Chapter_6/figure_6.2_Forward_selection.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Forward  Stepwise Selection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import r2_score,adjusted_rand_score\n",
    "\n",
    "import statsmodels.api as sm\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(400, 11)\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Income</th>\n",
       "      <th>Limit</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Cards</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Student</th>\n",
       "      <th>Married</th>\n",
       "      <th>Ethnicity</th>\n",
       "      <th>Balance</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14.891</td>\n",
       "      <td>3606</td>\n",
       "      <td>283</td>\n",
       "      <td>2</td>\n",
       "      <td>34</td>\n",
       "      <td>11</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Caucasian</td>\n",
       "      <td>333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>106.025</td>\n",
       "      <td>6645</td>\n",
       "      <td>483</td>\n",
       "      <td>3</td>\n",
       "      <td>82</td>\n",
       "      <td>15</td>\n",
       "      <td>Female</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Asian</td>\n",
       "      <td>903</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>104.593</td>\n",
       "      <td>7075</td>\n",
       "      <td>514</td>\n",
       "      <td>4</td>\n",
       "      <td>71</td>\n",
       "      <td>11</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Asian</td>\n",
       "      <td>580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>148.924</td>\n",
       "      <td>9504</td>\n",
       "      <td>681</td>\n",
       "      <td>3</td>\n",
       "      <td>36</td>\n",
       "      <td>11</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>Asian</td>\n",
       "      <td>964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>55.882</td>\n",
       "      <td>4897</td>\n",
       "      <td>357</td>\n",
       "      <td>2</td>\n",
       "      <td>68</td>\n",
       "      <td>16</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>Caucasian</td>\n",
       "      <td>331</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Income  Limit  Rating  Cards  Age  Education  Gender Student Married  \\\n",
       "1   14.891   3606     283      2   34         11    Male      No     Yes   \n",
       "2  106.025   6645     483      3   82         15  Female     Yes     Yes   \n",
       "3  104.593   7075     514      4   71         11    Male      No      No   \n",
       "4  148.924   9504     681      3   36         11  Female      No      No   \n",
       "5   55.882   4897     357      2   68         16    Male      No     Yes   \n",
       "\n",
       "   Ethnicity  Balance  \n",
       "1  Caucasian      333  \n",
       "2      Asian      903  \n",
       "3      Asian      580  \n",
       "4      Asian      964  \n",
       "5  Caucasian      331  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(r'E:\\programming\\dataset\\Into_to_statstical_learning\\Credit.csv',index_col=0)\n",
    "print(data.shape)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "gender_encoding = {'Male':1,'Female':0}\n",
    "ethnicity = pd.get_dummies(data['Ethnicity'],drop_first=True)\n",
    "yes_no_encoding = {'Yes':1,'No':0}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['Gender'] = data['Gender'].map(gender_encoding)\n",
    "data['Student'] = data['Student'].map(yes_no_encoding)\n",
    "data['Married'] = data['Married'].map(yes_no_encoding)\n",
    "data.drop('Ethnicity',axis = 1,inplace = True)\n",
    "data = pd.concat([data,ethnicity],axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        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>Income</th>\n",
       "      <th>Limit</th>\n",
       "      <th>Rating</th>\n",
       "      <th>Cards</th>\n",
       "      <th>Age</th>\n",
       "      <th>Education</th>\n",
       "      <th>Gender</th>\n",
       "      <th>Student</th>\n",
       "      <th>Married</th>\n",
       "      <th>Balance</th>\n",
       "      <th>Asian</th>\n",
       "      <th>Caucasian</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>14.891</td>\n",
       "      <td>3606</td>\n",
       "      <td>283</td>\n",
       "      <td>2</td>\n",
       "      <td>34</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>333</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>106.025</td>\n",
       "      <td>6645</td>\n",
       "      <td>483</td>\n",
       "      <td>3</td>\n",
       "      <td>82</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>903</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>104.593</td>\n",
