Boruta-feature-selection-implementation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a95dc7cc",
   "metadata": {},
   "source": [
    "# Implementation of the Boruta Feature Selection Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "33c6dfe3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# important libraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from tqdm.notebook import tqdm\n",
    "import scipy as sp\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.utils import shuffle"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53e7c1cd",
   "metadata": {},
   "source": [
    "## Reading and processing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "81ab0de4",
   "metadata": {},
   "outputs": [],
   "source": [
    "data =  pd.read_csv(\"healthcare-dataset-stroke-data.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3b2cf722",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>gender</th>\n",
       "      <th>age</th>\n",
       "      <th>hypertension</th>\n",
       "      <th>heart_disease</th>\n",
       "      <th>ever_married</th>\n",
       "      <th>work_type</th>\n",
       "      <th>Residence_type</th>\n",
       "      <th>avg_glucose_level</th>\n",
       "      <th>bmi</th>\n",
       "      <th>smoking_status</th>\n",
       "      <th>stroke</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9046</td>\n",
       "      <td>Male</td>\n",
       "      <td>67.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Private</td>\n",
       "      <td>Urban</td>\n",
       "      <td>228.69</td>\n",
       "      <td>36.6</td>\n",
       "      <td>formerly smoked</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>51676</td>\n",
       "      <td>Female</td>\n",
       "      <td>61.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Self-employed</td>\n",
       "      <td>Rural</td>\n",
       "      <td>202.21</td>\n",
       "      <td>NaN</td>\n",
       "      <td>never smoked</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>31112</td>\n",
       "      <td>Male</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Private</td>\n",
       "      <td>Rural</td>\n",
       "      <td>105.92</td>\n",
       "      <td>32.5</td>\n",
       "      <td>never smoked</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60182</td>\n",
       "      <td>Female</td>\n",
       "      <td>49.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Private</td>\n",
       "      <td>Urban</td>\n",
       "      <td>171.23</td>\n",
       "      <td>34.4</td>\n",
       "      <td>smokes</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1665</td>\n",
       "      <td>Female</td>\n",
       "      <td>79.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Self-employed</td>\n",
       "      <td>Rural</td>\n",
       "      <td>174.12</td>\n",
       "      <td>24.0</td>\n",
       "      <td>never smoked</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      id  gender   age  hypertension  heart_disease ever_married  \\\n",
       "0   9046    Male  67.0             0              1          Yes   \n",
       "1  51676  Female  61.0             0              0          Yes   \n",
       "2  31112    Male  80.0             0              1          Yes   \n",
       "3  60182  Female  49.0             0              0          Yes   \n",
       "4   1665  Female  79.0             1              0          Yes   \n",
       "\n",
       "       work_type Residence_type  avg_glucose_level   bmi   smoking_status  \\\n",
       "0        Private          Urban             228.69  36.6  formerly smoked   \n",
       "1  Self-employed          Rural             202.21   NaN     never smoked   \n",
       "2        Private          Rural             105.92  32.5     never smoked   \n",
       "3        Private          Urban             171.23  34.4           smokes   \n",
       "4  Self-employed          Rural             174.12  24.0     never smoked   \n",
       "\n",
       "   stroke  \n",
       "0       1  \n",
       "1       1  \n",
       "2       1  \n",
       "3       1  \n",
       "4       1  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4648075c",
   "metadata": {},
   "source": [
    "### Data processing\n",
    " \n",
    "- Removing NaNs\n",
    "- Convert categorical variables to numeric representation\n",
    "- Drop Useless columns\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "a77cabce",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gender</th>\n",
       "      <th>age</th>\n",
       "      <th>hypertension</th>\n",
       "      <th>heart_disease</th>\n",
       "      <th>ever_married</th>\n",
       "      <th>work_type</th>\n",
       "      <th>Residence_type</th>\n",
       "      <th>avg_glucose_level</th>\n",
       "      <th>bmi</th>\n",
       "      <th>smoking_status</th>\n",
       "      <th>stroke</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>67.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>228.69</td>\n",
       "      <td>36.6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>105.92</td>\n",
       "      <td>32.5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>49.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>171.23</td>\n",
       "      <td>34.4</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>79.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>174.12</td>\n",
       "      <td>24.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>186.21</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   gender   age  hypertension  heart_disease  ever_married  work_type  \\\n",
       "0       0  67.0             0              1             0          0   \n",
       "1       0  80.0             0              1             0          0   \n",
       "2       1  49.0             0              0             0          0   \n",
       "3       1  79.0             1              0             0          1   \n",
       "4       0  81.0             0              0             0          0   \n",
       "\n",
