Bayesian network in Python.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chess Players' Bayesian Network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The network"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### This project aims to show an example of bayesian network architecture in action. It is based on a database taken from Kaggle, a platform providing <br> - along with other services and tools - a vast container of datasets. https://www.kaggle.com/datasets/goldian/chess. <br> For this purpose the *pgmpy* library has been very useful as it implements the kind of models we are interested in."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### The dataset contains approximately 378.000 rows and 14 columns. For our bayesian network the interesting columns are those that allow to think about <br> logically acceptable influences some variables can have over others. So the chosen columns regard ratings, titles, age, activity/inactivity flag and number of official games played in the last month."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>o_title</th>\n",
       "      <th>rating</th>\n",
       "      <th>k</th>\n",
       "      <th>rapid_rating</th>\n",
       "      <th>blitz_rating</th>\n",
       "      <th>birthday</th>\n",
       "      <th>flag</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1063.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1987.0</td>\n",
       "      <td>i</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1151.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1986.0</td>\n",
       "      <td>i</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1840.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>1836.0</td>\n",
       "      <td>1860.0</td>\n",
       "      <td>1974.0</td>\n",
       "      <td>i</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1728.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1741.0</td>\n",
       "      <td>2001.0</td>\n",
       "      <td>i</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1325.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>1593.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1970.0</td>\n",
       "      <td>i</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1598.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>i</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1777.0</td>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1964.0</td>\n",
       "      <td>i</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1915.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1993.0</td>\n",
       "      <td>wi</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  title o_title  rating     k  rapid_rating  blitz_rating  birthday flag\n",
       "0   NaN     NaN  1063.0  40.0           NaN           NaN    1987.0    i\n",
       "1   NaN     NaN  1151.0  40.0           NaN           NaN    1986.0    i\n",
       "2   NaN     NaN  1840.0  40.0        1836.0        1860.0    1974.0    i\n",
       "3   NaN     NaN  1728.0  40.0           NaN        1741.0    2001.0    i\n",
       "4   NaN     NaN  1325.0  40.0        1593.0           NaN    1970.0    i\n",
       "5   NaN     NaN  1598.0  20.0           NaN           NaN       NaN    i\n",
       "6   NaN     NaN  1777.0  20.0           NaN           NaN    1964.0    i\n",
       "7   NaN     NaN  1915.0  40.0           NaN           NaN    1993.0   wi"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "data = pd.read_csv(\"chess_players.csv\")\n",
    "\n",
    "for col in [\"Unnamed: 0\", \"fideid\", \"name\", \"sex\", \"country\", \"foa_title\"]:\n",
    "    data=data.drop(col, axis=1)\n",
    "\n",
    "data.head(8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### The code below converts female titles into general ones because the network will not take into account the sex of the players; due to the scarsity of data the column of other titles (o_titles) will be treated as boolean, while in the original dataset titles were diversified if present; moreover the discrete rating variables and <br> the dates of birthday have been quantized into 4 equally sized bins. The number of official games played recently is either 10, 15, 20 or 40."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>o_title</th>\n",
       "      <th>rating</th>\n",
       "      <th>k</th>\n",
       "      <th>rapid_rating</th>\n",
       "      <th>blitz_rating</th>\n",
       "      <th>birthday</th>\n",
       "      <th>flag</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>yes</td>\n",
       "      <td>(1000.999, 1365.0]</td>\n",
       "      <td>40.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>(1967.0, 1987.0]</td>\n",
       "      <td>inactive</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>yes</td>\n",
       "      <td>(1000.999, 1365.0]</td>\n",
       "      <td>40.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>(1967.0, 1987.0]</td>\n",
       "      <td>inactive</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>yes</td>\n",
       "      <td>(1650.0, 1917.0]</td>\n",
       "      <td>40.0</td>\n",
       "      <td>(1620.0, 1883.0]</td>\n",
       "      <td>(1690.0, 1938.0]</td>\n",
       "      <td>(1967.0, 1987.0]</td>\n",
       "      <td>inactive</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>yes</td>\n",
       "      <td>(1650.0, 1917.0]</td>\n",
       "      <td>40.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>(1690.0, 1938.0]</td>\n",
       "      <td>(1987.0, 2001.0]</td>\n",
       "      <td>inactive</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>yes</td>\n",
       "      <td>(1000.999, 1365.0]</td>\n",
       "      <td>40.0</td>\n",
       "      <td>(1351.0, 1620.0]</td>\n",
       "      <td>NaN</td>\n",
       "      <td>(1967.0, 1987.0]</td>\n",
       "      <td>inactive</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>yes</td>\n",
       "      <td>(1365.0, 1650.0]</td>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>inactive</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>NaN</td>\n",
       "      <td>yes</td>\n",
       "      <td>(1650.0, 1917.0]</td>\n",
       "      <td>20.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>(1918.999, 1967.0]</td>\n",
       "      <td>inactive</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NaN</td>\n",
       "      <td>yes</td>\n",
       "      <td>(1650.0, 1917.0]</td>\n",
       "      <td>40.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>(1987.0, 2001.0]</td>\n",
       "      <td>inactive</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>NaN</td>\n",
       "      <td>yes</td>\n",
       "      <td>(1365.0, 1650.0]</td>\n",
       "      <td>40.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>(1967.0, 1987.0]</td>\n",
       "      <td>inactive</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>NaN</td>\n",
       "      <td>yes</td>\n",
       "      <td>(1650.0, 1917.0]</td>\n",
       "      <td>40.0</td>\n",
       "      <td>(1883.0, 2847.0]</td>\n",
       "      <td>(1690.0, 1938.0]</td>\n",
       "      <td>NaN</td>\n",
       "      <td>inactive</td>\n",
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      "text/plain": [
       "  title o_title              rating     k      rapid_rating      blitz_rating  \\\n",
       "0   NaN     yes  (1000.999, 1365.0]  40.0               NaN               NaN   \n",
       "1   NaN     yes  (1000.999, 1365.0]  40.0               NaN               NaN   \n",
       "2   NaN     yes    (1650.0, 1917.0]  40.0  (1620.0, 1883.0]  (1690.0, 1938.0]   \n",
       "3   NaN     yes    (1650.0, 1917.0]  40.0               NaN  (1690.0, 1938.0]   \n",
       "4   NaN     yes  (1000.999, 1365.0]  40.0  (1351.0, 1620.0]               NaN   \n",
       "5   NaN     yes    (1365.0, 1650.0]  20.0               NaN               NaN   \n",
       "6   NaN     yes    (1650.0, 1917.0]  20.0               NaN               NaN   \n",
       "7   NaN     yes    (1650.0, 1917.0]  40.0               NaN               NaN   \n",
       "8   NaN     yes    (1365.0, 1650.0]  40.0               NaN               NaN   \n",
       "9   NaN     yes    (1650.0, 1917.0]  40.0  (1883.0, 2847.0]  (1690.0, 1938.0]   \n",
       "\n",
       "             birthday      flag  \n",
       "0    (1967.0, 1987.0]  inactive  \n",
       "1    (1967.0, 1987.0]  inactive  \n",
       "2    (1967.0, 1987.0]  inactive  \n",
       "3    (1987.0, 2001.0]  inactive  \n",
       "4    (1967.0, 1987.0]  inactive  \n",
       "5                 NaN  inactive  \n",
       "6  (1918.999, 1967.0]  inactive  \n",
       "7    (1987.0, 2001.0]  inactive  \n",
       "8    (1967.0, 1987.0]  inactive  \n",
       "9                 NaN  inactive  "
      ]
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     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Defining nan\n",
    "nan = np.NaN\n",
    "\n",
    "flag_dict={'wi':'i', 'i':'i', 'w':nan, nan:nan}\n",
    "\n",
    "titles=data['title'].unique()\n",
    "title_dict = dict(zip(list(titles),list(titles)))\n",
    "title_dict[\"WFM\"]=\"FM\"\n",
    "title_dict[\"WIM\"]=\"IM\"\n",
    "title_dict[\"WCM\"]=\"CM\"\n",
    "title_dict[\"WGM\"]=\"GM\"\n",
    "title_dict[\"WH\"]=nan\n",
    "\n",
    "o_titles=data['o_title'].unique()\n",
    "o_title_dict = dict(zip(list(o_titles),list(o_titles)))\n",
    "for o_title in o_titles:\n",
    "    if type(o_title)==str:\n",
    "        o_title_dict[o_title]='no'\n",
    "    else:\n",
    "        o_title_dict[o_title]='yes'\n",
    "\n",
    "flags=data['flag'].unique()\n",
    "flag_dict = dict(zip(list(flags),list(flags)))\n",
    "for flag in flags:\n",
    "    if type(flag)==str:\n",
    "        flag_dict[flag]='inactive'\n",
    "    else:\n",
    "        flag_dict[flag]='probably active'\n",
    "\n",
    "for col in [\"rating\",\"rapid_rating\",\"blitz_rating\",\"birthday\"]:\n",
    "    data[col]=pd.qcut(data[col], q=4)\n",
    "\n",
    "for col, dictionary in [(\"flag\", flag_dict),(\"title\",title_dict),(\"o_title\",o_title_dict)]:\n",
    "    data[col] = data[col].map(dictionary)\n",
    "\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### The arcs of the network are ready to be defined and the supposed influence diagram is as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pgmpy.models import BayesianNetwork\n",
    "\n",
    "chess_players_model = BayesianNetwork(\n",
    "    [\n",
    "        (\"rating\", \"rapid_rating\"),\n",
    "        (\"rapid_rating\", \"blitz_rating\"),\n",
    "        (\"rating\", \"title\"),\n",
    "        (\"title\", \"o_title\"),\n",
    "        (\"k\", \"flag\"),\n",
    "        (\"k\", \"title\"),\n",
    "        (\"birthday\", \"rating\"),\n",
    "        (\"birthday\", \"flag\")\n",
    "    ]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fit the data to create the model\n",
    "chess_players_model.fit(data, complete_samples_only=False) # complete_samples_only=False because we desire to retain as much information as possible "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython.display import Image, display\n",
    "display(Image(filename='image.png'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### In order to decide which arcs make more sense you ideally have some knowledge in the field."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Here it is possible to inspect some of the conditional probability tables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+----------------------------+-----+----------------------------+\n",
      "| birthday                   | ... | birthday((2001.0, 2016.0]) |\n",
      "+----------------------------+-----+----------------------------+\n",
      "| rating((1000.999, 1365.0]) | ... | 0.6098581828706281         |\n",
