model-5.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center><h2>Artificial and Computational Intelligence (Assignment - 2)</h2></center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem Statement\n",
    "\n",
    "As part of the 2nd Assignment, we'll implement Bayesian Networks and also learn to use the pomegranate library.\n",
    "\n",
    "You are required to create a bayesian network model which would help you predict the probability. The detailed problem description is attached as a PDF as a part of this assignment along with the marking scheme.  \n",
    "\n",
    "### What is a Bayesian Network ?\n",
    "\n",
    "A Bayesian network, Bayes network, belief network, decision network, Bayes(ian) model or probabilistic directed acyclic graphical model is a probabilistic graphical model (a type of statistical model) that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). \n",
    "\n",
    "Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. \n",
    "\n",
    "### Dataset\n",
    "\n",
    "The dataset is attached with the assignment as excel & can be converted to .csv \n",
    "\n",
    "#### Dataset Description\n",
    "##### Sample Tuple\n",
    "\n",
    "Y\twon\t5wickets\tlost\t2nd\tvWest_Indies\tHome\t6-Nov-11\n",
    "\n",
    "##### Explanation\n",
    "- The first column represents if Ashwin was in the playing 11 or not. \n",
    "- The second column represents the Result of the match . win indicates India won the match.\n",
    "- The third column represents the Margin of victory / losss.\n",
    "- The fourth column represents the results of the toss. won indicates India won the toss. \n",
    "- The fifth column represents the batting order. If India batted 1st or 2nd. \n",
    "- The sixth column represents the opponent.\n",
    "- The seventh column represents the location of the match. If the match was held in Home(India) or away. \n",
    "- The last column represents the start date of the match.\n",
    "\n",
    "\n",
    "### Evaluation\n",
    "We wish to evaluate based on \n",
    "- coding practices being followed\n",
    "- commenting to explain the code and logic behind doing something\n",
    "- your understanding and explanation of data\n",
    "- how good the model would perform"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# BITS RollNumbers , Names.\n",
    "\n",
    "# 2019ap04008, JITENDRA PAL SINGH\n",
    "# 2019ap04021, HARSH KHAJGIWALE\n",
    "# 2019ad04006, MAHESH MEHENDALE "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Import libraries\n",
    "import pandas as pd\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ashwin</th>\n",
       "      <th>Result</th>\n",
       "      <th>Margin</th>\n",
       "      <th>Toss</th>\n",
       "      <th>Bat</th>\n",
       "      <th>Opposition</th>\n",
       "      <th>Location</th>\n",
       "      <th>Start Date</th>\n",
       "      <th>Unnamed: 8</th>\n",
       "      <th>Unnamed: 9</th>\n",
       "      <th>Unnamed: 10</th>\n",
       "      <th>Unnamed: 11</th>\n",
       "      <th>Unnamed: 12</th>\n",
       "      <th>Unnamed: 13</th>\n",
       "      <th>Unnamed: 14</th>\n",
       "      <th>Unnamed: 15</th>\n",
       "      <th>Unnamed: 16</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Y</td>\n",
       "      <td>won</td>\n",
       "      <td>5 wickets</td>\n",
       "      <td>lost</td>\n",
       "      <td>2nd</td>\n",
       "      <td>v West Indies</td>\n",
       "      <td>Home</td>\n",
       "      <td>2011-11-06</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Y</td>\n",
       "      <td>won</td>\n",
       "      <td>inns &amp; 15 runs</td>\n",
       "      <td>won</td>\n",
       "      <td>1st</td>\n",
       "      <td>v West Indies</td>\n",
       "      <td>Home</td>\n",
       "      <td>2011-11-14</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Y</td>\n",
       "      <td>draw</td>\n",
       "      <td>-</td>\n",
       "      <td>lost</td>\n",
       "      <td>2nd</td>\n",
       "      <td>v West Indies</td>\n",
       "      <td>Home</td>\n",
       "      <td>2011-11-22</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Y</td>\n",
       "      <td>lost</td>\n",
       "      <td>122 runs</td>\n",
       "      <td>lost</td>\n",
       "      <td>2nd</td>\n",
       "      <td>v Australia</td>\n",
       "      <td>Away</td>\n",
       "      <td>2011-12-26</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Y</td>\n",
       "      <td>lost</td>\n",
       "      <td>inns &amp; 68 runs</td>\n",
       "      <td>won</td>\n",
       "      <td>1st</td>\n",
