wrapper_methods.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Feature Selection Using Wrapper Methods\n",
    "\n",
    "### Project Brief\n",
    "\n",
    "**Objective:** In this project, I will perform feature selection using three different wrapper methods on a dataset obtained from a survey about eating habits and weight. The goal is to identify a smaller subset of features that can accurately predict whether a survey respondent is obese or not.\n",
    "\n",
    "Data source: [UCI Machine Learning Repository - Estimation of obesity levels](https://archive.ics.uci.edu/dataset/544/estimation+of+obesity+levels+based+on+eating+habits+and+physical+condition)\n",
    "\n",
    "### Tasks Overview\n",
    "\n",
    "Here's a breakdown of the tasks I'll be performing using Python and various packages:\n",
    "\n",
    "1. **Data Loading and Inspection**: I'll load the dataset and inspect its structure using `pandas`. This will help me understand the available features and the target variable.\n",
    "\n",
    "2. **Logistic Regression Model**: I'll create a logistic regression model using `LogisticRegression` from `sklearn` to establish a baseline accuracy for comparison.\n",
    "\n",
    "3. **Sequential Forward Selection (SFS)**: I'll implement SFS using the `SequentialFeatureSelector` class from `mlxtend` to select a subset of features that maximizes accuracy. I'll then evaluate the model's accuracy on this reduced feature set.\n",
    "\n",
    "4. **Sequential Backward Selection (SBS)**: I'll implement SBS using the `SequentialFeatureSelector` class from `mlxtend` to select another subset of features that maximizes accuracy. Again, I'll evaluate the model's accuracy on this subset.\n",
    "\n",
    "5. **Recursive Feature Elimination (RFE)**: I'll standardize the data and apply RFE using `RFE` from `sklearn` to select a subset of features. I'll also evaluate the model's accuracy on this reduced feature set.\n",
    "\n",
    "6. **Visualizing Results**: I'll visualize the results of SFS and SBS by plotting the model accuracy as a function of the number of features used.\n",
    "\n",
    "Let's jump into it!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64503dd1",
   "metadata": {},
   "source": [
    "-----"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc1b18a0",
   "metadata": {},
   "source": [
    "## Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "ddd7f59a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from mlxtend.feature_selection import SequentialFeatureSelector as SFS\n",
    "from mlxtend.plotting import plot_sequential_feature_selection as plot_sfs\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.feature_selection import RFE\n",
    "from sklearn.preprocessing import LabelEncoder"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f227a381",
   "metadata": {},
   "source": [
    "## Evaluating a Logistic Regression Model\n",
    "\n",
    "The data set `obesity` contains 18 predictor variables. Here's a brief description of them.\n",
    "\n",
    "* `Gender` is `1` if a respondent is male and `0` if a respondent is female.\n",
    "* `Age` is a respondent's age in years.\n",
    "* `family_history_with_overweight` is `1` if a respondent has family member who is or was overweight, `0` if not.\n",
    "* `FAVC` is `1` if a respondent eats high caloric food frequently, `0` if not.\n",
    "* `FCVC` is `1` if a respondent usually eats vegetables in their meals, `0` if not.\n",
    "* `NCP` represents how many main meals a respondent has daily (`0` for 1-2 meals, `1` for 3 meals, and `2` for more than 3 meals).\n",
    "* `CAEC` represents how much food a respondent eats between meals on a scale of `0` to `3`.\n",
    "* `SMOKE` is `1` if a respondent smokes, `0` if not.\n",
    "* `CH2O` represents how much water a respondent drinks on a scale of `0` to `2`.\n",
    "* `SCC` is `1` if a respondent monitors their caloric intake, `0` if not.\n",
    "* `FAF` represents how much physical activity a respondent does on a scale of `0` to `3`.\n",
    "* `TUE` represents how much time a respondent spends looking at devices with screens on a scale of `0` to `2`.\n",
    "* `CALC` represents how often a respondent drinks alcohol on a scale of `0` to `3`.\n",
    "* `MTRANS`, with values `Automobile`, `Bike`, `Motorbike`, `Public_Transportation`, and `Walking` indicate a respondent's primary mode of transportation. Their primary mode of transportation is indicated by a `1` and the other columns will contain a `0`.\n",
    "\n",
    "The outcome variable, `NObeyesdad`, is a `1` if a patient is obese and a `0` if not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "d03154a2",
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age</th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>family_history_with_overweight</th>\n",