      "+----------------------------+-----+----------------------------+\n",
      "| rating((1365.0, 1650.0])   | ... | 0.2483135561146114         |\n",
      "+----------------------------+-----+----------------------------+\n",
      "| rating((1650.0, 1917.0])   | ... | 0.09587683950397399        |\n",
      "+----------------------------+-----+----------------------------+\n",
      "| rating((1917.0, 2865.0])   | ... | 0.045951421510786565       |\n",
      "+----------------------------+-----+----------------------------+\n",
      "['rating', 'birthday']\n",
      "[[0.10097125 0.12282589 0.19587618 0.60985818]\n",
      " [0.2435644  0.21434236 0.29807846 0.24831356]\n",
      " [0.323628   0.28041587 0.29053903 0.09587684]\n",
      " [0.33183635 0.38241589 0.21550633 0.04595142]]\n",
      "------------------------------\n",
      "+---------------------------------+-----+--------------------------+\n",
      "| rating                          | ... | rating((1917.0, 2865.0]) |\n",
      "+---------------------------------+-----+--------------------------+\n",
      "| rapid_rating((999.999, 1351.0]) | ... | 0.0009161823988272865    |\n",
      "+---------------------------------+-----+--------------------------+\n",
      "| rapid_rating((1351.0, 1620.0])  | ... | 0.01188419454478823      |\n",
      "+---------------------------------+-----+--------------------------+\n",
      "| rapid_rating((1620.0, 1883.0])  | ... | 0.11360661745458353      |\n",
      "+---------------------------------+-----+--------------------------+\n",
      "| rapid_rating((1883.0, 2847.0])  | ... | 0.873593005601801        |\n",
      "+---------------------------------+-----+--------------------------+\n",
      "['rapid_rating', 'rating']\n",
      "[[8.43011522e-01 1.39475156e-01 1.07473973e-02 9.16182399e-04]\n",
      " [1.49988504e-01 6.90154097e-01 1.38757963e-01 1.18841945e-02]\n",
      " [6.92333240e-03 1.66963332e-01 7.13161030e-01 1.13606617e-01]\n",
      " [7.66420561e-05 3.40741494e-03 1.37333610e-01 8.73593006e-01]]\n",
      "------------------------------\n",
      "+---------------------------------+-----+--------------------------------+\n",
      "| rapid_rating                    | ... | rapid_rating((1883.0, 2847.0]) |\n",
      "+---------------------------------+-----+--------------------------------+\n",
      "| blitz_rating((999.999, 1410.0]) | ... | 0.0001055112017725882          |\n",
      "+---------------------------------+-----+--------------------------------+\n",
      "| blitz_rating((1410.0, 1690.0])  | ... | 0.004748004079766469           |\n",
      "+---------------------------------+-----+--------------------------------+\n",
      "| blitz_rating((1690.0, 1938.0])  | ... | 0.2164738156367601             |\n",
      "+---------------------------------+-----+--------------------------------+\n",
      "| blitz_rating((1938.0, 2850.0])  | ... | 0.7786726690817009             |\n",
      "+---------------------------------+-----+--------------------------------+\n",
      "['blitz_rating', 'rapid_rating']\n",
      "[[9.15375759e-01 2.71679887e-01 9.60481869e-03 1.05511202e-04]\n",
      " [8.17981997e-02 6.61363938e-01 2.95673762e-01 4.74800408e-03]\n",
      " [2.82604145e-03 6.50064253e-02 6.43807741e-01 2.16473816e-01]\n",
      " [0.00000000e+00 1.94974963e-03 5.09136787e-02 7.78672669e-01]]\n",
      "------------------------------\n",
      "+-----------+-----+--------------------------+\n",
      "| k         | ... | k(40.0)                  |\n",
      "+-----------+-----+--------------------------+\n",
      "| rating    | ... | rating((1917.0, 2865.0]) |\n",
      "+-----------+-----+--------------------------+\n",
      "| title(CM) | ... | 0.3714670255720054       |\n",
      "+-----------+-----+--------------------------+\n",
      "| title(FM) | ... | 0.5975773889636609       |\n",
      "+-----------+-----+--------------------------+\n",
      "| title(GM) | ... | 0.0                      |\n",
      "+-----------+-----+--------------------------+\n",
      "| title(IM) | ... | 0.03095558546433378      |\n",
      "+-----------+-----+--------------------------+\n",
      "['title', 'k', 'rating']\n",
      "[[[2.50000000e-01 2.50000000e-01 0.00000000e+00 3.30469266e-04]\n",
      "  [2.50000000e-01 2.50000000e-01 2.50000000e-01 2.50000000e-01]\n",
      "  [8.00000000e-01 6.88995215e-01 5.14376997e-01 1.21681810e-01]\n",
      "  [9.62264151e-01 9.35960591e-01 7.94871795e-01 3.71467026e-01]]\n",
      "\n",
      " [[2.50000000e-01 2.50000000e-01 0.00000000e+00 1.26404494e-01]\n",
      "  [2.50000000e-01 2.50000000e-01 2.50000000e-01 2.50000000e-01]\n",
      "  [2.00000000e-01 2.87081340e-01 4.02555911e-01 7.51826118e-01]\n",
      "  [3.77358491e-02 6.40394089e-02 1.96581197e-01 5.97577389e-01]]\n",
      "\n",
      " [[2.50000000e-01 2.50000000e-01 0.00000000e+00 2.97587574e-01]\n",
      "  [2.50000000e-01 2.50000000e-01 2.50000000e-01 2.50000000e-01]\n",
      "  [0.00000000e+00 0.00000000e+00 2.12992545e-03 2.36059148e-02]\n",
      "  [0.00000000e+00 0.00000000e+00 0.00000000e+00 0.00000000e+00]]\n",
      "\n",
      " [[2.50000000e-01 2.50000000e-01 1.00000000e+00 5.75677462e-01]\n",
      "  [2.50000000e-01 2.50000000e-01 2.50000000e-01 2.50000000e-01]\n",
      "  [0.00000000e+00 2.39234450e-02 8.09371672e-02 1.02886157e-01]\n",
      "  [0.00000000e+00 0.00000000e+00 8.54700855e-03 3.09555855e-02]]]\n",
      "------------------------------\n",
      "+--------------+-----+----------------------+\n",
      "| title        | ... | title(IM)            |\n",
      "+--------------+-----+----------------------+\n",
      "| o_title(no)  | ... | 0.012005054759898905 |\n",
      "+--------------+-----+----------------------+\n",
      "| o_title(yes) | ... | 0.9879949452401011   |\n",
      "+--------------+-----+----------------------+\n",
      "['o_title', 'title']\n",
      "[[0.02133816 0.01053772 0.03529981 0.01200505]\n",
      " [0.97866184 0.98946228 0.96470019 0.98799495]]\n",
      "------------------------------\n",
      "+---------+-------------+\n",
      "| k(10.0) | 0.0170296   |\n",
      "+---------+-------------+\n",
      "| k(15.0) | 2.64887e-06 |\n",
      "+---------+-------------+\n",
      "| k(20.0) | 0.434916    |\n",
      "+---------+-------------+\n",
      "| k(40.0) | 0.548052    |\n",
      "+---------+-------------+\n",
      "['k']\n",
      "[1.70296065e-02 2.64887330e-06 4.34915859e-01 5.48051886e-01]\n",
      "------------------------------\n",
      "+-----------------------+-----+----------------------------+\n",
      "| birthday              | ... | birthday((2001.0, 2016.0]) |\n",
      "+-----------------------+-----+----------------------------+\n",
      "| k                     | ... | k(40.0)                    |\n",
      "+-----------------------+-----+----------------------------+\n",
      "| flag(inactive)        | ... | 0.5846450248067091         |\n",
      "+-----------------------+-----+----------------------------+\n",
      "| flag(probably active) | ... | 0.41535497519329084        |\n",
      "+-----------------------+-----+----------------------------+\n",
      "['flag', 'birthday', 'k']\n",
      "[[[0.53733602 1.         0.49150917 0.75707676]\n",
      "  [0.43108614 0.5        0.52612546 0.76310489]\n",
      "  [0.23837981 0.5        0.67428371 0.8272638 ]\n",
      "  [0.06140351 0.5        0.61616954 0.58464502]]\n",
      "\n",
      " [[0.46266398 0.         0.50849083 0.24292324]\n",
      "  [0.56891386 0.5        0.47387454 0.23689511]\n",
      "  [0.76162019 0.5        0.32571629 0.1727362 ]\n",
      "  [0.93859649 0.5        0.38383046 0.41535498]]]\n",
      "------------------------------\n",
      "+------------------------------+----------+\n",
      "| birthday((1918.999, 1967.0]) | 0.25224  |\n",
      "+------------------------------+----------+\n",
      "| birthday((1967.0, 1987.0])   | 0.249457 |\n",
      "+------------------------------+----------+\n",
      "| birthday((1987.0, 2001.0])   | 0.25485  |\n",
      "+------------------------------+----------+\n",
      "| birthday((2001.0, 2016.0])   | 0.243454 |\n",
      "+------------------------------+----------+\n",
      "['birthday']\n",
      "[0.25223985 0.24945664 0.25484962 0.24345389]\n",
      "------------------------------\n"
     ]
    }
   ],
   "source": [
    "for cpd in chess_players_model.get_cpds():\n",
    "    print(cpd)\n",
    "    print(cpd.variables)\n",
    "    print(cpd.values)\n",
    "    print(\"------------------------------\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### The pgmpy library provides an efficient method to compute all the conditional independencies between the considered variables. <br> For example, among the others, we can see that given the rating to have a title or not is independent from the rapid and blitz ratings and the birthday. <br>In symbols: <br>(title ⟂ rapid_rating, blitz_rating, birthday | rating)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(o_title ⟂ blitz_rating, rapid_rating, birthday | rating)\n",
       "(o_title ⟂ blitz_rating, rating, k, flag, rapid_rating, birthday | title)\n",
       "(o_title ⟂ blitz_rating | rapid_rating)\n",
       "(o_title ⟂ rapid_rating, birthday | blitz_rating, rating)\n",
       "(o_title ⟂ rating, k, flag, rapid_rating, birthday | blitz_rating, title)\n",
       "(o_title ⟂ blitz_rating, rapid_rating, flag, birthday | k, rating)\n",
       "(o_title ⟂ blitz_rating, rapid_rating | rating, flag)\n",
       "(o_title ⟂ blitz_rating, k, flag, rapid_rating, birthday | rating, title)\n",
       "(o_title ⟂ blitz_rating, birthday | rating, rapid_rating)\n",
       "(o_title ⟂ blitz_rating, rapid_rating | rating, birthday)\n",
       "(o_title ⟂ blitz_rating, rating, flag, rapid_rating, birthday | k, title)\n",
       "(o_title ⟂ blitz_rating | k, rapid_rating)\n",
       "(o_title ⟂ flag | k, birthday)\n",
       "(o_title ⟂ blitz_rating, k, rating, rapid_rating, birthday | flag, title)\n",
       "(o_title ⟂ blitz_rating | rapid_rating, flag)\n",
       "(o_title ⟂ blitz_rating, rating, k, flag, birthday | rapid_rating, title)\n",
       "(o_title ⟂ blitz_rating, k, rating, flag, rapid_rating | title, birthday)\n",
       "(o_title ⟂ blitz_rating | rapid_rating, birthday)\n",
       "(o_title ⟂ rapid_rating, flag, birthday | blitz_rating, k, rating)\n",
       "(o_title ⟂ rapid_rating | blitz_rating, rating, flag)\n",
       "(o_title ⟂ k, rapid_rating, flag, birthday | blitz_rating, rating, title)\n",
       "(o_title ⟂ birthday | blitz_rating, rating, rapid_rating)\n",
       "(o_title ⟂ rapid_rating | blitz_rating, rating, birthday)\n",
       "(o_title ⟂ rating, rapid_rating, flag, birthday | blitz_rating, k, title)\n",
       "(o_title ⟂ flag | blitz_rating, k, birthday)\n",
       "(o_title ⟂ k, rapid_rating, rating, birthday | blitz_rating, flag, title)\n",
       "(o_title ⟂ k, rating, flag, birthday | blitz_rating, rapid_rating, title)\n",
       "(o_title ⟂ k, rapid_rating, rating, flag | blitz_rating, title, birthday)\n",
       "(o_title ⟂ blitz_rating, rapid_rating, birthday | k, rating, flag)\n",
       "(o_title ⟂ blitz_rating, rapid_rating, flag, birthday | k, rating, title)\n",
       "(o_title ⟂ blitz_rating, flag, birthday | k, rating, rapid_rating)\n",
       "(o_title ⟂ blitz_rating, rapid_rating, flag | k, rating, birthday)\n",
       "(o_title ⟂ blitz_rating, k, rapid_rating, birthday | rating, flag, title)\n",
       "(o_title ⟂ blitz_rating | rating, rapid_rating, flag)\n",
       "(o_title ⟂ blitz_rating, rapid_rating | rating, flag, birthday)\n",
       "(o_title ⟂ blitz_rating, k, flag, birthday | rating, rapid_rating, title)\n",