       "   Residence_type  avg_glucose_level   bmi  smoking_status  stroke  \n",
       "0               0             228.69  36.6               0       1  \n",
       "1               1             105.92  32.5               1       1  \n",
       "2               0             171.23  34.4               2       1  \n",
       "3               1             174.12  24.0               1       1  \n",
       "4               0             186.21  29.0               0       1  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# converting to numeric\n",
    "data[\"gender\"] = pd.factorize(data[\"gender\"])[0]\n",
    "data[\"ever_married\"] = pd.factorize(data[\"ever_married\"])[0]\n",
    "data[\"work_type\"] = pd.factorize(data[\"work_type\"])[0]\n",
    "data[\"Residence_type\"] = pd.factorize(data[\"Residence_type\"])[0]\n",
    "data[\"smoking_status\"] = pd.factorize(data[\"smoking_status\"])[0]\n",
    "# additional cleaning\n",
    "data.dropna(inplace =True)\n",
    "data.drop(\"id\", axis =1, inplace = True)\n",
    "data.reset_index(inplace=True, drop=True)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b998d07",
   "metadata": {},
   "source": [
    "Seperate Input and Output columns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2cdef01c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# seperate input and output variables\n",
    "X = data.drop(\"stroke\", axis = 1)\n",
    "y = data[\"stroke\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "164b0ffd",
   "metadata": {},
   "source": [
    "## Create shadow features"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7bd81d7",
   "metadata": {},
   "source": [
    "Shadow features are created by randomly shuffling the original features (row-by-row).\n",
    "\n",
    "Each shuffled feature is then appended back to the original dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "fda7c7dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "for col in X.columns:\n",
    "    X[f\"shadow_{col}\"] = X[col].sample(frac=1).reset_index(drop=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2bfb90e7",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gender</th>\n",
       "      <th>age</th>\n",
       "      <th>hypertension</th>\n",
       "      <th>heart_disease</th>\n",
       "      <th>ever_married</th>\n",
       "      <th>work_type</th>\n",
       "      <th>Residence_type</th>\n",
       "      <th>avg_glucose_level</th>\n",
       "      <th>bmi</th>\n",
       "      <th>smoking_status</th>\n",
       "      <th>shadow_gender</th>\n",
       "      <th>shadow_age</th>\n",
       "      <th>shadow_hypertension</th>\n",
       "      <th>shadow_heart_disease</th>\n",
       "      <th>shadow_ever_married</th>\n",
       "      <th>shadow_work_type</th>\n",
       "      <th>shadow_Residence_type</th>\n",
       "      <th>shadow_avg_glucose_level</th>\n",
       "      <th>shadow_bmi</th>\n",
       "      <th>shadow_smoking_status</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>67.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>228.69</td>\n",
       "      <td>36.6</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>116.44</td>\n",
       "      <td>17.3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>80.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>105.92</td>\n",
       "      <td>32.5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>54.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>106.43</td>\n",
       "      <td>39.5</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>49.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>171.23</td>\n",
       "      <td>34.4</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>56.74</td>\n",
       "      <td>31.1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>79.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>174.12</td>\n",
       "      <td>24.0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>55.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>80.35</td>\n",
       "      <td>34.4</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>186.21</td>\n",
       "      <td>29.0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>42.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>76.99</td>\n",
       "      <td>19.5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   gender   age  hypertension  heart_disease  ever_married  work_type  \\\n",
       "0       0  67.0             0              1             0          0   \n",
       "1       0  80.0             0              1             0          0   \n",
       "2       1  49.0             0              0             0          0   \n",
       "3       1  79.0             1              0             0          1   \n",
       "4       0  81.0             0              0             0          0   \n",
       "\n",
       "   Residence_type  avg_glucose_level   bmi  smoking_status  shadow_gender  \\\n",
       "0               0             228.69  36.6               0              1   \n",
       "1               1             105.92  32.5               1              1   \n",
       "2               0             171.23  34.4               2              0   \n",
       "3               1             174.12  24.0               1              1   \n",
       "4               0             186.21  29.0               0              1   \n",
       "\n",
       "   shadow_age  shadow_hypertension  shadow_heart_disease  shadow_ever_married  \\\n",
       "0        54.0                    0                     0                    0   \n",
       "1        54.0                    0                     0                    0   \n",
       "2        21.0                    0                     0                    0   \n",
       "3        55.0                    0                     0                    1   \n",
       "4        42.0                    0                     0                    0   \n",
       "\n",
       "   shadow_work_type  shadow_Residence_type  shadow_avg_glucose_level  \\\n",
       "0                 0                      0                    116.44   \n",