       "      <td>v Australia</td>\n",
       "      <td>Away</td>\n",
       "      <td>2012-01-03</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaT</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 17 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Ashwin Result          Margin  Toss  Bat     Opposition Location  \\\n",
       "0       Y    won       5 wickets  lost  2nd  v West Indies     Home   \n",
       "1       Y    won  inns & 15 runs   won  1st  v West Indies     Home   \n",
       "2       Y   draw               -  lost  2nd  v West Indies     Home   \n",
       "3       Y   lost        122 runs  lost  2nd    v Australia     Away   \n",
       "4       Y   lost  inns & 68 runs   won  1st    v Australia     Away   \n",
       "..    ...    ...             ...   ...  ...            ...      ...   \n",
       "95    NaN    NaN             NaN   NaN  NaN            NaN      NaN   \n",
       "96    NaN    NaN             NaN   NaN  NaN            NaN      NaN   \n",
       "97    NaN    NaN             NaN   NaN  NaN            NaN      NaN   \n",
       "98    NaN    NaN             NaN   NaN  NaN            NaN      NaN   \n",
       "99    NaN    NaN             NaN   NaN  NaN            NaN      NaN   \n",
       "\n",
       "   Start Date  Unnamed: 8  Unnamed: 9  Unnamed: 10  Unnamed: 11  Unnamed: 12  \\\n",
       "0  2011-11-06         NaN         NaN          NaN          NaN          NaN   \n",
       "1  2011-11-14         NaN         NaN          NaN          NaN          NaN   \n",
       "2  2011-11-22         NaN         NaN          NaN          NaN          NaN   \n",
       "3  2011-12-26         NaN         NaN          NaN          NaN          NaN   \n",
       "4  2012-01-03         NaN         NaN          NaN          NaN          NaN   \n",
       "..        ...         ...         ...          ...          ...          ...   \n",
       "95        NaT         NaN         NaN          NaN          NaN          NaN   \n",
       "96        NaT         NaN         NaN          NaN          NaN          NaN   \n",
       "97        NaT         NaN         NaN          NaN          NaN          NaN   \n",
       "98        NaT         NaN         NaN          NaN          NaN          NaN   \n",
       "99        NaT         NaN         NaN          NaN          NaN          NaN   \n",
       "\n",
       "    Unnamed: 13  Unnamed: 14  Unnamed: 15  Unnamed: 16  \n",
       "0           NaN          NaN          NaN          NaN  \n",
       "1           NaN          NaN          NaN          NaN  \n",
       "2           NaN          NaN          NaN          NaN  \n",
       "3           NaN          NaN          NaN          NaN  \n",
       "4           NaN          NaN          NaN          NaN  \n",
       "..          ...          ...          ...          ...  \n",
       "95          NaN          NaN          NaN          NaN  \n",
       "96          NaN          NaN          NaN          NaN  \n",
       "97          NaN          NaN          NaN          NaN  \n",
       "98          NaN          NaN          NaN          NaN  \n",
       "99          NaN          NaN          NaN          NaN  \n",
       "\n",
       "[100 rows x 17 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Read data\n",
    "df = pd.read_excel(\"./India_Test_Stats.xlsx\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Margin</th>\n",
       "      <th>Start Date</th>\n",
       "      <th>Result_draw</th>\n",
       "      <th>Result_lost</th>\n",
       "      <th>Result_won</th>\n",
       "      <th>Bat_1st</th>\n",
       "      <th>Bat_2nd</th>\n",
       "      <th>Opposition_v Afghanistan</th>\n",
       "      <th>Opposition_v Australia</th>\n",
       "      <th>Opposition_v Bangladesh</th>\n",
       "      <th>...</th>\n",
       "      <th>Opposition_v New Zealand</th>\n",
       "      <th>Opposition_v South Africa</th>\n",
       "      <th>Opposition_v Sri Lanka</th>\n",
       "      <th>Opposition_v West Indies</th>\n",
       "      <th>Location_Away</th>\n",
       "      <th>Location_Home</th>\n",
       "      <th>Toss_lost</th>\n",
       "      <th>Toss_won</th>\n",
       "      <th>Ashwin_N</th>\n",
       "      <th>Ashwin_Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5 wickets</td>\n",
       "      <td>2011-11-06</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>inns &amp; 15 runs</td>\n",
       "      <td>2011-11-14</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-</td>\n",
       "      <td>2011-11-22</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>122 runs</td>\n",