       "(o_title ⟂ blitz_rating, k, rapid_rating, flag | rating, title, birthday)\n",
       "(o_title ⟂ blitz_rating | rating, rapid_rating, birthday)\n",
       "(o_title ⟂ blitz_rating, rating, rapid_rating, birthday | k, flag, title)\n",
       "(o_title ⟂ blitz_rating | k, rapid_rating, flag)\n",
       "(o_title ⟂ blitz_rating, rating, flag, birthday | k, rapid_rating, title)\n",
       "(o_title ⟂ blitz_rating, rating, rapid_rating, flag | k, title, birthday)\n",
       "(o_title ⟂ blitz_rating, flag | k, rapid_rating, birthday)\n",
       "(o_title ⟂ blitz_rating, k, rating, birthday | rapid_rating, flag, title)\n",
       "(o_title ⟂ blitz_rating, k, rapid_rating, rating | flag, birthday, title)\n",
       "(o_title ⟂ blitz_rating | rapid_rating, flag, birthday)\n",
       "(o_title ⟂ blitz_rating, k, rating, flag | rapid_rating, title, birthday)\n",
       "(o_title ⟂ rapid_rating, birthday | blitz_rating, k, rating, flag)\n",
       "(o_title ⟂ rapid_rating, flag, birthday | blitz_rating, k, rating, title)\n",
       "(o_title ⟂ flag, birthday | blitz_rating, k, rating, rapid_rating)\n",
       "(o_title ⟂ rapid_rating, flag | blitz_rating, k, rating, birthday)\n",
       "(o_title ⟂ k, rapid_rating, birthday | blitz_rating, rating, flag, title)\n",
       "(o_title ⟂ rapid_rating | blitz_rating, rating, flag, birthday)\n",
       "(o_title ⟂ k, flag, birthday | blitz_rating, rating, rapid_rating, title)\n",
       "(o_title ⟂ k, rapid_rating, flag | blitz_rating, rating, title, birthday)\n",
       "(o_title ⟂ rating, rapid_rating, birthday | blitz_rating, k, flag, title)\n",
       "(o_title ⟂ rating, flag, birthday | blitz_rating, k, rapid_rating, title)\n",
       "(o_title ⟂ rating, rapid_rating, flag | blitz_rating, k, title, birthday)\n",
       "(o_title ⟂ flag | blitz_rating, k, rapid_rating, birthday)\n",
       "(o_title ⟂ k, rating, birthday | blitz_rating, rapid_rating, flag, title)\n",
       "(o_title ⟂ k, rapid_rating, rating | blitz_rating, flag, birthday, title)\n",
       "(o_title ⟂ k, rating, flag | blitz_rating, rapid_rating, title, birthday)\n",
       "(o_title ⟂ blitz_rating, rapid_rating, birthday | k, rating, flag, title)\n",
       "(o_title ⟂ blitz_rating, birthday | k, rating, rapid_rating, flag)\n",
       "(o_title ⟂ blitz_rating, rapid_rating | k, rating, flag, birthday)\n",
       "(o_title ⟂ blitz_rating, flag, birthday | k, rating, rapid_rating, title)\n",
       "(o_title ⟂ blitz_rating, rapid_rating, flag | k, rating, title, birthday)\n",
       "(o_title ⟂ blitz_rating, flag | k, rating, rapid_rating, birthday)\n",
       "(o_title ⟂ blitz_rating, k, birthday | rating, rapid_rating, flag, title)\n",
       "(o_title ⟂ blitz_rating, k, rapid_rating | rating, flag, birthday, title)\n",
       "(o_title ⟂ blitz_rating | rating, rapid_rating, flag, birthday)\n",
       "(o_title ⟂ blitz_rating, k, flag | rating, rapid_rating, title, birthday)\n",
       "(o_title ⟂ blitz_rating, rating, birthday | k, rapid_rating, flag, title)\n",
       "(o_title ⟂ blitz_rating, rating, rapid_rating | k, flag, birthday, title)\n",
       "(o_title ⟂ blitz_rating | k, rapid_rating, flag, birthday)\n",
       "(o_title ⟂ blitz_rating, rating, flag | k, rapid_rating, title, birthday)\n",
       "(o_title ⟂ blitz_rating, k, rating | rapid_rating, flag, birthday, title)\n",
       "(o_title ⟂ rapid_rating, birthday | flag, blitz_rating, k, rating, title)\n",
       "(o_title ⟂ birthday | flag, blitz_rating, k, rating, rapid_rating)\n",
       "(o_title ⟂ rapid_rating | flag, birthday, blitz_rating, k, rating)\n",
       "(o_title ⟂ flag, birthday | blitz_rating, k, rating, title, rapid_rating)\n",
       "(o_title ⟂ rapid_rating, flag | birthday, blitz_rating, k, rating, title)\n",
       "(o_title ⟂ flag | birthday, blitz_rating, k, rating, rapid_rating)\n",
       "(o_title ⟂ k, birthday | flag, blitz_rating, rating, title, rapid_rating)\n",
       "(o_title ⟂ k, rapid_rating | flag, birthday, blitz_rating, rating, title)\n",
       "(o_title ⟂ k, flag | birthday, blitz_rating, rating, title, rapid_rating)\n",
       "(o_title ⟂ rating, birthday | flag, blitz_rating, k, title, rapid_rating)\n",
       "(o_title ⟂ rating, rapid_rating | flag, birthday, blitz_rating, k, title)\n",
       "(o_title ⟂ rating, flag | birthday, blitz_rating, k, title, rapid_rating)\n",
       "(o_title ⟂ k, rating | flag, birthday, blitz_rating, title, rapid_rating)\n",
       "(o_title ⟂ blitz_rating, birthday | flag, k, rating, title, rapid_rating)\n",
       "(o_title ⟂ blitz_rating, rapid_rating | flag, birthday, k, rating, title)\n",
       "(o_title ⟂ blitz_rating | flag, birthday, k, rating, rapid_rating)\n",
       "(o_title ⟂ blitz_rating, flag | birthday, k, rating, title, rapid_rating)\n",
       "(o_title ⟂ blitz_rating, k | flag, birthday, rating, title, rapid_rating)\n",
       "(o_title ⟂ blitz_rating, rating | flag, birthday, k, title, rapid_rating)\n",
       "(o_title ⟂ birthday | flag, blitz_rating, k, rating, title, rapid_rating)\n",
       "(o_title ⟂ rapid_rating | flag, birthday, blitz_rating, k, rating, title)\n",
       "(o_title ⟂ flag | birthday, blitz_rating, k, rating, title, rapid_rating)\n",
       "(o_title ⟂ k | flag, birthday, blitz_rating, rating, title, rapid_rating)\n",
       "(o_title ⟂ rating | flag, birthday, blitz_rating, k, title, rapid_rating)\n",
       "(o_title ⟂ blitz_rating | flag, birthday, k, rating, title, rapid_rating)\n",
       "(flag ⟂ blitz_rating, rapid_rating | rating)\n",
       "(flag ⟂ o_title | title)\n",
       "(flag ⟂ blitz_rating | rapid_rating)\n",
       "(flag ⟂ blitz_rating, rating, rapid_rating | birthday)\n",
       "(flag ⟂ rapid_rating | blitz_rating, rating)\n",
       "(flag ⟂ o_title | blitz_rating, title)\n",
       "(flag ⟂ rating, rapid_rating | blitz_rating, birthday)\n",
       "(flag ⟂ blitz_rating, rapid_rating | o_title, rating)\n",
       "(flag ⟂ blitz_rating | o_title, rapid_rating)\n",
       "(flag ⟂ blitz_rating, o_title, rapid_rating, title | k, rating)\n",
       "(flag ⟂ blitz_rating, o_title, rapid_rating | rating, title)\n",
       "(flag ⟂ blitz_rating | rating, rapid_rating)\n",
       "(flag ⟂ blitz_rating, rapid_rating | rating, birthday)\n",
       "(flag ⟂ o_title | k, title)\n",
       "(flag ⟂ blitz_rating | k, rapid_rating)\n",
       "(flag ⟂ blitz_rating, o_title, rating, title, rapid_rating | k, birthday)\n",
       "(flag ⟂ blitz_rating, o_title | rapid_rating, title)\n",
       "(flag ⟂ o_title | title, birthday)\n",
       "(flag ⟂ blitz_rating, rating | rapid_rating, birthday)\n",
       "(flag ⟂ rapid_rating | blitz_rating, o_title, rating)\n",
       "(flag ⟂ o_title, rapid_rating, title | blitz_rating, k, rating)\n",
       "(flag ⟂ o_title, rapid_rating | blitz_rating, rating, title)\n",
       "(flag ⟂ rapid_rating | blitz_rating, rating, birthday)\n",
       "(flag ⟂ o_title | blitz_rating, k, title)\n",
       "(flag ⟂ o_title, rating, rapid_rating, title | blitz_rating, k, birthday)\n",
       "(flag ⟂ o_title | blitz_rating, rapid_rating, title)\n",
       "(flag ⟂ o_title | blitz_rating, title, birthday)\n",
       "(flag ⟂ rating | blitz_rating, rapid_rating, birthday)\n",
       "(flag ⟂ blitz_rating, rapid_rating, title | k, o_title, rating)\n",
       "(flag ⟂ blitz_rating, rapid_rating | o_title, rating, title)\n",
       "(flag ⟂ blitz_rating | o_title, rating, rapid_rating)\n",
       "(flag ⟂ blitz_rating, rapid_rating | o_title, rating, birthday)\n",
       "(flag ⟂ blitz_rating | o_title, k, rapid_rating)\n",
       "(flag ⟂ blitz_rating, rating, rapid_rating, title | o_title, k, birthday)\n",
       "(flag ⟂ blitz_rating | o_title, rapid_rating, title)\n",
       "(flag ⟂ blitz_rating | o_title, rapid_rating, birthday)\n",
       "(flag ⟂ blitz_rating, o_title, rapid_rating | k, rating, title)\n",
       "(flag ⟂ blitz_rating, o_title, title | k, rating, rapid_rating)\n",
       "(flag ⟂ blitz_rating, o_title, rapid_rating, title | k, rating, birthday)\n",
       "(flag ⟂ blitz_rating, o_title | rating, rapid_rating, title)\n",
       "(flag ⟂ blitz_rating, o_title, rapid_rating | rating, title, birthday)\n",
       "(flag ⟂ blitz_rating | rating, rapid_rating, birthday)\n",
       "(flag ⟂ blitz_rating, o_title | k, rapid_rating, title)\n",
       "(flag ⟂ blitz_rating, o_title, rating, rapid_rating | k, title, birthday)\n",
       "(flag ⟂ blitz_rating, o_title, rating, title | k, rapid_rating, birthday)\n",
       "(flag ⟂ blitz_rating, o_title | rapid_rating, title, birthday)\n",
       "(flag ⟂ rapid_rating, title | blitz_rating, o_title, rating, k)\n",
       "(flag ⟂ rapid_rating | blitz_rating, o_title, rating, title)\n",
       "(flag ⟂ rapid_rating | blitz_rating, o_title, rating, birthday)\n",
       "(flag ⟂ rating, rapid_rating, title | blitz_rating, o_title, k, birthday)\n",
       "(flag ⟂ o_title, rapid_rating | blitz_rating, k, rating, title)\n",
       "(flag ⟂ o_title, title | blitz_rating, k, rating, rapid_rating)\n",
       "(flag ⟂ o_title, rapid_rating, title | blitz_rating, k, rating, birthday)\n",
       "(flag ⟂ o_title | blitz_rating, rating, rapid_rating, title)\n",
       "(flag ⟂ o_title, rapid_rating | blitz_rating, rating, title, birthday)\n",
       "(flag ⟂ o_title | blitz_rating, k, rapid_rating, title)\n",
       "(flag ⟂ o_title, rating, rapid_rating | blitz_rating, k, title, birthday)\n",
       "(flag ⟂ o_title, rating, title | blitz_rating, k, rapid_rating, birthday)\n",
       "(flag ⟂ o_title | blitz_rating, rapid_rating, title, birthday)\n",
       "(flag ⟂ blitz_rating, rapid_rating | k, o_title, rating, title)\n",
       "(flag ⟂ blitz_rating, title | k, o_title, rating, rapid_rating)\n",
       "(flag ⟂ blitz_rating, rapid_rating, title | k, o_title, rating, birthday)\n",
       "(flag ⟂ blitz_rating | o_title, rating, rapid_rating, title)\n",
       "(flag ⟂ blitz_rating, rapid_rating | o_title, rating, title, birthday)\n",
       "(flag ⟂ blitz_rating | o_title, rating, rapid_rating, birthday)\n",
       "(flag ⟂ blitz_rating | o_title, k, rapid_rating, title)\n",
       "(flag ⟂ blitz_rating, rating, rapid_rating | o_title, k, title, birthday)\n",
       "(flag ⟂ blitz_rating, rating, title | o_title, k, rapid_rating, birthday)\n",
       "(flag ⟂ blitz_rating | o_title, rapid_rating, title, birthday)\n",
       "(flag ⟂ blitz_rating, o_title | k, rating, rapid_rating, title)\n",
       "(flag ⟂ blitz_rating, o_title, rapid_rating | k, rating, title, birthday)\n",
       "(flag ⟂ blitz_rating, o_title, title | k, rating, rapid_rating, birthday)\n",
       "(flag ⟂ blitz_rating, o_title | rating, rapid_rating, title, birthday)\n",
       "(flag ⟂ blitz_rating, o_title, rating | k, rapid_rating, title, birthday)\n",
       "(flag ⟂ rapid_rating | o_title, blitz_rating, rating, k, title)\n",
       "(flag ⟂ title | o_title, blitz_rating, rating, k, rapid_rating)\n",
       "(flag ⟂ rapid_rating, title | o_title, birthday, blitz_rating, rating, k)\n",
       "(flag ⟂ rapid_rating | o_title, birthday, blitz_rating, rating, title)\n",
       "(flag ⟂ rating, rapid_rating | o_title, birthday, blitz_rating, k, title)\n",
       "(flag ⟂ rating, title | o_title, birthday, blitz_rating, k, rapid_rating)\n",
       "(flag ⟂ o_title | blitz_rating, k, rating, title, rapid_rating)\n",
       "(flag ⟂ o_title, rapid_rating | birthday, blitz_rating, k, rating, title)\n",
       "(flag ⟂ o_title, title | birthday, blitz_rating, k, rating, rapid_rating)\n",
       "(flag ⟂ o_title | birthday, blitz_rating, rating, title, rapid_rating)\n",
       "(flag ⟂ o_title, rating | birthday, blitz_rating, k, title, rapid_rating)\n",
       "(flag ⟂ blitz_rating | o_title, k, rating, title, rapid_rating)\n",
       "(flag ⟂ blitz_rating, rapid_rating | o_title, birthday, k, rating, title)\n",