       "1                 0                      1                    106.43   \n",
       "2                 1                      1                     56.74   \n",
       "3                 3                      0                     80.35   \n",
       "4                 3                      0                     76.99   \n",
       "\n",
       "   shadow_bmi  shadow_smoking_status  \n",
       "0        17.3                      3  \n",
       "1        39.5                      3  \n",
       "2        31.1                      0  \n",
       "3        34.4                      1  \n",
       "4        19.5                      0  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2108398b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>gender</th>\n",
       "      <th>age</th>\n",
       "      <th>hypertension</th>\n",
       "      <th>heart_disease</th>\n",
       "      <th>ever_married</th>\n",
       "      <th>work_type</th>\n",
       "      <th>Residence_type</th>\n",
       "      <th>avg_glucose_level</th>\n",
       "      <th>bmi</th>\n",
       "      <th>smoking_status</th>\n",
       "      <th>shadow_gender</th>\n",
       "      <th>shadow_age</th>\n",
       "      <th>shadow_hypertension</th>\n",
       "      <th>shadow_heart_disease</th>\n",
       "      <th>shadow_ever_married</th>\n",
       "      <th>shadow_work_type</th>\n",
       "      <th>shadow_Residence_type</th>\n",
       "      <th>shadow_avg_glucose_level</th>\n",
       "      <th>shadow_bmi</th>\n",
       "      <th>shadow_smoking_status</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>4904</th>\n",
       "      <td>1</td>\n",
       "      <td>13.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>103.08</td>\n",
       "      <td>18.6</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>56.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>92.16</td>\n",
       "      <td>16.3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4905</th>\n",
       "      <td>1</td>\n",
       "      <td>81.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>125.20</td>\n",
       "      <td>40.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>82.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>81.88</td>\n",
       "      <td>21.2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4906</th>\n",
       "      <td>1</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>82.99</td>\n",
       "      <td>30.6</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>61.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>96.58</td>\n",
       "      <td>29.3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4907</th>\n",
       "      <td>0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>166.29</td>\n",
       "      <td>25.6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>51.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>92.32</td>\n",
       "      <td>30.1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4908</th>\n",
       "      <td>1</td>\n",
       "      <td>44.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>85.28</td>\n",
       "      <td>26.2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>43.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>56.67</td>\n",
       "      <td>22.8</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      gender   age  hypertension  heart_disease  ever_married  work_type  \\\n",
       "4904       1  13.0             0              0             1          3   \n",
       "4905       1  81.0             0              0             0          1   \n",
       "4906       1  35.0             0              0             0          1   \n",
       "4907       0  51.0             0              0             0          0   \n",
       "4908       1  44.0             0              0             0          2   \n",
       "\n",
       "      Residence_type  avg_glucose_level   bmi  smoking_status  shadow_gender  \\\n",
       "4904               1             103.08  18.6               3              1   \n",
       "4905               0             125.20  40.0               1              0   \n",
       "4906               1              82.99  30.6               1              0   \n",
       "4907               1             166.29  25.6               0              0   \n",
       "4908               0              85.28  26.2               3              1   \n",
       "\n",
       "      shadow_age  shadow_hypertension  shadow_heart_disease  \\\n",
       "4904        56.0                    0                     0   \n",
       "4905        82.0                    1                     0   \n",
       "4906        61.0                    0                     0   \n",
       "4907        51.0                    0                     0   \n",
       "4908        43.0                    0                     0   \n",
       "\n",
       "      shadow_ever_married  shadow_work_type  shadow_Residence_type  \\\n",
       "4904                    1                 4                      0   \n",
       "4905                    1                 3                      1   \n",
       "4906                    0                 0                      0   \n",
       "4907                    0                 0                      0   \n",
       "4908                    1                 0                      0   \n",
       "\n",
       "      shadow_avg_glucose_level  shadow_bmi  shadow_smoking_status  \n",
       "4904                     92.16        16.3                      1  \n",
       "4905                     81.88        21.2                      1  \n",
       "4906                     96.58        29.3                      1  \n",
       "4907                     92.32        30.1                      1  \n",
       "4908                     56.67        22.8                      3  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "165f9f5f",
   "metadata": {},
   "source": [
    "### Getting importance of features\n",
    "\n",