       "      <td>2011-12-26</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>inns &amp; 68 runs</td>\n",
       "      <td>2012-01-03</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
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       "      <td>0</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>203 runs</td>\n",
       "      <td>2019-10-02</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>inns &amp; 137 runs</td>\n",
       "      <td>2019-10-10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>inns &amp; 202 runs</td>\n",
       "      <td>2019-10-19</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>inns &amp; 130 runs</td>\n",
       "      <td>2019-11-14</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>inns &amp; 46 runs</td>\n",
       "      <td>2019-11-22</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>85 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Margin Start Date  Result_draw  Result_lost  Result_won  Bat_1st  \\\n",
       "0         5 wickets 2011-11-06            0            0           1        0   \n",
       "1    inns & 15 runs 2011-11-14            0            0           1        1   \n",
       "2                 - 2011-11-22            1            0           0        0   \n",
       "3          122 runs 2011-12-26            0            1           0        0   \n",
       "4    inns & 68 runs 2012-01-03            0            1           0        1   \n",
       "..              ...        ...          ...          ...         ...      ...   \n",
       "80         203 runs 2019-10-02            0            0           1        1   \n",
       "81  inns & 137 runs 2019-10-10            0            0           1        1   \n",
       "82  inns & 202 runs 2019-10-19            0            0           1        1   \n",
       "83  inns & 130 runs 2019-11-14            0            0           1        0   \n",
       "84   inns & 46 runs 2019-11-22            0            0           1        0   \n",
       "\n",
       "    Bat_2nd  Opposition_v Afghanistan  Opposition_v Australia  \\\n",
       "0         1                         0                       0   \n",
       "1         0                         0                       0   \n",
       "2         1                         0                       0   \n",
       "3         1                         0                       1   \n",
       "4         0                         0                       1   \n",
       "..      ...                       ...                     ...   \n",
       "80        0                         0                       0   \n",
       "81        0                         0                       0   \n",
       "82        0                         0                       0   \n",
       "83        1                         0                       0   \n",
       "84        1                         0                       0   \n",
       "\n",
       "    Opposition_v Bangladesh  ...  Opposition_v New Zealand  \\\n",
       "0                         0  ...                         0   \n",
       "1                         0  ...                         0   \n",
       "2                         0  ...                         0   \n",
       "3                         0  ...                         0   \n",
       "4                         0  ...                         0   \n",
       "..                      ...  ...                       ...   \n",
       "80                        0  ...                         0   \n",
       "81                        0  ...                         0   \n",
       "82                        0  ...                         0   \n",
       "83                        1  ...                         0   \n",
       "84                        1  ...                         0   \n",
       "\n",
       "    Opposition_v South Africa  Opposition_v Sri Lanka  \\\n",
       "0                           0                       0   \n",
       "1                           0                       0   \n",
       "2                           0                       0   \n",
       "3                           0                       0   \n",
       "4                           0                       0   \n",
       "..                        ...                     ...   \n",
       "80                          1                       0   \n",
       "81                          1                       0   \n",
       "82                          1                       0   \n",