       "(flag ⟂ blitz_rating, title | o_title, birthday, k, rating, rapid_rating)\n",
       "(flag ⟂ blitz_rating | o_title, birthday, rating, title, rapid_rating)\n",
       "(flag ⟂ blitz_rating, rating | o_title, birthday, k, title, rapid_rating)\n",
       "(flag ⟂ blitz_rating, o_title | birthday, k, rating, title, rapid_rating)\n",
       "(flag ⟂ rapid_rating | o_title, birthday, blitz_rating, rating, k, title)\n",
       "(flag ⟂ title | o_title, birthday, blitz_rating, rating, k, rapid_rating)\n",
       "(flag ⟂ rating | o_title, birthday, blitz_rating, k, title, rapid_rating)\n",
       "(flag ⟂ o_title | birthday, blitz_rating, k, rating, title, rapid_rating)\n",
       "(flag ⟂ blitz_rating | o_title, birthday, k, rating, title, rapid_rating)\n",
       "(birthday ⟂ k)\n",
       "(birthday ⟂ k | blitz_rating)\n",
       "(birthday ⟂ blitz_rating, o_title, k, title, rapid_rating | rating)\n",
       "(birthday ⟂ o_title | title)\n",
       "(birthday ⟂ blitz_rating, k | rapid_rating)\n",
       "(birthday ⟂ o_title, k, rapid_rating, title | blitz_rating, rating)\n",
       "(birthday ⟂ o_title | blitz_rating, title)\n",
       "(birthday ⟂ k | blitz_rating, rapid_rating)\n",
       "(birthday ⟂ blitz_rating, k, rapid_rating, title | o_title, rating)\n",
       "(birthday ⟂ blitz_rating | o_title, rapid_rating)\n",
       "(birthday ⟂ blitz_rating, o_title, rapid_rating, title | k, rating)\n",
       "(birthday ⟂ blitz_rating, rapid_rating | rating, flag)\n",
       "(birthday ⟂ blitz_rating, o_title, k, rapid_rating | rating, title)\n",
       "(birthday ⟂ blitz_rating, o_title, k, title | rating, rapid_rating)\n",
       "(birthday ⟂ o_title | k, title)\n",
       "(birthday ⟂ blitz_rating | k, rapid_rating)\n",
       "(birthday ⟂ o_title | flag, title)\n",
       "(birthday ⟂ blitz_rating | rapid_rating, flag)\n",
       "(birthday ⟂ blitz_rating, o_title | rapid_rating, title)\n",
       "(birthday ⟂ k, rapid_rating, title | blitz_rating, o_title, rating)\n",
       "(birthday ⟂ o_title, rapid_rating, title | blitz_rating, k, rating)\n",
       "(birthday ⟂ rapid_rating | blitz_rating, rating, flag)\n",
       "(birthday ⟂ o_title, k, rapid_rating | blitz_rating, rating, title)\n",
       "(birthday ⟂ o_title, k, title | blitz_rating, rating, rapid_rating)\n",
       "(birthday ⟂ o_title | blitz_rating, k, title)\n",
       "(birthday ⟂ o_title | blitz_rating, flag, title)\n",
       "(birthday ⟂ o_title | blitz_rating, rapid_rating, title)\n",
       "(birthday ⟂ blitz_rating, rapid_rating, title | k, o_title, rating)\n",
       "(birthday ⟂ blitz_rating, rapid_rating | o_title, rating, flag)\n",
       "(birthday ⟂ blitz_rating, k, rapid_rating | o_title, rating, title)\n",
       "(birthday ⟂ blitz_rating, k, title | o_title, rating, rapid_rating)\n",
       "(birthday ⟂ blitz_rating | o_title, k, rapid_rating)\n",
       "(birthday ⟂ blitz_rating | o_title, rapid_rating, flag)\n",
       "(birthday ⟂ blitz_rating | o_title, rapid_rating, title)\n",
       "(birthday ⟂ blitz_rating, o_title, rapid_rating, title | k, rating, flag)\n",
       "(birthday ⟂ blitz_rating, o_title, rapid_rating | k, rating, title)\n",
       "(birthday ⟂ blitz_rating, o_title, title | k, rating, rapid_rating)\n",
       "(birthday ⟂ blitz_rating, o_title, rapid_rating | rating, flag, title)\n",
       "(birthday ⟂ blitz_rating | rating, rapid_rating, flag)\n",
       "(birthday ⟂ blitz_rating, o_title, k | rating, rapid_rating, title)\n",
       "(birthday ⟂ o_title | k, flag, title)\n",
       "(birthday ⟂ blitz_rating | k, rapid_rating, flag)\n",
       "(birthday ⟂ blitz_rating, o_title | k, rapid_rating, title)\n",
       "(birthday ⟂ blitz_rating, o_title | rapid_rating, flag, title)\n",
       "(birthday ⟂ rapid_rating, title | blitz_rating, o_title, rating, k)\n",
       "(birthday ⟂ rapid_rating | blitz_rating, o_title, rating, flag)\n",
       "(birthday ⟂ k, rapid_rating | blitz_rating, o_title, rating, title)\n",
       "(birthday ⟂ k, title | blitz_rating, o_title, rating, rapid_rating)\n",
       "(birthday ⟂ o_title, rapid_rating, title | blitz_rating, k, rating, flag)\n",
       "(birthday ⟂ o_title, rapid_rating | blitz_rating, k, rating, title)\n",
       "(birthday ⟂ o_title, title | blitz_rating, k, rating, rapid_rating)\n",
       "(birthday ⟂ o_title, rapid_rating | blitz_rating, rating, flag, title)\n",
       "(birthday ⟂ o_title, k | blitz_rating, rating, rapid_rating, title)\n",
       "(birthday ⟂ o_title | blitz_rating, k, flag, title)\n",
       "(birthday ⟂ o_title | blitz_rating, k, rapid_rating, title)\n",
       "(birthday ⟂ o_title | blitz_rating, rapid_rating, flag, title)\n",
       "(birthday ⟂ blitz_rating, rapid_rating, title | k, o_title, rating, flag)\n",
       "(birthday ⟂ blitz_rating, rapid_rating | k, o_title, rating, title)\n",
       "(birthday ⟂ blitz_rating, title | k, o_title, rating, rapid_rating)\n",
       "(birthday ⟂ blitz_rating, rapid_rating | o_title, rating, flag, title)\n",
       "(birthday ⟂ blitz_rating | o_title, rating, rapid_rating, flag)\n",
       "(birthday ⟂ blitz_rating, k | o_title, rating, rapid_rating, title)\n",
       "(birthday ⟂ blitz_rating | o_title, k, rapid_rating, flag)\n",
       "(birthday ⟂ blitz_rating | o_title, k, rapid_rating, title)\n",
       "(birthday ⟂ blitz_rating | o_title, rapid_rating, flag, title)\n",
       "(birthday ⟂ blitz_rating, o_title, rapid_rating | k, rating, flag, title)\n",
       "(birthday ⟂ blitz_rating, o_title, title | k, rating, rapid_rating, flag)\n",
       "(birthday ⟂ blitz_rating, o_title | k, rating, rapid_rating, title)\n",
       "(birthday ⟂ blitz_rating, o_title | rating, rapid_rating, flag, title)\n",
       "(birthday ⟂ blitz_rating, o_title | k, rapid_rating, flag, title)\n",
       "(birthday ⟂ rapid_rating, title | o_title, flag, blitz_rating, rating, k)\n",
       "(birthday ⟂ rapid_rating | o_title, blitz_rating, rating, k, title)\n",
       "(birthday ⟂ title | o_title, blitz_rating, rating, k, rapid_rating)\n",
       "(birthday ⟂ rapid_rating | o_title, flag, blitz_rating, rating, title)\n",
       "(birthday ⟂ k | o_title, blitz_rating, rating, title, rapid_rating)\n",
       "(birthday ⟂ o_title, rapid_rating | flag, blitz_rating, k, rating, title)\n",
       "(birthday ⟂ o_title, title | flag, blitz_rating, k, rating, rapid_rating)\n",
       "(birthday ⟂ o_title | blitz_rating, k, rating, title, rapid_rating)\n",
       "(birthday ⟂ o_title | flag, blitz_rating, rating, title, rapid_rating)\n",
       "(birthday ⟂ o_title | flag, blitz_rating, k, title, rapid_rating)\n",
       "(birthday ⟂ blitz_rating, rapid_rating | o_title, flag, k, rating, title)\n",
       "(birthday ⟂ blitz_rating, title | o_title, flag, k, rating, rapid_rating)\n",
       "(birthday ⟂ blitz_rating | o_title, k, rating, title, rapid_rating)\n",
       "(birthday ⟂ blitz_rating | o_title, flag, rating, title, rapid_rating)\n",
       "(birthday ⟂ blitz_rating | o_title, flag, k, title, rapid_rating)\n",
       "(birthday ⟂ blitz_rating, o_title | flag, k, rating, title, rapid_rating)\n",
       "(birthday ⟂ rapid_rating | o_title, flag, blitz_rating, rating, k, title)\n",
       "(birthday ⟂ title | o_title, flag, blitz_rating, rating, k, rapid_rating)\n",
       "(birthday ⟂ o_title | flag, blitz_rating, k, rating, title, rapid_rating)\n",
       "(birthday ⟂ blitz_rating | o_title, flag, k, rating, title, rapid_rating)\n",
       "(blitz_rating ⟂ k)\n",
       "(blitz_rating ⟂ o_title, k, flag, title, birthday | rating)\n",
       "(blitz_rating ⟂ o_title | title)\n",
       "(blitz_rating ⟂ o_title, rating, k, flag, title, birthday | rapid_rating)\n",
       "(blitz_rating ⟂ k, flag | birthday)\n",
       "(blitz_rating ⟂ k, flag, birthday, title | o_title, rating)\n",
       "(blitz_rating ⟂ rating, k, flag, title, birthday | o_title, rapid_rating)\n",
       "(blitz_rating ⟂ o_title, flag, birthday, title | k, rating)\n",
       "(blitz_rating ⟂ o_title, k, title, birthday | rating, flag)\n",
       "(blitz_rating ⟂ o_title, k, flag, birthday | rating, title)\n",
       "(blitz_rating ⟂ o_title, k, flag, title, birthday | rating, rapid_rating)\n",
       "(blitz_rating ⟂ o_title, k, flag, title | rating, birthday)\n",
       "(blitz_rating ⟂ o_title | k, title)\n",
       "(blitz_rating ⟂ o_title, rating, flag, title, birthday | k, rapid_rating)\n",
       "(blitz_rating ⟂ flag | k, birthday)\n",
       "(blitz_rating ⟂ o_title | flag, title)\n",
       "(blitz_rating ⟂ o_title, k, rating, title, birthday | rapid_rating, flag)\n",
       "(blitz_rating ⟂ k | flag, birthday)\n",
       "(blitz_rating ⟂ o_title, rating, k, flag, birthday | rapid_rating, title)\n",
       "(blitz_rating ⟂ o_title | title, birthday)\n",
       "(blitz_rating ⟂ o_title, rating, k, flag, title | rapid_rating, birthday)\n",
       "(blitz_rating ⟂ flag, birthday, title | k, o_title, rating)\n",
       "(blitz_rating ⟂ k, title, birthday | o_title, rating, flag)\n",
       "(blitz_rating ⟂ k, flag, birthday | o_title, rating, title)\n",
       "(blitz_rating ⟂ k, flag, birthday, title | o_title, rating, rapid_rating)\n",
       "(blitz_rating ⟂ k, flag, title | o_title, rating, birthday)\n",
       "(blitz_rating ⟂ rating, flag, birthday, title | o_title, k, rapid_rating)\n",
       "(blitz_rating ⟂ flag | o_title, k, birthday)\n",
       "(blitz_rating ⟂ k, rating, birthday, title | o_title, rapid_rating, flag)\n",
       "(blitz_rating ⟂ k, rating, flag, birthday | o_title, rapid_rating, title)\n",
       "(blitz_rating ⟂ k, rating, flag, title | o_title, rapid_rating, birthday)\n",
       "(blitz_rating ⟂ o_title, title, birthday | k, rating, flag)\n",
       "(blitz_rating ⟂ o_title, flag, birthday | k, rating, title)\n",
       "(blitz_rating ⟂ o_title, flag, birthday, title | k, rating, rapid_rating)\n",
       "(blitz_rating ⟂ o_title, flag, title | k, rating, birthday)\n",
       "(blitz_rating ⟂ o_title, k, birthday | rating, flag, title)\n",
       "(blitz_rating ⟂ o_title, k, title, birthday | rating, rapid_rating, flag)\n",
       "(blitz_rating ⟂ o_title, k, title | rating, flag, birthday)\n",
       "(blitz_rating ⟂ o_title, k, flag, birthday | rating, rapid_rating, title)\n",
       "(blitz_rating ⟂ o_title, k, flag | rating, title, birthday)\n",
       "(blitz_rating ⟂ o_title, k, flag, title | rating, rapid_rating, birthday)\n",
       "(blitz_rating ⟂ o_title | k, flag, title)\n",
       "(blitz_rating ⟂ o_title, rating, title, birthday | k, rapid_rating, flag)\n",
       "(blitz_rating ⟂ o_title, rating, flag, birthday | k, rapid_rating, title)\n",
       "(blitz_rating ⟂ o_title, flag | k, title, birthday)\n",
       "(blitz_rating ⟂ o_title, rating, flag, title | k, rapid_rating, birthday)\n",
       "(blitz_rating ⟂ o_title, k, rating, birthday | rapid_rating, flag, title)\n",
       "(blitz_rating ⟂ o_title | flag, birthday, title)\n",
       "(blitz_rating ⟂ o_title, k, rating, title | rapid_rating, flag, birthday)\n",
       "(blitz_rating ⟂ o_title, k, rating, flag | rapid_rating, title, birthday)\n",
       "(blitz_rating ⟂ title, birthday | k, o_title, rating, flag)\n",
       "(blitz_rating ⟂ flag, birthday | k, o_title, rating, title)\n",
       "(blitz_rating ⟂ flag, birthday, title | k, o_title, rating, rapid_rating)\n",
       "(blitz_rating ⟂ flag, title | k, o_title, rating, birthday)\n",
       "(blitz_rating ⟂ k, birthday | o_title, rating, flag, title)\n",
       "(blitz_rating ⟂ k, title, birthday | o_title, rating, rapid_rating, flag)\n",
       "(blitz_rating ⟂ k, title | o_title, rating, flag, birthday)\n",
       "(blitz_rating ⟂ k, flag, birthday | o_title, rating, rapid_rating, title)\n",
       "(blitz_rating ⟂ k, flag | o_title, rating, title, birthday)\n",