       "      <th>FAVC</th>\n",
       "      <th>FCVC</th>\n",
       "      <th>NCP</th>\n",
       "      <th>CAEC</th>\n",
       "      <th>SMOKE</th>\n",
       "      <th>CH2O</th>\n",
       "      <th>SCC</th>\n",
       "      <th>FAF</th>\n",
       "      <th>TUE</th>\n",
       "      <th>CALC</th>\n",
       "      <th>MTRANS</th>\n",
       "      <th>NObeyesdad</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Female</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1.62</td>\n",
       "      <td>64.0</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
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       "      <td>2.0</td>\n",
       "      <td>no</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>no</td>\n",
       "      <td>Public_Transportation</td>\n",
       "      <td>Normal_Weight</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Female</td>\n",
       "      <td>21.0</td>\n",
       "      <td>1.52</td>\n",
       "      <td>56.0</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>Sometimes</td>\n",
       "      <td>yes</td>\n",
       "      <td>3.0</td>\n",
       "      <td>yes</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Sometimes</td>\n",
       "      <td>Public_Transportation</td>\n",
       "      <td>Normal_Weight</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Male</td>\n",
       "      <td>23.0</td>\n",
       "      <td>1.80</td>\n",
       "      <td>77.0</td>\n",
       "      <td>yes</td>\n",
       "      <td>no</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>Sometimes</td>\n",
       "      <td>no</td>\n",
       "      <td>2.0</td>\n",
       "      <td>no</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Frequently</td>\n",
       "      <td>Public_Transportation</td>\n",
       "      <td>Normal_Weight</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Male</td>\n",
       "      <td>27.0</td>\n",
       "      <td>1.80</td>\n",
       "      <td>87.0</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>3.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>Sometimes</td>\n",
       "      <td>no</td>\n",
       "      <td>2.0</td>\n",
       "      <td>no</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Frequently</td>\n",
       "      <td>Walking</td>\n",
       "      <td>Overweight_Level_I</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Male</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1.78</td>\n",
       "      <td>89.8</td>\n",
       "      <td>no</td>\n",
       "      <td>no</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>Sometimes</td>\n",
       "      <td>no</td>\n",
       "      <td>2.0</td>\n",
       "      <td>no</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>Sometimes</td>\n",
       "      <td>Public_Transportation</td>\n",
       "      <td>Overweight_Level_II</td>\n",
       "    </tr>\n",
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      ],
      "text/plain": [
       "   Gender   Age  Height  Weight family_history_with_overweight FAVC  FCVC  \\\n",
       "0  Female  21.0    1.62    64.0                            yes   no   2.0   \n",
       "1  Female  21.0    1.52    56.0                            yes   no   3.0   \n",
       "2    Male  23.0    1.80    77.0                            yes   no   2.0   \n",
       "3    Male  27.0    1.80    87.0                             no   no   3.0   \n",
       "4    Male  22.0    1.78    89.8                             no   no   2.0   \n",
       "\n",
       "   NCP       CAEC SMOKE  CH2O  SCC  FAF  TUE        CALC  \\\n",
       "0  3.0  Sometimes    no   2.0   no  0.0  1.0          no   \n",
       "1  3.0  Sometimes   yes   3.0  yes  3.0  0.0   Sometimes   \n",
       "2  3.0  Sometimes    no   2.0   no  2.0  1.0  Frequently   \n",
       "3  3.0  Sometimes    no   2.0   no  2.0  0.0  Frequently   \n",
       "4  1.0  Sometimes    no   2.0   no  0.0  0.0   Sometimes   \n",
       "\n",
       "                  MTRANS           NObeyesdad  \n",
       "0  Public_Transportation        Normal_Weight  \n",
       "1  Public_Transportation        Normal_Weight  \n",
       "2  Public_Transportation        Normal_Weight  \n",
       "3                Walking   Overweight_Level_I  \n",
       "4  Public_Transportation  Overweight_Level_II  "
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the data\n",
    "obesity = pd.read_csv(\"dataset/obesity.csv\")\n",
    "\n",
    "# Inspect the data\n",
    "obesity.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "46c16d44",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Convert the \"MTRANS\" column to dummies\n",
    "X_dummies = pd.get_dummies(obesity[\"MTRANS\"])\n",
    "\n",
    "# Add the dummy variables back into the original DataFrame\n",