       "83                          0                       0   \n",
       "84                          0                       0   \n",
       "\n",
       "    Opposition_v West Indies  Location_Away  Location_Home  Toss_lost  \\\n",
       "0                          1              0              1          1   \n",
       "1                          1              0              1          0   \n",
       "2                          1              0              1          1   \n",
       "3                          0              1              0          1   \n",
       "4                          0              1              0          0   \n",
       "..                       ...            ...            ...        ...   \n",
       "80                         0              0              1          0   \n",
       "81                         0              0              1          0   \n",
       "82                         0              0              1          0   \n",
       "83                         0              0              1          1   \n",
       "84                         0              0              1          1   \n",
       "\n",
       "    Toss_won  Ashwin_N  Ashwin_Y  \n",
       "0          0         0         1  \n",
       "1          1         0         1  \n",
       "2          0         0         1  \n",
       "3          0         0         1  \n",
       "4          1         0         1  \n",
       "..       ...       ...       ...  \n",
       "80         1         0         1  \n",
       "81         1         0         1  \n",
       "82         1         0         1  \n",
       "83         0         0         1  \n",
       "84         0         0         1  \n",
       "\n",
       "[85 rows x 21 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Pre-process data (Whatever you feel might be required)\n",
    "\n",
    "\n",
    "df = df.dropna(how='all', axis=0)\n",
    "df = df.dropna(how='all', axis=1)\n",
    "\n",
    "df = pd.get_dummies(df, columns=['Result'], )\n",
    "df = pd.get_dummies(df, columns=['Bat'])\n",
    "df = pd.get_dummies(df, columns=['Opposition'])\n",
    "df = pd.get_dummies(df, columns=['Location'])\n",
    "df = pd.get_dummies(df, columns=['Toss'])\n",
    "df = pd.get_dummies(df, columns=['Ashwin'])\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Margin</th>\n",
       "      <th>Start Date</th>\n",
       "      <th>draw</th>\n",
       "      <th>lost</th>\n",
       "      <th>won</th>\n",
       "      <th>bat_1st</th>\n",
       "      <th>bat_2nd</th>\n",
       "      <th>v_afghanistan</th>\n",
       "      <th>v_australia</th>\n",
       "      <th>v_bangladesh</th>\n",
       "      <th>...</th>\n",
       "      <th>v_new_zealand</th>\n",
       "      <th>v_south_africa</th>\n",
       "      <th>v_sri_lanka</th>\n",
       "      <th>v_west_indies</th>\n",
       "      <th>away</th>\n",
       "      <th>home</th>\n",
       "      <th>toss_lost</th>\n",
       "      <th>toss_won</th>\n",
       "      <th>N</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5 wickets</td>\n",
       "      <td>2011-11-06</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>inns &amp; 15 runs</td>\n",
       "      <td>2011-11-14</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-</td>\n",
       "      <td>2011-11-22</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>122 runs</td>\n",
       "      <td>2011-12-26</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>inns &amp; 68 runs</td>\n",
       "      <td>2012-01-03</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>203 runs</td>\n",
       "      <td>2019-10-02</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>inns &amp; 137 runs</td>\n",
       "      <td>2019-10-10</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>inns &amp; 202 runs</td>\n",
       "      <td>2019-10-19</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>inns &amp; 130 runs</td>\n",
       "      <td>2019-11-14</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>inns &amp; 46 runs</td>\n",
       "      <td>2019-11-22</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>85 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             Margin Start Date  draw  lost  won  bat_1st  bat_2nd  \\\n",
       "0         5 wickets 2011-11-06     0     0    1        0        1   \n",
       "1    inns & 15 runs 2011-11-14     0     0    1        1        0   \n",
       "2                 - 2011-11-22     1     0    0        0        1   \n",
       "3          122 runs 2011-12-26     0     1    0        0        1   \n",