       "(blitz_rating ⟂ k, flag, title | o_title, rating, rapid_rating, birthday)\n",
       "(blitz_rating ⟂ rating, title, birthday | o_title, k, rapid_rating, flag)\n",
       "(blitz_rating ⟂ rating, flag, birthday | o_title, k, rapid_rating, title)\n",
       "(blitz_rating ⟂ flag | o_title, k, title, birthday)\n",
       "(blitz_rating ⟂ rating, flag, title | o_title, k, rapid_rating, birthday)\n",
       "(blitz_rating ⟂ k, rating, birthday | o_title, rapid_rating, flag, title)\n",
       "(blitz_rating ⟂ k, rating, title | o_title, rapid_rating, flag, birthday)\n",
       "(blitz_rating ⟂ k, rating, flag | o_title, rapid_rating, title, birthday)\n",
       "(blitz_rating ⟂ o_title, birthday | k, rating, flag, title)\n",
       "(blitz_rating ⟂ o_title, title, birthday | k, rating, rapid_rating, flag)\n",
       "(blitz_rating ⟂ o_title, title | k, rating, flag, birthday)\n",
       "(blitz_rating ⟂ o_title, flag, birthday | k, rating, rapid_rating, title)\n",
       "(blitz_rating ⟂ o_title, flag | k, rating, title, birthday)\n",
       "(blitz_rating ⟂ o_title, flag, title | k, rating, rapid_rating, birthday)\n",
       "(blitz_rating ⟂ o_title, k, birthday | rating, rapid_rating, flag, title)\n",
       "(blitz_rating ⟂ o_title, k | rating, flag, birthday, title)\n",
       "(blitz_rating ⟂ o_title, k, title | rating, rapid_rating, flag, birthday)\n",
       "(blitz_rating ⟂ o_title, k, flag | rating, rapid_rating, title, birthday)\n",
       "(blitz_rating ⟂ o_title, rating, birthday | k, rapid_rating, flag, title)\n",
       "(blitz_rating ⟂ o_title | k, flag, birthday, title)\n",
       "(blitz_rating ⟂ o_title, rating, title | k, rapid_rating, flag, birthday)\n",
       "(blitz_rating ⟂ o_title, rating, flag | k, rapid_rating, title, birthday)\n",
       "(blitz_rating ⟂ o_title, k, rating | rapid_rating, flag, birthday, title)\n",
       "(blitz_rating ⟂ birthday | o_title, flag, k, rating, title)\n",
       "(blitz_rating ⟂ title, birthday | o_title, flag, k, rating, rapid_rating)\n",
       "(blitz_rating ⟂ title | o_title, flag, birthday, k, rating)\n",
       "(blitz_rating ⟂ flag, birthday | o_title, k, rating, title, rapid_rating)\n",
       "(blitz_rating ⟂ flag | o_title, birthday, k, rating, title)\n",
       "(blitz_rating ⟂ flag, title | o_title, birthday, k, rating, rapid_rating)\n",
       "(blitz_rating ⟂ k, birthday | o_title, flag, rating, title, rapid_rating)\n",
       "(blitz_rating ⟂ k | o_title, flag, birthday, rating, title)\n",
       "(blitz_rating ⟂ k, title | o_title, flag, birthday, rating, rapid_rating)\n",
       "(blitz_rating ⟂ k, flag | o_title, birthday, rating, title, rapid_rating)\n",
       "(blitz_rating ⟂ rating, birthday | o_title, flag, k, title, rapid_rating)\n",
       "(blitz_rating ⟂ rating, title | o_title, flag, birthday, k, rapid_rating)\n",
       "(blitz_rating ⟂ rating, flag | o_title, birthday, k, title, rapid_rating)\n",
       "(blitz_rating ⟂ k, rating | o_title, flag, birthday, title, rapid_rating)\n",
       "(blitz_rating ⟂ o_title, birthday | flag, k, rating, title, rapid_rating)\n",
       "(blitz_rating ⟂ o_title | flag, birthday, k, rating, title)\n",
       "(blitz_rating ⟂ o_title, title | flag, birthday, k, rating, rapid_rating)\n",
       "(blitz_rating ⟂ o_title, flag | birthday, k, rating, title, rapid_rating)\n",
       "(blitz_rating ⟂ o_title, k | flag, birthday, rating, title, rapid_rating)\n",
       "(blitz_rating ⟂ o_title, rating | flag, birthday, k, title, rapid_rating)\n",
       "(blitz_rating ⟂ birthday | o_title, flag, k, rating, title, rapid_rating)\n",
       "(blitz_rating ⟂ title | o_title, flag, birthday, k, rating, rapid_rating)\n",
       "(blitz_rating ⟂ flag | o_title, birthday, k, rating, title, rapid_rating)\n",
       "(blitz_rating ⟂ k | o_title, flag, birthday, rating, title, rapid_rating)\n",
       "(blitz_rating ⟂ rating | o_title, flag, birthday, k, title, rapid_rating)\n",
       "(blitz_rating ⟂ o_title | flag, birthday, k, rating, title, rapid_rating)\n",
       "(rating ⟂ k)\n",
       "(rating ⟂ k | blitz_rating)\n",
       "(rating ⟂ o_title | title)\n",
       "(rating ⟂ blitz_rating, k | rapid_rating)\n",
       "(rating ⟂ k, flag | birthday)\n",
       "(rating ⟂ o_title | blitz_rating, title)\n",
       "(rating ⟂ k | blitz_rating, rapid_rating)\n",
       "(rating ⟂ k, flag | blitz_rating, birthday)\n",
       "(rating ⟂ blitz_rating | o_title, rapid_rating)\n",
       "(rating ⟂ o_title | k, title)\n",
       "(rating ⟂ blitz_rating | k, rapid_rating)\n",
       "(rating ⟂ flag | k, birthday)\n",
       "(rating ⟂ o_title | flag, title)\n",
       "(rating ⟂ blitz_rating | rapid_rating, flag)\n",
       "(rating ⟂ k | flag, birthday)\n",
       "(rating ⟂ blitz_rating, o_title | rapid_rating, title)\n",
       "(rating ⟂ o_title | title, birthday)\n",
       "(rating ⟂ blitz_rating, k, flag | rapid_rating, birthday)\n",
       "(rating ⟂ o_title | blitz_rating, k, title)\n",
       "(rating ⟂ flag | blitz_rating, k, birthday)\n",
       "(rating ⟂ o_title | blitz_rating, flag, title)\n",
       "(rating ⟂ k | blitz_rating, flag, birthday)\n",
       "(rating ⟂ o_title | blitz_rating, rapid_rating, title)\n",
       "(rating ⟂ o_title | blitz_rating, title, birthday)\n",
       "(rating ⟂ k, flag | blitz_rating, rapid_rating, birthday)\n",
       "(rating ⟂ blitz_rating | o_title, k, rapid_rating)\n",
       "(rating ⟂ flag | o_title, k, birthday)\n",
       "(rating ⟂ blitz_rating | o_title, rapid_rating, flag)\n",
       "(rating ⟂ blitz_rating | o_title, rapid_rating, title)\n",
       "(rating ⟂ blitz_rating | o_title, rapid_rating, birthday)\n",
       "(rating ⟂ o_title | k, flag, title)\n",
       "(rating ⟂ blitz_rating | k, rapid_rating, flag)\n",
       "(rating ⟂ blitz_rating, o_title | k, rapid_rating, title)\n",
       "(rating ⟂ o_title, flag | k, title, birthday)\n",
       "(rating ⟂ blitz_rating, flag | k, rapid_rating, birthday)\n",
       "(rating ⟂ blitz_rating, o_title | rapid_rating, flag, title)\n",
       "(rating ⟂ o_title | flag, birthday, title)\n",
       "(rating ⟂ blitz_rating, k | rapid_rating, flag, birthday)\n",
       "(rating ⟂ blitz_rating, o_title | rapid_rating, title, birthday)\n",
       "(rating ⟂ flag | blitz_rating, o_title, k, birthday)\n",
       "(rating ⟂ o_title | blitz_rating, k, flag, title)\n",
       "(rating ⟂ o_title | blitz_rating, k, rapid_rating, title)\n",
       "(rating ⟂ o_title, flag | blitz_rating, k, title, birthday)\n",
       "(rating ⟂ flag | blitz_rating, k, rapid_rating, birthday)\n",
       "(rating ⟂ o_title | blitz_rating, rapid_rating, flag, title)\n",
       "(rating ⟂ o_title | blitz_rating, flag, birthday, title)\n",
       "(rating ⟂ k | blitz_rating, rapid_rating, flag, birthday)\n",
       "(rating ⟂ o_title | blitz_rating, rapid_rating, title, birthday)\n",
       "(rating ⟂ blitz_rating | o_title, k, rapid_rating, flag)\n",
       "(rating ⟂ blitz_rating | o_title, k, rapid_rating, title)\n",
       "(rating ⟂ flag | o_title, k, title, birthday)\n",
       "(rating ⟂ blitz_rating, flag | o_title, k, rapid_rating, birthday)\n",
       "(rating ⟂ blitz_rating | o_title, rapid_rating, flag, title)\n",
       "(rating ⟂ blitz_rating | o_title, rapid_rating, flag, birthday)\n",
       "(rating ⟂ blitz_rating | o_title, rapid_rating, title, birthday)\n",
       "(rating ⟂ blitz_rating, o_title | k, rapid_rating, flag, title)\n",
       "(rating ⟂ o_title | k, flag, birthday, title)\n",
       "(rating ⟂ blitz_rating | k, rapid_rating, flag, birthday)\n",
       "(rating ⟂ blitz_rating, o_title, flag | k, rapid_rating, title, birthday)\n",
       "(rating ⟂ blitz_rating, o_title | rapid_rating, flag, birthday, title)\n",
       "(rating ⟂ flag | o_title, birthday, blitz_rating, k, title)\n",
       "(rating ⟂ flag | o_title, birthday, blitz_rating, k, rapid_rating)\n",
       "(rating ⟂ o_title | flag, blitz_rating, k, title, rapid_rating)\n",
       "(rating ⟂ o_title | flag, birthday, blitz_rating, k, title)\n",
       "(rating ⟂ o_title, flag | birthday, blitz_rating, k, title, rapid_rating)\n",
       "(rating ⟂ o_title | flag, birthday, blitz_rating, title, rapid_rating)\n",
       "(rating ⟂ blitz_rating | o_title, flag, k, title, rapid_rating)\n",
       "(rating ⟂ blitz_rating | o_title, flag, birthday, k, rapid_rating)\n",
       "(rating ⟂ blitz_rating, flag | o_title, birthday, k, title, rapid_rating)\n",
       "(rating ⟂ blitz_rating | o_title, flag, birthday, title, rapid_rating)\n",
       "(rating ⟂ blitz_rating, o_title | flag, birthday, k, title, rapid_rating)\n",
       "(rating ⟂ flag | o_title, birthday, blitz_rating, k, title, rapid_rating)\n",
       "(rating ⟂ o_title | flag, birthday, blitz_rating, k, title, rapid_rating)\n",
       "(rating ⟂ blitz_rating | o_title, flag, birthday, k, title, rapid_rating)\n",
       "(k ⟂ blitz_rating, rating, rapid_rating, birthday)\n",
       "(k ⟂ rating, rapid_rating, birthday | blitz_rating)\n",
       "(k ⟂ blitz_rating, rapid_rating, birthday | rating)\n",
       "(k ⟂ o_title | title)\n",
       "(k ⟂ blitz_rating, rating, birthday | rapid_rating)\n",
       "(k ⟂ blitz_rating, rating, rapid_rating | birthday)\n",
       "(k ⟂ rapid_rating, birthday | blitz_rating, rating)\n",
       "(k ⟂ o_title | blitz_rating, title)\n",
       "(k ⟂ rating, birthday | blitz_rating, rapid_rating)\n",
       "(k ⟂ rating, rapid_rating | blitz_rating, birthday)\n",
       "(k ⟂ blitz_rating, rapid_rating, birthday | o_title, rating)\n",
       "(k ⟂ blitz_rating | o_title, rapid_rating)\n",
       "(k ⟂ blitz_rating, rapid_rating | rating, flag)\n",
       "(k ⟂ blitz_rating, o_title, rapid_rating, birthday | rating, title)\n",
       "(k ⟂ blitz_rating, birthday | rating, rapid_rating)\n",
       "(k ⟂ blitz_rating, rapid_rating | rating, birthday)\n",
       "(k ⟂ o_title | flag, title)\n",
       "(k ⟂ blitz_rating | rapid_rating, flag)\n",
       "(k ⟂ blitz_rating, rating, rapid_rating | flag, birthday)\n",
       "(k ⟂ blitz_rating, o_title | rapid_rating, title)\n",
       "(k ⟂ o_title | title, birthday)\n",
       "(k ⟂ blitz_rating, rating | rapid_rating, birthday)\n",
       "(k ⟂ rapid_rating, birthday | blitz_rating, o_title, rating)\n",
       "(k ⟂ rapid_rating | blitz_rating, rating, flag)\n",
       "(k ⟂ o_title, rapid_rating, birthday | blitz_rating, rating, title)\n",
       "(k ⟂ birthday | blitz_rating, rating, rapid_rating)\n",
       "(k ⟂ rapid_rating | blitz_rating, rating, birthday)\n",
       "(k ⟂ o_title | blitz_rating, flag, title)\n",
       "(k ⟂ rating, rapid_rating | blitz_rating, flag, birthday)\n",
       "(k ⟂ o_title | blitz_rating, rapid_rating, title)\n",
       "(k ⟂ o_title | blitz_rating, title, birthday)\n",
       "(k ⟂ rating | blitz_rating, rapid_rating, birthday)\n",
       "(k ⟂ blitz_rating, rapid_rating | o_title, rating, flag)\n",
       "(k ⟂ blitz_rating, rapid_rating, birthday | o_title, rating, title)\n",
       "(k ⟂ blitz_rating, birthday | o_title, rating, rapid_rating)\n",
       "(k ⟂ blitz_rating, rapid_rating | o_title, rating, birthday)\n",
       "(k ⟂ blitz_rating | o_title, rapid_rating, flag)\n",
       "(k ⟂ blitz_rating | o_title, rapid_rating, title)\n",
       "(k ⟂ blitz_rating | o_title, rapid_rating, birthday)\n",
       "(k ⟂ blitz_rating, o_title, rapid_rating | rating, flag, title)\n",
       "(k ⟂ blitz_rating | rating, rapid_rating, flag)\n",
       "(k ⟂ blitz_rating, rapid_rating | rating, flag, birthday)\n",
       "(k ⟂ blitz_rating, o_title, birthday | rating, rapid_rating, title)\n",
       "(k ⟂ blitz_rating, o_title, rapid_rating | rating, title, birthday)\n",
       "(k ⟂ blitz_rating | rating, rapid_rating, birthday)\n",
       "(k ⟂ blitz_rating, o_title | rapid_rating, flag, title)\n",
       "(k ⟂ o_title | flag, birthday, title)\n",