    "obesity = pd.concat([obesity, X_dummies], axis=1)\n",
    "\n",
    "# Drop the original \"MTRANS\" column\n",
    "obesity.drop(columns=[\"MTRANS\"], inplace=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "366a26e2",
   "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>Age</th>\n",
       "      <th>Height</th>\n",
       "      <th>Weight</th>\n",
       "      <th>FCVC</th>\n",
       "      <th>NCP</th>\n",
       "      <th>CH2O</th>\n",
       "      <th>FAF</th>\n",
       "      <th>TUE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>2111.000000</td>\n",
       "      <td>2111.000000</td>\n",
       "      <td>2111.000000</td>\n",
       "      <td>2111.000000</td>\n",
       "      <td>2111.000000</td>\n",
       "      <td>2111.000000</td>\n",
       "      <td>2111.000000</td>\n",
       "      <td>2111.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>24.312600</td>\n",
       "      <td>1.701677</td>\n",
       "      <td>86.586058</td>\n",
       "      <td>2.419043</td>\n",
       "      <td>2.685628</td>\n",
       "      <td>2.008011</td>\n",
       "      <td>1.010298</td>\n",
       "      <td>0.657866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>6.345968</td>\n",
       "      <td>0.093305</td>\n",
       "      <td>26.191172</td>\n",
       "      <td>0.533927</td>\n",
       "      <td>0.778039</td>\n",
       "      <td>0.612953</td>\n",
       "      <td>0.850592</td>\n",
       "      <td>0.608927</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>14.000000</td>\n",
       "      <td>1.450000</td>\n",
       "      <td>39.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>19.947192</td>\n",
       "      <td>1.630000</td>\n",
       "      <td>65.473343</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.658738</td>\n",
       "      <td>1.584812</td>\n",
       "      <td>0.124505</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>22.777890</td>\n",
       "      <td>1.700499</td>\n",
       "      <td>83.000000</td>\n",
       "      <td>2.385502</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.625350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>26.000000</td>\n",
       "      <td>1.768464</td>\n",
       "      <td>107.430682</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.477420</td>\n",
       "      <td>1.666678</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>61.000000</td>\n",
       "      <td>1.980000</td>\n",
       "      <td>173.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>2.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               Age       Height       Weight         FCVC          NCP  \\\n",
       "count  2111.000000  2111.000000  2111.000000  2111.000000  2111.000000   \n",
       "mean     24.312600     1.701677    86.586058     2.419043     2.685628   \n",
       "std       6.345968     0.093305    26.191172     0.533927     0.778039   \n",
       "min      14.000000     1.450000    39.000000     1.000000     1.000000   \n",
       "25%      19.947192     1.630000    65.473343     2.000000     2.658738   \n",
       "50%      22.777890     1.700499    83.000000     2.385502     3.000000   \n",
       "75%      26.000000     1.768464   107.430682     3.000000     3.000000   \n",
       "max      61.000000     1.980000   173.000000     3.000000     4.000000   \n",
       "\n",
       "              CH2O          FAF          TUE  \n",
       "count  2111.000000  2111.000000  2111.000000  \n",
       "mean      2.008011     1.010298     0.657866  \n",
       "std       0.612953     0.850592     0.608927  \n",
       "min       1.000000     0.000000     0.000000  \n",
       "25%       1.584812     0.124505     0.000000  \n",
       "50%       2.000000     1.000000     0.625350  \n",
       "75%       2.477420     1.666678     1.000000  \n",
       "max       3.000000     3.000000     2.000000  "
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "obesity.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04ef46c3",
   "metadata": {},
   "source": [
    "### Split the data into `X` and `y`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "eb59645f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split the data into predictor variables and an outcome variable\n",
    "X = obesity.drop([\"NObeyesdad\"], axis=1)\n",
    "y = obesity.NObeyesdad\n",
    "\n",
    "# Get feature names\n",
    "features = X.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "84c9e8fd",
   "metadata": {},
   "source": [
    "### Identify all categorical variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "13e2a161",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Gender', 'family_history_with_overweight', 'FAVC', 'CAEC', 'SMOKE', 'SCC', 'CALC']\n"
     ]
    }
   ],
   "source": [
    "# Identify categorical columns (object type)\n",