       "4    inns & 68 runs 2012-01-03     0     1    0        1        0   \n",
       "..              ...        ...   ...   ...  ...      ...      ...   \n",
       "80         203 runs 2019-10-02     0     0    1        1        0   \n",
       "81  inns & 137 runs 2019-10-10     0     0    1        1        0   \n",
       "82  inns & 202 runs 2019-10-19     0     0    1        1        0   \n",
       "83  inns & 130 runs 2019-11-14     0     0    1        0        1   \n",
       "84   inns & 46 runs 2019-11-22     0     0    1        0        1   \n",
       "\n",
       "    v_afghanistan  v_australia  v_bangladesh  ...  v_new_zealand  \\\n",
       "0               0            0             0  ...              0   \n",
       "1               0            0             0  ...              0   \n",
       "2               0            0             0  ...              0   \n",
       "3               0            1             0  ...              0   \n",
       "4               0            1             0  ...              0   \n",
       "..            ...          ...           ...  ...            ...   \n",
       "80              0            0             0  ...              0   \n",
       "81              0            0             0  ...              0   \n",
       "82              0            0             0  ...              0   \n",
       "83              0            0             1  ...              0   \n",
       "84              0            0             1  ...              0   \n",
       "\n",
       "    v_south_africa  v_sri_lanka  v_west_indies  away  home  toss_lost  \\\n",
       "0                0            0              1     0     1          1   \n",
       "1                0            0              1     0     1          0   \n",
       "2                0            0              1     0     1          1   \n",
       "3                0            0              0     1     0          1   \n",
       "4                0            0              0     1     0          0   \n",
       "..             ...          ...            ...   ...   ...        ...   \n",
       "80               1            0              0     0     1          0   \n",
       "81               1            0              0     0     1          0   \n",
       "82               1            0              0     0     1          0   \n",
       "83               0            0              0     0     1          1   \n",
       "84               0            0              0     0     1          1   \n",
       "\n",
       "    toss_won  N  Y  \n",
       "0          0  0  1  \n",
       "1          1  0  1  \n",
       "2          0  0  1  \n",
       "3          0  0  1  \n",
       "4          1  0  1  \n",
       "..       ... .. ..  \n",
       "80         1  0  1  \n",
       "81         1  0  1  \n",
       "82         1  0  1  \n",
       "83         0  0  1  \n",
       "84         0  0  1  \n",
       "\n",
       "[85 rows x 21 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Data Description\n",
    "mapping_dict = {\n",
    "    'Location': {\n",
    "        'Location_Home': 'home',\n",
    "        'Location_Away': 'away'\n",
    "    },\n",
    "    'Ashwin': {\n",
    "        'Ashwin_Y': 'Y',\n",
    "        'Ashwin_N': 'N'\n",
    "    },\n",
    "    'Result': {\n",
    "        'Result_lost': 'lost',\n",
    "        'Result_won': 'won',\n",
    "        'Result_draw': 'draw'\n",
    "    },\n",
    "    'Toss': {\n",
    "        'Toss_won': 'toss_won',\n",
    "        'Toss_lost': 'toss_lost'\n",
    "    },\n",
    "    'Bat': {\n",
    "        'Bat_1st': 'bat_1st',\n",
    "        'Bat_2nd': 'bat_2nd',\n",
    "    },\n",
    "    'Opposition': {\n",
    "        'Opposition_v Afghanistan': 'v_afghanistan',\n",
    "        'Opposition_v Australia': 'v_australia',\n",
    "        'Opposition_v Bangladesh': 'v_bangladesh',\n",
    "        'Opposition_v England': 'v_england',\n",
    "        'Opposition_v New Zealand': 'v_new_zealand',\n",
    "        'Opposition_v South Africa': 'v_south_africa',\n",
    "        'Opposition_v Sri Lanka': 'v_sri_lanka',\n",
    "        'Opposition_v West Indies': 'v_west_indies'\n",
    "    },\n",
    "    'Ashwin Playing': {     # for matching display with the problem statement, errors=ignore to suppress any errors due to 'Ashwin' or 'Ashwin Playing'\n",
    "        'Ashwin_Y': 'Y',\n",
    "        'Ashwin_N': 'N'\n",
    "    },\n",
    "    'Batting': {\n",
    "        'Bat_1st': 'bat_1st',\n",