       "(k ⟂ blitz_rating, rating | rapid_rating, flag, birthday)\n",
       "(k ⟂ blitz_rating, o_title | rapid_rating, title, birthday)\n",
       "(k ⟂ rapid_rating | blitz_rating, o_title, rating, flag)\n",
       "(k ⟂ rapid_rating, birthday | blitz_rating, o_title, rating, title)\n",
       "(k ⟂ birthday | blitz_rating, o_title, rating, rapid_rating)\n",
       "(k ⟂ rapid_rating | blitz_rating, o_title, rating, birthday)\n",
       "(k ⟂ o_title, rapid_rating | blitz_rating, rating, flag, title)\n",
       "(k ⟂ rapid_rating | blitz_rating, rating, flag, birthday)\n",
       "(k ⟂ o_title, birthday | blitz_rating, rating, rapid_rating, title)\n",
       "(k ⟂ o_title, rapid_rating | blitz_rating, rating, title, birthday)\n",
       "(k ⟂ o_title | blitz_rating, rapid_rating, flag, title)\n",
       "(k ⟂ o_title | blitz_rating, flag, birthday, title)\n",
       "(k ⟂ rating | blitz_rating, rapid_rating, flag, birthday)\n",
       "(k ⟂ o_title | blitz_rating, rapid_rating, title, birthday)\n",
       "(k ⟂ blitz_rating, rapid_rating | o_title, rating, flag, title)\n",
       "(k ⟂ blitz_rating | o_title, rating, rapid_rating, flag)\n",
       "(k ⟂ blitz_rating, rapid_rating | o_title, rating, flag, birthday)\n",
       "(k ⟂ blitz_rating, birthday | o_title, rating, rapid_rating, title)\n",
       "(k ⟂ blitz_rating, rapid_rating | o_title, rating, title, birthday)\n",
       "(k ⟂ blitz_rating | o_title, rating, rapid_rating, birthday)\n",
       "(k ⟂ blitz_rating | o_title, rapid_rating, flag, title)\n",
       "(k ⟂ blitz_rating | o_title, rapid_rating, flag, birthday)\n",
       "(k ⟂ blitz_rating | o_title, rapid_rating, title, birthday)\n",
       "(k ⟂ blitz_rating, o_title | rating, rapid_rating, flag, title)\n",
       "(k ⟂ blitz_rating, o_title, rapid_rating | rating, flag, birthday, title)\n",
       "(k ⟂ blitz_rating | rating, rapid_rating, flag, birthday)\n",
       "(k ⟂ blitz_rating, o_title | rating, rapid_rating, title, birthday)\n",
       "(k ⟂ blitz_rating, o_title | rapid_rating, flag, birthday, title)\n",
       "(k ⟂ rapid_rating | o_title, flag, blitz_rating, rating, title)\n",
       "(k ⟂ rapid_rating | o_title, flag, birthday, blitz_rating, rating)\n",
       "(k ⟂ birthday | o_title, blitz_rating, rating, title, rapid_rating)\n",
       "(k ⟂ rapid_rating | o_title, birthday, blitz_rating, rating, title)\n",
       "(k ⟂ o_title | flag, blitz_rating, rating, title, rapid_rating)\n",
       "(k ⟂ o_title, rapid_rating | flag, birthday, blitz_rating, rating, title)\n",
       "(k ⟂ o_title | birthday, blitz_rating, rating, title, rapid_rating)\n",
       "(k ⟂ o_title | flag, birthday, blitz_rating, title, rapid_rating)\n",
       "(k ⟂ blitz_rating | o_title, flag, rating, title, rapid_rating)\n",
       "(k ⟂ blitz_rating, rapid_rating | o_title, flag, birthday, rating, title)\n",
       "(k ⟂ blitz_rating | o_title, flag, birthday, rating, rapid_rating)\n",
       "(k ⟂ blitz_rating | o_title, birthday, rating, title, rapid_rating)\n",
       "(k ⟂ blitz_rating | o_title, flag, birthday, title, rapid_rating)\n",
       "(k ⟂ blitz_rating, o_title | flag, birthday, rating, title, rapid_rating)\n",
       "(k ⟂ rapid_rating | o_title, flag, birthday, blitz_rating, rating, title)\n",
       "(k ⟂ o_title | flag, birthday, blitz_rating, rating, title, rapid_rating)\n",
       "(k ⟂ blitz_rating | o_title, flag, birthday, rating, title, rapid_rating)\n",
       "(title ⟂ blitz_rating, rapid_rating, birthday | rating)\n",
       "(title ⟂ blitz_rating | rapid_rating)\n",
       "(title ⟂ rapid_rating, birthday | blitz_rating, rating)\n",
       "(title ⟂ blitz_rating, rapid_rating, birthday | o_title, rating)\n",
       "(title ⟂ blitz_rating | o_title, rapid_rating)\n",
       "(title ⟂ blitz_rating, rapid_rating, flag, birthday | k, rating)\n",
       "(title ⟂ blitz_rating, rapid_rating | rating, flag)\n",
       "(title ⟂ blitz_rating, birthday | rating, rapid_rating)\n",
       "(title ⟂ blitz_rating, rapid_rating | rating, birthday)\n",
       "(title ⟂ blitz_rating | k, rapid_rating)\n",
       "(title ⟂ flag | k, birthday)\n",
       "(title ⟂ blitz_rating | rapid_rating, flag)\n",
       "(title ⟂ blitz_rating | rapid_rating, birthday)\n",
       "(title ⟂ rapid_rating, birthday | blitz_rating, o_title, rating)\n",
       "(title ⟂ rapid_rating, flag, birthday | blitz_rating, k, rating)\n",
       "(title ⟂ rapid_rating | blitz_rating, rating, flag)\n",
       "(title ⟂ birthday | blitz_rating, rating, rapid_rating)\n",
       "(title ⟂ rapid_rating | blitz_rating, rating, birthday)\n",
       "(title ⟂ flag | blitz_rating, k, birthday)\n",
       "(title ⟂ blitz_rating, rapid_rating, flag, birthday | k, o_title, rating)\n",
       "(title ⟂ blitz_rating, rapid_rating | o_title, rating, flag)\n",
       "(title ⟂ blitz_rating, birthday | o_title, rating, rapid_rating)\n",
       "(title ⟂ blitz_rating, rapid_rating | o_title, rating, birthday)\n",
       "(title ⟂ blitz_rating | o_title, k, rapid_rating)\n",
       "(title ⟂ flag | o_title, k, birthday)\n",
       "(title ⟂ blitz_rating | o_title, rapid_rating, flag)\n",
       "(title ⟂ blitz_rating | o_title, rapid_rating, birthday)\n",
       "(title ⟂ blitz_rating, rapid_rating, birthday | k, rating, flag)\n",
       "(title ⟂ blitz_rating, flag, birthday | k, rating, rapid_rating)\n",
       "(title ⟂ blitz_rating, rapid_rating, flag | k, rating, birthday)\n",
       "(title ⟂ blitz_rating | rating, rapid_rating, flag)\n",
       "(title ⟂ blitz_rating, rapid_rating | rating, flag, birthday)\n",
       "(title ⟂ blitz_rating | rating, rapid_rating, birthday)\n",
       "(title ⟂ blitz_rating | k, rapid_rating, flag)\n",
       "(title ⟂ blitz_rating, flag | k, rapid_rating, birthday)\n",
       "(title ⟂ blitz_rating | rapid_rating, flag, birthday)\n",
       "(title ⟂ rapid_rating, flag, birthday | blitz_rating, o_title, rating, k)\n",
       "(title ⟂ rapid_rating | blitz_rating, o_title, rating, flag)\n",
       "(title ⟂ birthday | blitz_rating, o_title, rating, rapid_rating)\n",
       "(title ⟂ rapid_rating | blitz_rating, o_title, rating, birthday)\n",
       "(title ⟂ flag | blitz_rating, o_title, k, birthday)\n",
       "(title ⟂ rapid_rating, birthday | blitz_rating, k, rating, flag)\n",
       "(title ⟂ flag, birthday | blitz_rating, k, rating, rapid_rating)\n",
       "(title ⟂ rapid_rating, flag | blitz_rating, k, rating, birthday)\n",
       "(title ⟂ rapid_rating | blitz_rating, rating, flag, birthday)\n",
       "(title ⟂ flag | blitz_rating, k, rapid_rating, birthday)\n",
       "(title ⟂ blitz_rating, rapid_rating, birthday | k, o_title, rating, flag)\n",
       "(title ⟂ blitz_rating, flag, birthday | k, o_title, rating, rapid_rating)\n",
       "(title ⟂ blitz_rating, rapid_rating, flag | k, o_title, rating, birthday)\n",
       "(title ⟂ blitz_rating | o_title, rating, rapid_rating, flag)\n",
       "(title ⟂ blitz_rating, rapid_rating | o_title, rating, flag, birthday)\n",
       "(title ⟂ blitz_rating | o_title, rating, rapid_rating, birthday)\n",
       "(title ⟂ blitz_rating | o_title, k, rapid_rating, flag)\n",
       "(title ⟂ blitz_rating, flag | o_title, k, rapid_rating, birthday)\n",
       "(title ⟂ blitz_rating | o_title, rapid_rating, flag, birthday)\n",
       "(title ⟂ blitz_rating, birthday | k, rating, rapid_rating, flag)\n",
       "(title ⟂ blitz_rating, rapid_rating | k, rating, flag, birthday)\n",
       "(title ⟂ blitz_rating, flag | k, rating, rapid_rating, birthday)\n",
       "(title ⟂ blitz_rating | rating, rapid_rating, flag, birthday)\n",
       "(title ⟂ blitz_rating | k, rapid_rating, flag, birthday)\n",
       "(title ⟂ rapid_rating, birthday | o_title, flag, blitz_rating, rating, k)\n",
       "(title ⟂ flag, birthday | o_title, blitz_rating, rating, k, rapid_rating)\n",
       "(title ⟂ rapid_rating, flag | o_title, birthday, blitz_rating, rating, k)\n",
       "(title ⟂ rapid_rating | o_title, flag, birthday, blitz_rating, rating)\n",
       "(title ⟂ flag | o_title, birthday, blitz_rating, k, rapid_rating)\n",
       "(title ⟂ birthday | flag, blitz_rating, k, rating, rapid_rating)\n",
       "(title ⟂ rapid_rating | flag, birthday, blitz_rating, k, rating)\n",
       "(title ⟂ flag | birthday, blitz_rating, k, rating, rapid_rating)\n",
       "(title ⟂ blitz_rating, birthday | o_title, flag, k, rating, rapid_rating)\n",
       "(title ⟂ blitz_rating, rapid_rating | o_title, flag, birthday, k, rating)\n",
       "(title ⟂ blitz_rating, flag | o_title, birthday, k, rating, rapid_rating)\n",
       "(title ⟂ blitz_rating | o_title, flag, birthday, rating, rapid_rating)\n",
       "(title ⟂ blitz_rating | o_title, flag, birthday, k, rapid_rating)\n",
       "(title ⟂ blitz_rating | flag, birthday, k, rating, rapid_rating)\n",
       "(title ⟂ birthday | o_title, flag, blitz_rating, rating, k, rapid_rating)\n",
       "(title ⟂ rapid_rating | o_title, flag, birthday, blitz_rating, rating, k)\n",
       "(title ⟂ flag | o_title, birthday, blitz_rating, rating, k, rapid_rating)\n",
       "(title ⟂ blitz_rating | o_title, flag, birthday, k, rating, rapid_rating)\n",
       "(rapid_rating ⟂ k)\n",
       "(rapid_rating ⟂ k | blitz_rating)\n",
       "(rapid_rating ⟂ o_title, k, flag, title, birthday | rating)\n",
       "(rapid_rating ⟂ o_title | title)\n",
       "(rapid_rating ⟂ k, flag | birthday)\n",
       "(rapid_rating ⟂ o_title, k, flag, title, birthday | blitz_rating, rating)\n",
       "(rapid_rating ⟂ o_title | blitz_rating, title)\n",
       "(rapid_rating ⟂ k, flag | blitz_rating, birthday)\n",
       "(rapid_rating ⟂ k, flag, birthday, title | o_title, rating)\n",
       "(rapid_rating ⟂ o_title, flag, birthday, title | k, rating)\n",
       "(rapid_rating ⟂ o_title, k, title, birthday | rating, flag)\n",
       "(rapid_rating ⟂ o_title, k, flag, birthday | rating, title)\n",
       "(rapid_rating ⟂ o_title, k, flag, title | rating, birthday)\n",
       "(rapid_rating ⟂ o_title | k, title)\n",
       "(rapid_rating ⟂ flag | k, birthday)\n",
       "(rapid_rating ⟂ o_title | flag, title)\n",
       "(rapid_rating ⟂ k | flag, birthday)\n",
       "(rapid_rating ⟂ o_title | title, birthday)\n",
       "(rapid_rating ⟂ k, flag, birthday, title | blitz_rating, o_title, rating)\n",
       "(rapid_rating ⟂ o_title, flag, birthday, title | blitz_rating, k, rating)\n",
       "(rapid_rating ⟂ o_title, k, title, birthday | blitz_rating, rating, flag)\n",
       "(rapid_rating ⟂ o_title, k, flag, birthday | blitz_rating, rating, title)\n",
       "(rapid_rating ⟂ o_title, k, flag, title | blitz_rating, rating, birthday)\n",
       "(rapid_rating ⟂ o_title | blitz_rating, k, title)\n",
       "(rapid_rating ⟂ flag | blitz_rating, k, birthday)\n",
       "(rapid_rating ⟂ o_title | blitz_rating, flag, title)\n",
       "(rapid_rating ⟂ k | blitz_rating, flag, birthday)\n",
       "(rapid_rating ⟂ o_title | blitz_rating, title, birthday)\n",
       "(rapid_rating ⟂ flag, birthday, title | k, o_title, rating)\n",
       "(rapid_rating ⟂ k, title, birthday | o_title, rating, flag)\n",
       "(rapid_rating ⟂ k, flag, birthday | o_title, rating, title)\n",
       "(rapid_rating ⟂ k, flag, title | o_title, rating, birthday)\n",
       "(rapid_rating ⟂ flag | o_title, k, birthday)\n",
       "(rapid_rating ⟂ o_title, title, birthday | k, rating, flag)\n",
       "(rapid_rating ⟂ o_title, flag, birthday | k, rating, title)\n",
       "(rapid_rating ⟂ o_title, flag, title | k, rating, birthday)\n",
       "(rapid_rating ⟂ o_title, k, birthday | rating, flag, title)\n",
       "(rapid_rating ⟂ o_title, k, title | rating, flag, birthday)\n",
       "(rapid_rating ⟂ o_title, k, flag | rating, title, birthday)\n",
       "(rapid_rating ⟂ o_title | k, flag, title)\n",