    "categorical_columns = [column for column, dtype in X.dtypes.items() if dtype == 'object']\n",
    "\n",
    "# Remove \"NObeyesdad\" from the list if it exists\n",
    "if \"NObeyesdad\" in categorical_columns:\n",
    "    categorical_columns.remove(\"NObeyesdad\")\n",
    "\n",
    "# 'categorical_columns' now contains the names of other categorical columns\n",
    "print(categorical_columns)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc2dfaee",
   "metadata": {},
   "source": [
    "### Encode categoricals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "d13cf76d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Initialize the LabelEncoder\n",
    "le = LabelEncoder()\n",
    "\n",
    "# Create a new DataFrame to store the encoded categorical variables\n",
    "X_enc = X.copy()\n",
    "\n",
    "# Loop through each categorical column and encode it\n",
    "for column in categorical_columns:\n",
    "    X_enc[column] = le.fit_transform(X[column])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "508b62ad",
   "metadata": {},
   "source": [
    "### Standardize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "ad2a72ed",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standardize the data\n",
    "scaler = StandardScaler()\n",
    "X_enc_scaled = scaler.fit_transform(X_enc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54da3a49",
   "metadata": {},
   "source": [
    "### Logistic regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "6ad2e322",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a logistic regression model\n",
    "lr = LogisticRegression(max_iter=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ee0a792",
   "metadata": {},
   "source": [
    "### Fit the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "2a3fbca1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-7 {color: black;}#sk-container-id-7 pre{padding: 0;}#sk-container-id-7 div.sk-toggleable {background-color: white;}#sk-container-id-7 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-7 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-7 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-7 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-7 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-7 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-7 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-7 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-7 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-7 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-7 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-7 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-7 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-7 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-7 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-7 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-7 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-7 div.sk-item {position: relative;z-index: 1;}#sk-container-id-7 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-7 div.sk-item::before, #sk-container-id-7 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-7 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-7 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-7 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-7 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-7 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-7 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-7 div.sk-label-container {text-align: center;}#sk-container-id-7 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-7 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-7\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(max_iter=1000)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-13\" type=\"checkbox\" checked><label for=\"sk-estimator-id-13\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(max_iter=1000)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(max_iter=1000)"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the logistic regression model\n",
    "lr.fit(X_enc_scaled, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5133388a",
   "metadata": {},
   "source": [
    "### Model accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "5236cc41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9052581714827096\n"
     ]
    }
   ],
   "source": [
    "# Print the accuracy of the model\n",
    "print(lr.score(X_enc_scaled,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e6dac94",
   "metadata": {},
   "source": [
    "## Feature Selection"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cea6d8b0",
   "metadata": {},
   "source": [
    "### Sequential Forward Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "c231365f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a sequential forward selection model\n",