    "        'Bat_2nd': 'bat_2nd',\n",
    "    },\n",
    "\n",
    "}\n",
    "\n",
    "rename_dict = dict()\n",
    "for orig_name, options in mapping_dict.items():\n",
    "    for dummies_name, new_dummies_name in options.items():\n",
    "        rename_dict[dummies_name] = new_dummies_name\n",
    "\n",
    "df = df.rename(columns=rename_dict, errors='ignore')\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Construction of Bayesian Network goes here "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'won': 0.5529411764705883,\n",
       " 'lost': 0.25882352941176473,\n",
       " 'draw': 0.18823529411764706,\n",
       " 'bat_1st': 0.5411764705882353,\n",
       " 'bat_2nd': 0.4588235294117647,\n",
       " 'v_afghanistan': 0.011764705882352941,\n",
       " 'v_australia': 0.23529411764705882,\n",
       " 'v_bangladesh': 0.047058823529411764,\n",
       " 'v_england': 0.2235294117647059,\n",
       " 'v_new_zealand': 0.08235294117647059,\n",
       " 'v_south_africa': 0.1411764705882353,\n",
       " 'v_sri_lanka': 0.10588235294117647,\n",
       " 'v_west_indies': 0.15294117647058825,\n",
       " 'away': 0.49411764705882355,\n",
       " 'home': 0.5058823529411764,\n",
       " 'toss_lost': 0.5294117647058824,\n",
       " 'toss_won': 0.47058823529411764,\n",
       " 'Y': 0.8235294117647058,\n",
       " 'N': 0.17647058823529413}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Solution for part 1\n",
    "from typing import List, Dict\n",
    "    \n",
    "def prior_probability(columns: List) -> Dict:\n",
    "    result = dict()\n",
    "    for column in columns:\n",
    "        result[column] = sum(df[column])/len(df[column])\n",
    "    return result\n",
    "    \n",
    "# prior_probability(['won', 'lost', 'draw'])\n",
    "prior_probability([ 'won', 'lost', 'draw',\n",
    "                    'bat_1st', 'bat_2nd', \n",
    "                    'v_afghanistan', 'v_australia','v_bangladesh', 'v_england', 'v_new_zealand', 'v_south_africa', 'v_sri_lanka', 'v_west_indies', \n",
    "                    'away', 'home',\n",
    "                    'toss_lost', 'toss_won',\n",
    "                    'Y', 'N'\n",
    "                  ])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[['Y', 'lost', 0.2142857142857143], ['Y', 'won', 0.6000000000000001], ['Y', 'draw', 0.18571428571428575], ['N', 'lost', 0.4666666666666666], ['N', 'won', 0.3333333333333333], ['N', 'draw', 0.19999999999999998]]\n"
     ]
    }
   ],
   "source": [
    "#Solution for part 2 \n",
    "import itertools\n",
    "\n",
    "def joint_probability(items: List) -> float:\n",
    "    df_filtered = df\n",
    "    for item in items:\n",
    "        df_filtered = df_filtered[df_filtered[item]==1]\n",
    "    \n",
    "    return df_filtered.shape[0] / df.shape[0]\n",
    "\n",
    "\n",
    "def posterior_probability(conditions: List) -> List:    \n",
    "    \n",
    "    result = list()\n",
    "    \n",
    "    # calculate p(x|y) = p(x,y) / p(y)\n",
    "    items_x = conditions[1]       # Location, Toss, ...\n",
    "    items_y = conditions[0]       # Ashwin_Playing\n",
    "    \n",
    "    lists = list()\n",
    "    for i in range(len(items_y)):\n",
    "        values = list(mapping_dict[items_y[i]].values())\n",
    "        lists.append(values)     # items_y = ['Location', 'Toss']  =>  lists = [['Y', 'N'], ['away', 'home'], ['toss_won', 'toss_lost']]\n",
    "\n",
    "    lists.append(list(mapping_dict[items_x[0]].values()))    # items_x[0] = 'Ashwin Playing' => lists = [['Y', 'N']]\n",
    "\n",
    "\n",
    "    xy_product = list(itertools.product(*lists))  # xy_product = [['Y', 'home', 'toss_won'], ['Y', 'home', 'toss_lost'], ['Y', 'away', 'toss_won'] ... ]\n",
    "\n",
    "    for item in xy_product:\n",
    "        x = item[0]\n",
    "        conditional_prob = joint_probability(item) / prior_probability([x])[x]\n",
    "        lst = list(item)\n",
    "        lst.append(conditional_prob)    \n",
    "        result.append(lst)\n",
    "\n",
    "    return result\n",
    "      \n",
    "\n",
    "# # P(Ashwin Playing | Location)\n",
    "# print(posterior_probability([\n",
    "#     ['Location'],\n",
    "#     ['Ashwin Playing']\n",
    "# ]))\n",
    "\n",
    "# P(Result | Ashwin Playing)\n",
    "print(posterior_probability([\n",
    "    ['Ashwin Playing'],\n",
    "    ['Result']\n",
    "]))\n",
    "\n",
    "# # P(Result | Ashwin Playing, Toss)\n",
    "# print(posterior_probability([\n",
    "#     ['Location', 'Toss'],\n",
    "#     ['Ashwin Playing']\n",
