian Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "384f1976",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.scatter(X[:,0], X[:,1], c=y, s=50, cmap='RdBu')\n",
    "\n",
    "xlim = (min(X[:,0])-2, max(X[:,0])+2)\n",
    "ylim = (min(X[:,1])-2, max(X[:,1])+2)\n",
    "\n",
    "xg = np.linspace(xlim[0],xlim[1],60)\n",
    "yg = np.linspace(ylim[0],ylim[1],40)\n",
    "xx, yy = np.meshgrid(xg, yg)\n",
    "Xgrid = np.vstack([xx.ravel(), yy.ravel()]).T\n",
    "for label, colour in enumerate(['red','blue']):\n",
    "    mask = (y==label)\n",
    "    mu, std = X[mask].mean(0), X[mask].std(0)\n",
    "    P = np.exp(-0.5 * (Xgrid-mu)**2/std**2).prod(1)\n",
    "    Pm = np.ma.masked_array(P,P<0.03)\n",
    "    ax.pcolorfast(xg, yg, Pm.reshape(xx.shape), alpha=0.5, cmap=colour.title()+'s')\n",
    "    ax.contour(xx, yy, P.reshape(xx.shape), levels=[0.01,0.1,0.5,0.9], colors=colour, alpha=0.2)\n",
    "ax.set(xlim=xlim,ylim=ylim)\n",
    "plt.title('Gaussian Distribution of Data')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "388482b5",
   "metadata": {},
   "source": [
    "##### Lets get class predictions for the test set and generate classification report to see how the classifier is doing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "03f6c9dc",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       1.00      1.00      1.00        12\n",
      "           1       1.00      1.00      1.00         8\n",
      "\n",
      "    accuracy                           1.00        20\n",
      "   macro avg       1.00      1.00      1.00        20\n",
      "weighted avg       1.00      1.00      1.00        20\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import classification_report\n",
    "gaussian_nb.predict(X_test)\n",
    "print(classification_report(y_test,gaussian_nb.predict(X_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7d07fde",
   "metadata": {},
   "source": [
    "Sources\n",
    "\n",
    "1. https://towardsdatascience.com/generative-vs-discriminative-classifiers-in-machine-learning-9ee265be859e\n",
    "2. https://www.cs.cornell.edu/courses/cs4780/2018fa/lectures/lecturenote05.html\n",
    "3. https://www.atoti.io/how-to-solve-the-zero-frequency-problem-in-naive-bayes/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "49c4a639",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}