       "(rapid_rating ⟂ o_title, flag | k, title, birthday)\n",
       "(rapid_rating ⟂ o_title | flag, birthday, title)\n",
       "(rapid_rating ⟂ flag, birthday, title | blitz_rating, o_title, rating, k)\n",
       "(rapid_rating ⟂ k, title, birthday | blitz_rating, o_title, rating, flag)\n",
       "(rapid_rating ⟂ k, flag, birthday | blitz_rating, o_title, rating, title)\n",
       "(rapid_rating ⟂ k, flag, title | blitz_rating, o_title, rating, birthday)\n",
       "(rapid_rating ⟂ flag | blitz_rating, o_title, k, birthday)\n",
       "(rapid_rating ⟂ o_title, title, birthday | blitz_rating, k, rating, flag)\n",
       "(rapid_rating ⟂ o_title, flag, birthday | blitz_rating, k, rating, title)\n",
       "(rapid_rating ⟂ o_title, flag, title | blitz_rating, k, rating, birthday)\n",
       "(rapid_rating ⟂ o_title, k, birthday | blitz_rating, rating, flag, title)\n",
       "(rapid_rating ⟂ o_title, k, title | blitz_rating, rating, flag, birthday)\n",
       "(rapid_rating ⟂ o_title, k, flag | blitz_rating, rating, title, birthday)\n",
       "(rapid_rating ⟂ o_title | blitz_rating, k, flag, title)\n",
       "(rapid_rating ⟂ o_title, flag | blitz_rating, k, title, birthday)\n",
       "(rapid_rating ⟂ o_title | blitz_rating, flag, birthday, title)\n",
       "(rapid_rating ⟂ title, birthday | k, o_title, rating, flag)\n",
       "(rapid_rating ⟂ flag, birthday | k, o_title, rating, title)\n",
       "(rapid_rating ⟂ flag, title | k, o_title, rating, birthday)\n",
       "(rapid_rating ⟂ k, birthday | o_title, rating, flag, title)\n",
       "(rapid_rating ⟂ k, title | o_title, rating, flag, birthday)\n",
       "(rapid_rating ⟂ k, flag | o_title, rating, title, birthday)\n",
       "(rapid_rating ⟂ flag | o_title, k, title, birthday)\n",
       "(rapid_rating ⟂ o_title, birthday | k, rating, flag, title)\n",
       "(rapid_rating ⟂ o_title, title | k, rating, flag, birthday)\n",
       "(rapid_rating ⟂ o_title, flag | k, rating, title, birthday)\n",
       "(rapid_rating ⟂ o_title, k | rating, flag, birthday, title)\n",
       "(rapid_rating ⟂ o_title | k, flag, birthday, title)\n",
       "(rapid_rating ⟂ title, birthday | o_title, flag, blitz_rating, rating, k)\n",
       "(rapid_rating ⟂ flag, birthday | o_title, blitz_rating, rating, k, title)\n",
       "(rapid_rating ⟂ flag, title | o_title, birthday, blitz_rating, rating, k)\n",
       "(rapid_rating ⟂ k, birthday | o_title, flag, blitz_rating, rating, title)\n",
       "(rapid_rating ⟂ k, title | o_title, flag, birthday, blitz_rating, rating)\n",
       "(rapid_rating ⟂ k, flag | o_title, birthday, blitz_rating, rating, title)\n",
       "(rapid_rating ⟂ flag | o_title, birthday, blitz_rating, k, title)\n",
       "(rapid_rating ⟂ o_title, birthday | flag, blitz_rating, k, rating, title)\n",
       "(rapid_rating ⟂ o_title, title | flag, birthday, blitz_rating, k, rating)\n",
       "(rapid_rating ⟂ o_title, flag | birthday, blitz_rating, k, rating, title)\n",
       "(rapid_rating ⟂ o_title, k | flag, birthday, blitz_rating, rating, title)\n",
       "(rapid_rating ⟂ o_title | flag, birthday, blitz_rating, k, title)\n",
       "(rapid_rating ⟂ birthday | o_title, flag, k, rating, title)\n",
       "(rapid_rating ⟂ title | o_title, flag, birthday, k, rating)\n",
       "(rapid_rating ⟂ flag | o_title, birthday, k, rating, title)\n",
       "(rapid_rating ⟂ k | o_title, flag, birthday, rating, title)\n",
       "(rapid_rating ⟂ o_title | flag, birthday, k, rating, title)\n",
       "(rapid_rating ⟂ birthday | o_title, flag, blitz_rating, rating, k, title)\n",
       "(rapid_rating ⟂ title | o_title, flag, birthday, blitz_rating, rating, k)\n",
       "(rapid_rating ⟂ flag | o_title, birthday, blitz_rating, rating, k, title)\n",
       "(rapid_rating ⟂ k | o_title, flag, birthday, blitz_rating, rating, title)\n",
       "(rapid_rating ⟂ o_title | flag, birthday, blitz_rating, k, rating, title)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chess_players_model.get_independencies()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### It is also provided a tool to compute the so called \"markov blanket\" of a node, i.e. the set of nodes that in case they are given they make the node in question conditional independent from the rest of the network. <br> For example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['k', 'o_title', 'rating']"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chess_players_model.get_markov_blanket(\"title\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exact inference: variable elimination."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Let's compute the most probable status and the related marginal probability of the variable \"activity flag\" (flag) given the number of recent official games (k) and the age interval (birthday) of a player."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "born in the interval (1918.999, 1967.0]\n",
      "number of recent official games: 10\n",
      "{'flag': 'inactive'}\n",
      "0.5373360242179617\n",
      "\n",
      "born in the interval (1967.0, 1987.0]\n",
      "number of recent official games: 10\n",
      "{'flag': 'probably active'}\n",
      "0.5689138576779026\n",
      "\n",
      "born in the interval (1987.0, 2001.0]\n",
      "number of recent official games: 10\n",
      "{'flag': 'probably active'}\n",
      "0.7616201859229748\n",
      "\n",
      "born in the interval (2001.0, 2016.0]\n",
      "number of recent official games: 10\n",
      "{'flag': 'probably active'}\n",
      "0.9385964912280702\n",
      "\n",
      "born in the interval (1918.999, 1967.0]\n",
      "number of recent official games: 15\n",
      "{'flag': 'inactive'}\n",
      "1.0\n",
      "\n",
      "born in the interval (1967.0, 1987.0]\n",
      "number of recent official games: 15\n",
      "{'flag': 'inactive'}\n",
      "0.5\n",
      "\n",
      "born in the interval (1987.0, 2001.0]\n",
      "number of recent official games: 15\n",
      "{'flag': 'inactive'}\n",
      "0.5\n",
      "\n",
      "born in the interval (2001.0, 2016.0]\n",
      "number of recent official games: 15\n",
      "{'flag': 'inactive'}\n",
      "0.5\n",
      "\n",
      "born in the interval (1918.999, 1967.0]\n",
      "number of recent official games: 20\n",
      "{'flag': 'probably active'}\n",
      "0.508490834162285\n",
      "\n",
      "born in the interval (1967.0, 1987.0]\n",
      "number of recent official games: 20\n",
      "{'flag': 'inactive'}\n",
      "0.5261254597382318\n",
      "\n",
      "born in the interval (1987.0, 2001.0]\n",
      "number of recent official games: 20\n",
      "{'flag': 'inactive'}\n",
      "0.6742837130912513\n",
      "\n",
      "born in the interval (2001.0, 2016.0]\n",
      "number of recent official games: 20\n",
      "{'flag': 'inactive'}\n",
      "0.6161695447409733\n",
      "\n",
      "born in the interval (1918.999, 1967.0]\n",
      "number of recent official games: 40\n",
      "{'flag': 'inactive'}\n",
      "0.7570767594907607\n",
      "\n",
      "born in the interval (1967.0, 1987.0]\n",
      "number of recent official games: 40\n",
      "{'flag': 'inactive'}\n",
      "0.7631048882338491\n",
      "\n",
      "born in the interval (1987.0, 2001.0]\n",
      "number of recent official games: 40\n",
      "{'flag': 'inactive'}\n",
      "0.8272638005379328\n",
      "\n",
      "born in the interval (2001.0, 2016.0]\n",
      "number of recent official games: 40\n",
      "{'flag': 'inactive'}\n",
      "0.5846450248067091\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from pgmpy.inference import VariableElimination\n",
    "from pgmpy.factors.discrete import State\n",
    "\n",
    "inference = VariableElimination(chess_players_model)\n",
    "\n",
    "# Birthday intervals\n",
    "\n",
    "birthday_interval1 = pd._libs.interval.Interval(1918.999, 1967.0, closed='right')\n",
    "birthday_interval2 = pd._libs.interval.Interval(1967.0, 1987.0, closed='right')\n",
    "birthday_interval3 = pd._libs.interval.Interval(1987.0, 2001.0, closed='right')\n",
    "birthday_interval4 = pd._libs.interval.Interval(2001.0, 2016.0, closed='right')\n",
    "\n",
    "birthday_intervals = [birthday_interval1, birthday_interval2, birthday_interval3, birthday_interval4]\n",
    "\n",
    "# Rapid rating intervals\n",
    "\n",
    "rapid_interval1 = pd._libs.interval.Interval(999.999, 1351.0, closed='right')\n",
    "rapid_interval2 = pd._libs.interval.Interval(1351.0, 1620.0, closed='right')\n",
    "rapid_interval3 = pd._libs.interval.Interval(1620.0, 1883.0, closed='right')\n",
    "rapid_interval4 = pd._libs.interval.Interval(1883.0, 2847.0, closed='right')\n",
    "\n",
    "rapid_intervals = [rapid_interval1, rapid_interval2, rapid_interval3, rapid_interval4]\n",
    "\n",
    "# Normal rating intervals\n",
    "\n",
    "interval1 = pd._libs.interval.Interval(1000.999, 1365.0, closed='right')\n",
    "interval2 = pd._libs.interval.Interval(1365.0, 1650.0, closed='right')\n",
    "interval3 = pd._libs.interval.Interval(1650.0, 1917.0, closed='right')\n",
    "interval4 = pd._libs.interval.Interval(1917.0, 2865.0, closed='right')\n",
    "\n",
    "intervals = [interval1,interval2,interval3,interval4]\n",
    "\n",
    "k_values = [10,15,20,40]\n",
    "\n",
    "first_variable=k_values\n",
    "second_variable=birthday_intervals\n",
    "\n",
    "for k_value in first_variable:\n",
    "    for interval in second_variable:\n",
    "        print(\"born in the interval \"+str(interval))\n",
    "        print(\"number of recent official games: \"+str(k_value))\n",
    "        phi_query = inference.map_query(variables=['flag'], evidence={'birthday':interval,'k':k_value}, show_progress=False)\n",
    "        print(phi_query)\n",
    "        phi_query = inference.max_marginal(variables=['flag'], evidence={'birthday':interval,'k':k_value}, show_progress=False)\n",
    "        print(phi_query)\n",
    "        print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### As we can see the number of recent official games is the most relevant factor in determining the activity flag of a player, while the age is not so relevant. <br> One of the possible interpretation of the relation we observe between the number of recent official games and the activity flag is that typically after a busy season of tournaments professional chess players switch to an off period."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Approximate inference: sample rejection, likelihood weighted sample and Gibbs sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generating for node: o_title: 100%|██████████| 8/8 [00:00<00:00, 299.33it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SAMPLE REJECTION WITHOUT EVIDENCE\n",
      "\n",
      "                rating       rapid_rating       blitz_rating title o_title  \\\n",
      "0   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "1   (1000.999, 1365.0]   (1351.0, 1620.0]  (999.999, 1410.0]    CM     yes   \n",
      "2     (1917.0, 2865.0]   (1883.0, 2847.0]   (1690.0, 1938.0]    CM     yes   \n",
      "3   (1000.999, 1365.0]  (999.999, 1351.0]   (1410.0, 1690.0]    CM     yes   \n",
      "4   (1000.999, 1365.0]   (1351.0, 1620.0]   (1410.0, 1690.0]    CM     yes   \n",
      "5   (1000.999, 1365.0]   (1620.0, 1883.0]   (1690.0, 1938.0]    CM     yes   \n",
      "6     (1650.0, 1917.0]   (1620.0, 1883.0]   (1938.0, 2850.0]    CM     yes   \n",
      "7     (1365.0, 1650.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "8     (1365.0, 1650.0]   (1351.0, 1620.0]  (999.999, 1410.0]    CM     yes   \n",
      "9   (1000.999, 1365.0]  (999.999, 1351.0]   (1410.0, 1690.0]    CM     yes   \n",
      "10    (1650.0, 1917.0]   (1620.0, 1883.0]   (1938.0, 2850.0]    CM     yes   \n",