    "# ]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "home\tY\ttoss_won\t0.5116279069767442\n",
      "home\tY\ttoss_lost\t0.48837209302325585\n",
      "home\tN\ttoss_won\t0.0\n",
      "home\tN\ttoss_lost\t0.0\n",
      "away\tY\ttoss_won\t0.2619047619047619\n",
      "away\tY\ttoss_lost\t0.38095238095238093\n",
      "away\tN\ttoss_won\t0.16666666666666669\n",
      "away\tN\ttoss_lost\t0.19047619047619047\n",
      "toss_won\tbat_1st\t0.9\n",
      "toss_won\tbat_2nd\t0.10000000000000002\n",
      "toss_lost\tbat_1st\t0.2222222222222222\n",
      "toss_lost\tbat_2nd\t0.7777777777777777\n",
      "bat_1st\tlost\t0.1956521739130435\n",
      "bat_1st\twon\t0.6739130434782609\n",
      "bat_1st\tdraw\t0.13043478260869565\n",
      "bat_2nd\tlost\t0.33333333333333337\n",
      "bat_2nd\twon\t0.41025641025641024\n",
      "bat_2nd\tdraw\t0.25641025641025644\n"
     ]
    },
    {
     "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": [
    "#Solution for part 3 \n",
    "from pomegranate import DiscreteDistribution, ConditionalProbabilityTable, State, BayesianNetwork\n",
    "from matplotlib import pyplot\n",
    "import pygraphviz\n",
    "\n",
    "location = DiscreteDistribution(prior_probability(list(mapping_dict['Location'].values())))        # location is independent\n",
    "ashwin_playing = DiscreteDistribution(prior_probability(list(mapping_dict['Ashwin Playing'].values())))          # ashwin playing or not\n",
    "\n",
    "p1 = posterior_probability([['Location', 'Ashwin Playing'], ['Toss']])\n",
    "toss = ConditionalProbabilityTable(p1, [location, ashwin_playing])            # winning/losing toss is independent\n",
    "\n",
    "p2 = posterior_probability([['Toss'], ['Batting']])\n",
    "batting = ConditionalProbabilityTable(p2, [toss])          # batting first or second can be considered independent\n",
    "\n",
    "p3 = posterior_probability([['Batting'], ['Result']])\n",
    "result = ConditionalProbabilityTable(p3, [batting])          # batting first or second can be considered independent\n",
    "print(toss)\n",
    "print(batting)\n",
    "print(result)\n",
    "\n",
    "# A favorable outcome would decide whether or not Ashwin should play\n",
    "\n",
    "s1 = State(location, name=\"Location\")\n",
    "s2 = State(ashwin_playing, name=\"Ashwin Playing\")\n",
    "s3 = State(toss, name=\"Toss\")\n",
    "s4 = State(batting, name=\"Batting\")\n",
    "\n",
    "s5 = State(result, name=\"Result\")\n",
    "\n",
    "model = BayesianNetwork(\"Assignment 2 - Spinning the Bayes Net\")\n",
    "model.add_states(s1, s2, s3, s4, s5)\n",
    "\n",
    "model.add_edge(s1, s3)\n",
    "model.add_edge(s2, s3)\n",
    "model.add_edge(s3, s4)\n",
    "model.add_edge(s4, s5)\n",
    "model.plot()\n",
    "\n",
    "model.bake()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Location\t\t[{\n",
      "     \"class\" : \"Distribution\",\n",
      "     \"dtype\" : \"str\",\n",
      "     \"name\" : \"DiscreteDistribution\",\n",
      "     \"parameters\" : [\n",
      "         {\n",
      "             \"home\" : 0.57776238309664,\n",
      "             \"away\" : 0.42223761690336004\n",
      "         }\n",
      "     ],\n",
      "     \"frozen\" : false\n",
      " }                                        'Y'\n",
      " {\n",
      "     \"class\" : \"Distribution\",\n",
      "     \"dtype\" : \"str\",\n",
      "     \"name\" : \"DiscreteDistribution\",\n",
      "     \"parameters\" : [\n",
      "         {\n",
      "             \"toss_lost\" : 0.8971250432975405,\n",
      "             \"toss_won\" : 0.1028749567024595\n",
      "         }\n",
      "     ],\n",
      "     \"frozen\" : false\n",
      " }                                             'bat_2nd' 'won']\n"
     ]
    }
   ],
   "source": [
    "#Solution for part 4\n",
    "# a)\n",
    "beliefs = map( str, model.predict_proba([{'Result': 'won', 'Batting': 'bat_2nd', 'Ashwin Playing': 'Y', }]) )\n",
    "print(\"\\n\".join( \"{}\\t\\t{}\".format( state.name, belief ) for state, belief in zip( model.states, beliefs ) ))\n",
    "\n",
    "# conclusion :\n",
    "# Probability of India winning, while batting 2nd and Ashwin playing \n",
    "# is 67% on home locations, 33% in away locations.\n",
    "# 94.5% when losing toss, 5.5% when winning toss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Batting\t\t['bat_2nd' {\n",
      "               \"class\" : \"Distribution\",\n",
      "               \"dtype\" : \"str\",\n",
      "               \"name\" : \"DiscreteDistribution\",\n",
      "               \"parameters\" : [\n",
      "                   {\n",