    "The new (extended) dataset is then trained using a tree classifier (Random Forest in our case) and the feature importance it returns is stored.\n",
    "\n",
    "Whatever is the most important *shadow* feature is taken as a threshold. Any feature above this threshold is considered **Important**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bfc2d341",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_important_features(X, y):\n",
    "    # Initiliaze Random Forest CLassifier\n",
    "    rf = RandomForestClassifier(max_depth=20)\n",
    "    \n",
    "    # Fit Random Forest on provided data\n",
    "    rf.fit(X,y)\n",
    "    \n",
    "    # Create dictionary of feature importances\n",
    "    importances = {feature_name: f_importance for feature_name, f_importance in zip(X.columns, rf.feature_importances_)}\n",
    "    \n",
    "    # Isolate importances of Shadow features\n",
    "    only_shadow_feat_importance = {key:value for key,value in importances.items() if \"shadow\" in key}\n",
    "    \n",
    "    # get importance level of most important shadow feature\n",
    "    highest_shadow_feature = list(dict(sorted(only_shadow_feat_importance.items(), key=lambda item: item[1], reverse=True)).values())[0]\n",
    "    \n",
    "    # get original feature which fulfill boruta selection criteria\n",
    "    selected_features = [key for key, value in importances.items() if value > highest_shadow_feature]\n",
    "    \n",
    "    \n",
    "    return selected_features"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a9893293",
   "metadata": {},
   "source": [
    "### Multiple trials\n",
    "\n",
    "Since any classifier randomly initialises its weight, it is important that we perform the trials enough times to see which features make it to the **Important Feature** zone. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "19c08a32",
   "metadata": {},
   "outputs": [],
   "source": [
    "TRIALS = 50"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d0b536ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a76023174cd34b1bbe936189e18a01e2",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/50 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "feature_hits = {i:0 for i in data.columns}\n",
    "for _ in tqdm(range(TRIALS)): \n",
    "    imp_features = get_important_features(X, y)\n",
    "    for key, _ in feature_hits.items(): \n",
    "        if key in imp_features: feature_hits[key] += 1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "f10b3f90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'gender': 0,\n",
       " 'age': 50,\n",
       " 'hypertension': 0,\n",
       " 'heart_disease': 0,\n",
       " 'ever_married': 0,\n",
       " 'work_type': 0,\n",
       " 'Residence_type': 0,\n",
       " 'avg_glucose_level': 50,\n",
       " 'bmi': 0,\n",
       " 'smoking_status': 0,\n",
       " 'stroke': 0}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_hits"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14aada97",
   "metadata": {},
   "source": [
    "### Binomial Distribution\n",
    "\n",
    "When we conduct multiple trials of an event, a binomial distribution helps us determine the probabilistic significance of the number of trials.\n",
    "\n",
    "In simpler terms, how many trials are significant to ensure our desired result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ac8b4ebe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the probability mass function\n",
    "pmf = [sp.stats.binom.pmf(x, TRIALS, .5) for x in range(TRIALS + 1)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "887ae968",
   "metadata": {},
   "outputs": [],
   "source": [
    "# trails_in_green_zone\n",
    "def get_tail_items(pmf):\n",
    "    total = 0\n",
    "    for i, x in enumerate(pmf):\n",
    "        total += x\n",
    "        if total >= 0.05:\n",
    "            break\n",
    "    return i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c2c89ba8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the binomial distribution\n",
    "plt.plot([i for i in range(TRIALS + 1)], pmf,\"-o\")\n",
    "plt.title(f\"Binomial distribution for {TRIALS} trials\")\n",
    "plt.xlabel(\"No. of trials\")\n",
    "plt.ylabel(\"Probability\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d44b6b09",
   "metadata": {},
   "source": [
    "Now we define features are either **extremely important, moderately important or completely unimportant**.\n",
    "\n",
    "General rule is that: \n",
    "- *Extremely Important* features are kept.\n",
    "- *Moderately Important* features can be played around with\n",
    "- *Unimportant* features are removed\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "15eb38e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# select features from n number of trials\n",
    "def choose_features(feature_hits, TRIALS, thresh):\n",
    "    \n",
    "    #define boundries\n",
    "    green_zone_thresh = TRIALS - thresh\n",
    "    blue_zone_upper = green_zone_thresh\n",
    "    blue_zone_lower = thresh\n",
    "    \n",
    "    green_zone = [key for key, value in feature_hits.items() if value >= green_zone_thresh]\n",
    "    blue_zone = [key for key, value in feature_hits.items() if (value >= blue_zone_lower and value < blue_zone_upper)]\n",
    "    \n",
    "    return green_zone, blue_zone"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5666fb4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "thresh = get_tail_items(pmf)\n",
    "green, blue = choose_features(feature_hits, TRIALS, thresh)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e7246d96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(['age', 'avg_glucose_level'], [])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "green,blue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4b6a044d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "745acbd60b3d3a97c5945352b8ea4157d78b838f777f5ff9015d2ad09d6a6d28"
  },
  "kernelspec": {
   "display_name": "Python 3.9.7 ('base')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}