      "11    (1365.0, 1650.0]   (1351.0, 1620.0]   (1410.0, 1690.0]    CM     yes   \n",
      "\n",
      "       k      flag            birthday  \n",
      "0   40.0  inactive    (2001.0, 2016.0]  \n",
      "1   20.0  inactive    (2001.0, 2016.0]  \n",
      "2   40.0  inactive    (1967.0, 1987.0]  \n",
      "3   20.0  inactive    (2001.0, 2016.0]  \n",
      "4   20.0  inactive    (2001.0, 2016.0]  \n",
      "5   40.0  inactive    (2001.0, 2016.0]  \n",
      "6   40.0  inactive  (1918.999, 1967.0]  \n",
      "7   20.0  inactive    (1987.0, 2001.0]  \n",
      "8   40.0  inactive    (1987.0, 2001.0]  \n",
      "9   40.0  inactive    (2001.0, 2016.0]  \n",
      "10  40.0  inactive    (1987.0, 2001.0]  \n",
      "11  40.0  inactive    (1967.0, 1987.0]  \n",
      "\n",
      "SAMPLE REJECTION WITH EVIDENCE\n",
      "\n",
      "                rating       rapid_rating       blitz_rating title o_title  \\\n",
      "0   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "1   (1000.999, 1365.0]  (999.999, 1351.0]   (1410.0, 1690.0]    CM     yes   \n",
      "2   (1000.999, 1365.0]   (1351.0, 1620.0]   (1410.0, 1690.0]    CM     yes   \n",
      "3   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    FM     yes   \n",
      "4   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "5   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "6   (1000.999, 1365.0]   (1351.0, 1620.0]   (1410.0, 1690.0]    CM     yes   \n",
      "7   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "8   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "9   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "10  (1000.999, 1365.0]   (1351.0, 1620.0]   (1410.0, 1690.0]    CM     yes   \n",
      "11  (1000.999, 1365.0]   (1351.0, 1620.0]   (1410.0, 1690.0]    CM     yes   \n",
      "12  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "13  (1000.999, 1365.0]  (999.999, 1351.0]   (1410.0, 1690.0]    CM     yes   \n",
      "14  (1000.999, 1365.0]   (1351.0, 1620.0]   (1410.0, 1690.0]    CM     yes   \n",
      "15  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "16  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    FM     yes   \n",
      "17  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "18  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    FM     yes   \n",
      "19  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "\n",
      "       k             flag          birthday  \n",
      "0   20.0         inactive  (2001.0, 2016.0]  \n",
      "1   40.0         inactive  (2001.0, 2016.0]  \n",
      "2   40.0  probably active  (2001.0, 2016.0]  \n",
      "3   40.0         inactive  (2001.0, 2016.0]  \n",
      "4   20.0  probably active  (2001.0, 2016.0]  \n",
      "5   20.0  probably active  (1987.0, 2001.0]  \n",
      "6   20.0         inactive  (1987.0, 2001.0]  \n",
      "7   20.0  probably active  (1967.0, 1987.0]  \n",
      "8   40.0         inactive  (2001.0, 2016.0]  \n",
      "9   40.0         inactive  (2001.0, 2016.0]  \n",
      "10  20.0  probably active  (1967.0, 1987.0]  \n",
      "11  20.0  probably active  (2001.0, 2016.0]  \n",
      "12  20.0         inactive  (2001.0, 2016.0]  \n",
      "13  40.0         inactive  (2001.0, 2016.0]  \n",
      "14  20.0         inactive  (1987.0, 2001.0]  \n",
      "15  20.0  probably active  (2001.0, 2016.0]  \n",
      "16  20.0         inactive  (2001.0, 2016.0]  \n",
      "17  40.0         inactive  (2001.0, 2016.0]  \n",
      "18  20.0         inactive  (2001.0, 2016.0]  \n",
      "19  40.0         inactive  (1967.0, 1987.0]  \n",
      "\n",
      "LIKELIHOOD WEIGHTED SAMPLE\n",
      "\n",
      "                rating       rapid_rating       blitz_rating title o_title  \\\n",
      "0   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "1   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "2   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "3   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "4   (1000.999, 1365.0]  (999.999, 1351.0]   (1690.0, 1938.0]    FM     yes   \n",
      "5   (1000.999, 1365.0]   (1351.0, 1620.0]   (1410.0, 1690.0]    CM     yes   \n",
      "6   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "7   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "8   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "9   (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM      no   \n",
      "10  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "11  (1000.999, 1365.0]   (1351.0, 1620.0]  (999.999, 1410.0]    CM     yes   \n",
      "12  (1000.999, 1365.0]   (1351.0, 1620.0]  (999.999, 1410.0]    CM     yes   \n",
      "13  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "14  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "15  (1000.999, 1365.0]   (1351.0, 1620.0]   (1410.0, 1690.0]    CM     yes   \n",
      "16  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "17  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "18  (1000.999, 1365.0]  (999.999, 1351.0]  (999.999, 1410.0]    CM     yes   \n",
      "19  (1000.999, 1365.0]   (1351.0, 1620.0]   (1410.0, 1690.0]    CM     yes   \n",
      "\n",
      "       k             flag            birthday   _weight  \n",
      "0   40.0  probably active    (1987.0, 2001.0]  0.195876  \n",
      "1   20.0         inactive    (1967.0, 1987.0]  0.122826  \n",
      "2   40.0         inactive    (1987.0, 2001.0]  0.195876  \n",
      "3   20.0  probably active  (1918.999, 1967.0]  0.100971  \n",
      "4   20.0  probably active  (1918.999, 1967.0]  0.100971  \n",
      "5   40.0         inactive  (1918.999, 1967.0]  0.100971  \n",
      "6   40.0  probably active    (2001.0, 2016.0]  0.609858  \n",
      "7   40.0         inactive    (1967.0, 1987.0]  0.122826  \n",
      "8   20.0         inactive  (1918.999, 1967.0]  0.100971  \n",
      "9   40.0  probably active    (1967.0, 1987.0]  0.122826  \n",
      "10  40.0         inactive    (1967.0, 1987.0]  0.122826  \n",
      "11  20.0         inactive  (1918.999, 1967.0]  0.100971  \n",
      "12  20.0  probably active  (1918.999, 1967.0]  0.100971  \n",
      "13  40.0  probably active    (2001.0, 2016.0]  0.609858  \n",
      "14  40.0         inactive  (1918.999, 1967.0]  0.100971  \n",
      "15  20.0         inactive    (1987.0, 2001.0]  0.195876  \n",
      "16  20.0  probably active    (1967.0, 1987.0]  0.122826  \n",
      "17  40.0         inactive    (1987.0, 2001.0]  0.195876  \n",
      "18  40.0         inactive    (1987.0, 2001.0]  0.195876  \n",
      "19  20.0  probably active  (1918.999, 1967.0]  0.100971  \n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "from pgmpy.sampling import BayesianModelSampling\n",
    "\n",
    "inference = BayesianModelSampling(chess_players_model)\n",
    "\n",
    "inference_samples = inference.rejection_sample(size=12, show_progress=False) # the \"size\" argument stands for the number of samples\n",
    "\n",
    "print(\"SAMPLE REJECTION WITHOUT EVIDENCE\")\n",
    "print()\n",
    "\n",
    "print(inference_samples)\n",
    "\n",
    "\n",
    "\n",
    "print()\n",
    "print(\"SAMPLE REJECTION WITH EVIDENCE\")\n",
    "print()\n",
    "\n",
    "interval1 = pd._libs.interval.Interval(1000.999, 1365.0, closed='right')  # 1690.0, 1938.0 is another interval\n",
    "evidence = [State(var='rating', state=interval1)]\n",
    "inference_samples = inference.rejection_sample(evidence=evidence, size=20, show_progress=False)\n",
    "print(inference_samples)\n",
    "\n",
    "\n",
    "\n",
    "print()\n",
    "print(\"LIKELIHOOD WEIGHTED SAMPLE\")\n",
    "print()\n",
    "\n",
    "inference_samples = inference.likelihood_weighted_sample(evidence=evidence, size=20, show_progress=False)\n",
    "print(inference_samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hint: for the sake of repeatability we can also set the seed by specifying the argument *seed*! <br> For example:\n",
    "\n",
    "```python\n",
    "inference.rejection_sample(size=10, show_progress=False, seed=9)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GIBBS SAMPLING\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 9/9 [00:00<00:00, 2209.34it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   rating  rapid_rating  blitz_rating  title  o_title  k  flag  birthday\n",
      "0       2             3             3      0        0  3     1         1\n",
      "1       3             3             3      0        1  2     0         1\n",
      "2       2             3             3      0        1  3     0         0\n",
      "3       3             3             2      1        1  2     0         2\n",
      "4       3             3             3      1        1  2     1         0\n",
      "5       3             3             3      1        1  2     1         1\n",
      "6       3             3             2      0        1  3     1         0\n",
      "7       3             2             2      1        1  2     0         2\n",
      "8       3             3             2      1        1  2     0         2\n",
      "9       3             3             2      1        1  3     0         1\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "from pgmpy.sampling import GibbsSampling\n",
    "\n",
    "print(\"GIBBS SAMPLING\")\n",
    "\n",
    "gibbs = GibbsSampling(chess_players_model)\n",
    "print(gibbs.sample(size=10))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### In order to better visualize the table above the ordinal mapping used by *pgmpy* should be reversed, however as it is ordinal the table can be read without much difficulty."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Inference methods comparison"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variable Elimination took 0.01005101203918457 seconds\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Generating for node: o_title: 100%|██████████| 8/8 [00:00<00:00, 460.59it/s]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rejection sample took 0.0300140380859375 seconds\n",
      "\n",
      "Likelihood weighted sample took 0.018068552017211914 seconds\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "0it [00:00, ?it/s]"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gibbs sampling took 2.076493978500366 seconds\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "import time\n",
    "SIZE=1\n",
    "\n",
    "interval1 = pd._libs.interval.Interval(1650.0, 1917.0, closed='right')\n",
    "k_value=20\n",
    "\n",
    "start=time.time()\n",
    "inference = VariableElimination(chess_players_model)\n",
    "phi_query = inference.map_query(show_progress=False)\n",
    "print(\"Variable Elimination took \"+str(time.time()-start)+\" seconds\")\n",
    "\n",
    "print()\n",
    "\n",
    "start=time.time()\n",
    "inference = BayesianModelSampling(chess_players_model)\n",
    "inference_samples = inference.rejection_sample(show_progress=False, size=SIZE)\n",
    "print(\"Rejection sample took \"+str(time.time()-start)+\" seconds\")\n",
    "\n",
    "print()\n",
    "\n",
    "start=time.time()\n",
    "inference = BayesianModelSampling(chess_players_model)\n",
    "inference_samples = inference.likelihood_weighted_sample(show_progress=False, size=SIZE)\n",
    "print(\"Likelihood weighted sample took \"+str(time.time()-start)+\" seconds\")\n",
    "\n",
    "start=time.time()\n",
    "inference = GibbsSampling(chess_players_model)\n",
    "inference_samples = inference.sample(size=SIZE)\n",
    "print(\"Gibbs sampling took \"+str(time.time()-start)+\" seconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### In this case Variable Elimination achieves a faster result compared to approximate inference methods. <br> The reason why this happen is the limited size of the network."
   ]
  }
 ],
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