      "                       \"toss_won\" : 0.47058823529411764,\n",
      "                       \"toss_lost\" : 0.5294117647058824\n",
      "                   }\n",
      "               ],\n",
      "               \"frozen\" : false\n",
      "           }\n",
      " {\n",
      "     \"class\" : \"Distribution\",\n",
      "     \"dtype\" : \"str\",\n",
      "     \"name\" : \"DiscreteDistribution\",\n",
      "     \"parameters\" : [\n",
      "         {\n",
      "             \"home\" : 0.5058823529411764,\n",
      "             \"away\" : 0.49411764705882355\n",
      "         }\n",
      "     ],\n",
      "     \"frozen\" : false\n",
      " }                                        'N' 'won']\n"
     ]
    }
   ],
   "source": [
    "#Solution for part 4\n",
    "# b)\n",
    "\n",
    "beliefs = map( str, model.predict_proba([{'Result': 'won', 'Batting': 'bat_2nd', 'Ashwin Playing': 'N', }]) )\n",
    "print(\"\\n\".join( \"{}\\t\\t{}\".format( state.name, belief ) for state, belief in zip( model.states, beliefs ) ))\n",
    "\n",
    "# conclusion :\n",
    "# Probability of India winning, while batting 2nd and Ashwin NOT playing \n",
    "# is 0% on home locations, 100% in away locations.\n",
    "# 69% when losing toss, 31% when winning toss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Batting\t\t['bat_2nd' {\n",
      "               \"class\" : \"Distribution\",\n",
      "               \"dtype\" : \"str\",\n",
      "               \"name\" : \"DiscreteDistribution\",\n",
      "               \"parameters\" : [\n",
      "                   {\n",
      "                       \"toss_won\" : 0.0,\n",
      "                       \"toss_lost\" : 1.0\n",
      "                   }\n",
      "               ],\n",
      "               \"frozen\" : false\n",
      "           }\n",
      " {\n",
      "     \"class\" : \"Distribution\",\n",
      "     \"dtype\" : \"str\",\n",
      "     \"name\" : \"DiscreteDistribution\",\n",
      "     \"parameters\" : [\n",
      "         {\n",
      "             \"home\" : 0.6142857142857143,\n",
      "             \"away\" : 0.3857142857142858\n",
      "         }\n",
      "     ],\n",
      "     \"frozen\" : false\n",
      " }                                        'Y' 'lost']\n"
     ]
    }
   ],
   "source": [
    "#Solution for part 4\n",
    "# c)\n",
    "\n",
    "beliefs = map( str, model.predict_proba([{'Result': 'lost', 'Batting': 'bat_2nd', 'Ashwin Playing': 'Y', }]) )\n",
    "print(\"\\n\".join( \"{}\\t\\t{}\".format( state.name, belief ) for state, belief in zip( model.states, beliefs ) ))\n",
    "\n",
    "# conclusion :\n",
    "# Probability of India losing, while batting 2nd and Ashwin playing \n",
    "# is 67% on home locations, 33% in away locations.\n",
    "# 94.5% when losing toss, 5.5% when winning toss."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Batting\t\t['bat_2nd' {\n",
      "               \"class\" : \"Distribution\",\n",
      "               \"dtype\" : \"str\",\n",
      "               \"name\" : \"DiscreteDistribution\",\n",
      "               \"parameters\" : [\n",
      "                   {\n",
      "                       \"toss_won\" : 0.1818181818181819,\n",
      "                       \"toss_lost\" : 0.818181818181818\n",
      "                   }\n",
      "               ],\n",
      "               \"frozen\" : false\n",
      "           }\n",
      " {\n",
      "     \"class\" : \"Distribution\",\n",
      "     \"dtype\" : \"str\",\n",
      "     \"name\" : \"DiscreteDistribution\",\n",
      "     \"parameters\" : [\n",
      "         {\n",
      "             \"home\" : 0.0,\n",
      "             \"away\" : 1.0\n",
      "         }\n",
      "     ],\n",
      "     \"frozen\" : false\n",
      " }                                    'N' 'lost']\n"
     ]
    }
   ],
   "source": [
    "#Solution for part 4\n",
    "# d)\n",
    "\n",
    "beliefs = map( str, model.predict_proba([{'Result': 'lost', 'Batting': 'bat_2nd', 'Ashwin Playing': 'N', }]) )\n",
    "print(\"\\n\".join( \"{}\\t\\t{}\".format( state.name, belief ) for state, belief in zip( model.states, beliefs ) ))\n",
    "\n",
    "# conclusion :\n",
    "# Probability of India losing, while batting 2nd and Ashwin NOT playing \n",
    "# is 0% on home locations, 100% in away locations.\n",
    "# 69% when losing toss, 31% when winning toss."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3><center> Happy Coding!</center></h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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