    "sfs = SFS(lr, \n",
    "          k_features=6, \n",
    "          forward=True, \n",
    "          floating=False, \n",
    "          scoring='accuracy',\n",
    "          cv=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "076b69cc",
   "metadata": {},
   "source": [
    "### Fit the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "fa6ee31b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'feature_idx': (0, 2, 3, 6, 16, 17), 'cv_scores': array([0.92325912]), 'avg_score': 0.9232591189009948, 'feature_names': ('0', '2', '3', '6', '16', '17')}\n"
     ]
    }
   ],
   "source": [
    "# Fit the sequential forward selection model to X and y\n",
    "sfs.fit(X_enc_scaled, y)\n",
    "\n",
    "# Inspect the results of sequential forward selection\n",
    "print(sfs.subsets_[6])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9aadd02",
   "metadata": {},
   "source": [
    "### Chosen features and model accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "5d20ca62",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Gender', 'Height', 'Weight', 'FCVC', 'Bike', 'Motorbike']\n",
      "0.9232591189009948\n"
     ]
    }
   ],
   "source": [
    "# Indexes selected by sequential backward selection\n",
    "selected_indexes = [int(idx) for idx in sfs.subsets_[6]['feature_names']]\n",
    "\n",
    "# Get the corresponding column names\n",
    "selected_column_names = [features[idx] for idx in selected_indexes]\n",
    "print(selected_column_names)\n",
    "\n",
    "# Print the model accuracy after doing sequential forward selection\n",
    "print(sfs.subsets_[6]['avg_score'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79c2f2c0",
   "metadata": {},
   "source": [
    "**Summary:** Compared to model’s accuracy (i.e., .905) on all available features, the accuracy of the model using sequential forward selection for 6 features (i.e., .923) marginally increased."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bef60d98",
   "metadata": {},
   "source": [
    "### Visualize model accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "b1fb53da",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Marc\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\_methods.py:206: RuntimeWarning: Degrees of freedom <= 0 for slice\n",
      "  ret = _var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,\n",
      "C:\\Users\\Marc\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\_methods.py:198: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  ret = ret.dtype.type(ret / rcount)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the model accuracy as a function of the number of features used\n",
    "plot_sfs(sfs.get_metric_dict())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac4c7a0f",
   "metadata": {},
   "source": [
    "### Sequential Backward Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "867544c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a sequential backward selection model\n",
    "sbs = SFS(lr, \n",
    "          k_features=7, \n",
    "          forward=False, \n",
    "          floating=False, \n",
    "          scoring='accuracy',\n",
    "          cv=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d54aa404",
   "metadata": {},
   "source": [
    "### Fit the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "d4a6c682",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'feature_idx': (0, 2, 3, 4, 5, 11, 14), 'cv_scores': array([0.91662719]), 'avg_score': 0.9166271909047845, 'feature_names': ('0', '2', '3', '4', '5', '11', '14')}\n"
     ]
    }
   ],
   "source": [
    "# Fit the sequential backward selection model to X and y\n",
    "sbs.fit(X_enc_scaled, y)\n",
    "\n",
    "# Inspect the results of sequential backward selection\n",
    "print(sbs.subsets_[7])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7a24cf2",
   "metadata": {},
   "source": [
    "### Chosen features and model accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "1837a953",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Gender', 'Height', 'Weight', 'family_history_with_overweight', 'FAVC', 'SCC', 'CALC']\n",
      "0.9166271909047845\n"
     ]
    }
   ],
   "source": [
    "# Indexes selected by sequential backward selection\n",
    "selected_indexes = [int(idx) for idx in sbs.subsets_[7]['feature_names']]\n",
    "\n",
    "# Get the corresponding column names\n",
    "selected_column_names = [features[idx] for idx in selected_indexes]\n",
    "print(selected_column_names)\n",
    "\n",
    "# Print the model accuracy after doing sequential backward selection\n",
    "print(sbs.subsets_[7]['avg_score'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d8b5906",
   "metadata": {},
   "source": [
    "**Summary:** Compared to model’s accuracy (i.e., .905) on all available features and the accuracy of the model using sequential forward selection (i.e., 923), the accuracy of the model using sequential backward selection for 7 features (i.e., .917) marginally decreased."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e4e5b06",
   "metadata": {},
   "source": [
    "### Visualize model accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "01048c61",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Marc\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\_methods.py:206: RuntimeWarning: Degrees of freedom <= 0 for slice\n",
      "  ret = _var(a, axis=axis, dtype=dtype, out=out, ddof=ddof,\n",
      "C:\\Users\\Marc\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.11_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python311\\site-packages\\numpy\\core\\_methods.py:198: RuntimeWarning: invalid value encountered in scalar divide\n",
      "  ret = ret.dtype.type(ret / rcount)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the model accuracy as a function of the number of features used\n",
    "plot_sfs(sbs.get_metric_dict())\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c1890c0",
   "metadata": {},
   "source": [
    "### Recursive Feature Elimination"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "2c15e6e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Standardize the data\n",
    "X = pd.DataFrame(StandardScaler().fit_transform(X_enc_scaled))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9d9d44d",
   "metadata": {},
   "source": [
    "### Create and Fit the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "a4a01bfb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-8 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-8\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>RFE(estimator=LogisticRegression(max_iter=1000), n_features_to_select=6)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-14\" type=\"checkbox\" ><label for=\"sk-estimator-id-14\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">RFE</label><div class=\"sk-toggleable__content\"><pre>RFE(estimator=LogisticRegression(max_iter=1000), n_features_to_select=6)</pre></div></div></div><div class=\"sk-parallel\"><div class=\"sk-parallel-item\"><div class=\"sk-item\"><div class=\"sk-label-container\"><div class=\"sk-label sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-15\" type=\"checkbox\" ><label for=\"sk-estimator-id-15\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">estimator: LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(max_iter=1000)</pre></div></div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-16\" type=\"checkbox\" ><label for=\"sk-estimator-id-16\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(max_iter=1000)</pre></div></div></div></div></div></div></div></div></div></div>"
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       "RFE(estimator=LogisticRegression(max_iter=1000), n_features_to_select=6)"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a recursive feature elimination model\n",
    "rfe = RFE(estimator=lr, n_features_to_select=6)\n",
    "\n",
    "#   Fit the recursive feature elimination model to X and y\n",
    "rfe.fit(X_enc_scaled, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7416057",
   "metadata": {},
   "source": [
    "### Inspect chosen features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "cc77523e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Gender', 'Age', 'Height', 'Weight', 'FCVC', 'Public_Transportation']\n"
     ]
    }
   ],
   "source": [
    "# See which features recursive feature elimination chose\n",
    "rfe_features = [f for (f, support) in zip(features, rfe.support_) if support]\n",
    "print(rfe_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57563e83",
   "metadata": {},
   "source": [
    "### Model accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "8cf94f21",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9090478446234013\n"
     ]
    }
   ],
   "source": [
    "# Print the model accuracy after doing recursive feature elimination\n",
    "print(rfe.score(X_enc_scaled, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f53f80e3",
   "metadata": {},
   "source": [
    "**Summary:** Compared to model’s accuracy (i.e., .905) on all available features, the accuracy of the model using sequential forward selection (i.e., 923) or sequential backward selection for 7 features (i.e., .917), the accuracy of the model using recursive feature elimination (i.e., .909) marginally decreased. <br>   \n",
    "Leads to following feature list:  \n",
    "- 'Gender', \n",
    "- 'Height', \n",
    "- 'Weight', \n",
    "- 'FCVC', \n",
    "- 'Bike', \n",
    "- 'Motorbike'"
   ]
  }
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