       "      <td>7075</td>\n",
       "      <td>514</td>\n",
       "      <td>4</td>\n",
       "      <td>71</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>580</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>148.924</td>\n",
       "      <td>9504</td>\n",
       "      <td>681</td>\n",
       "      <td>3</td>\n",
       "      <td>36</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>964</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>55.882</td>\n",
       "      <td>4897</td>\n",
       "      <td>357</td>\n",
       "      <td>2</td>\n",
       "      <td>68</td>\n",
       "      <td>16</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>331</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Income  Limit  Rating  Cards  Age  Education  Gender  Student  Married  \\\n",
       "1   14.891   3606     283      2   34         11       1        0        1   \n",
       "2  106.025   6645     483      3   82         15       0        1        1   \n",
       "3  104.593   7075     514      4   71         11       1        0        0   \n",
       "4  148.924   9504     681      3   36         11       0        0        0   \n",
       "5   55.882   4897     357      2   68         16       1        0        1   \n",
       "\n",
       "   Balance  Asian  Caucasian  \n",
       "1      333      0          1  \n",
       "2      903      1          0  \n",
       "3      580      1          0  \n",
       "4      964      1          0  \n",
       "5      331      0          1  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "features = [col for col in data.columns if not col == 'Balance']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forward_stepwise_selection(data,target):\n",
    "    total_features = [[]]\n",
    "    score_dict = {}\n",
    "    remaining_features = [col for col in data.columns if not col == target]\n",
    "    for i in range(1,len(data.columns)):\n",
    "        best_score = 0;best_feature = None\n",
    "        for feature in remaining_features:\n",
    "\n",
    "            X = total_features[i-1] + [feature]\n",
    "            model = LinearRegression().fit(data[X],data[target])\n",
    "            score = r2_score(data[target],model.predict(data[X]))\n",
    "#             print('For len {}, feature - {}, score is {}'.format(i,feature,score))\n",
    "\n",
    "            if score > best_score:\n",
    "                best_score = score\n",
    "                best_feature = feature\n",
    "        total_features.append(total_features[i-1] + [best_feature])\n",
    "        remaining_features.remove(best_feature)\n",
    "        score_dict[i] = best_score\n",
    "    return total_features,score_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "total_predictors,score_dict = forward_stepwise_selection(data,'Balance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Lenovo\\Anaconda3\\lib\\site-packages\\seaborn\\axisgrid.py:230: UserWarning: The `size` paramter has been renamed to `height`; please update your code.\n",
      "  warnings.warn(msg, UserWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1, 'Forward Selection')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 864x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "temp = pd.DataFrame({'Number of predictors':list(score_dict.keys()),'R2_Score':list(score_dict.values())})\n",
    "plt.figure(figsize = (12,6))\n",
    "g = sns.FacetGrid(data = temp,size=5)\n",
    "g.map(plt.scatter, 'Number of predictors' , 'R2_Score')\n",
    "g.map(plt.plot, 'Number of predictors', 'R2_Score')\n",
    "plt.title('Forward Selection')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Subset of size 0 is []\n",
      "Subset of size 1 is ['Rating']\n",
      "Subset of size 2 is ['Rating', 'Income']\n",
      "Subset of size 3 is ['Rating', 'Income', 'Student']\n",
      "Subset of size 4 is ['Rating', 'Income', 'Student', 'Limit']\n",
      "Subset of size 5 is ['Rating', 'Income', 'Student', 'Limit', 'Cards']\n",
      "Subset of size 6 is ['Rating', 'Income', 'Student', 'Limit', 'Cards', 'Age']\n",
      "Subset of size 7 is ['Rating', 'Income', 'Student', 'Limit', 'Cards', 'Age', 'Gender']\n",
      "Subset of size 8 is ['Rating', 'Income', 'Student', 'Limit', 'Cards', 'Age', 'Gender', 'Asian']\n",
      "Subset of size 9 is ['Rating', 'Income', 'Student', 'Limit', 'Cards', 'Age', 'Gender', 'Asian', 'Married']\n",
      "Subset of size 10 is ['Rating', 'Income', 'Student', 'Limit', 'Cards', 'Age', 'Gender', 'Asian', 'Married', 'Caucasian']\n",
      "Subset of size 11 is ['Rating', 'Income', 'Student', 'Limit', 'Cards', 'Age', 'Gender', 'Asian', 'Married', 'Caucasian', 'Education']\n"
     ]
    }
   ],
   "source": [
    "for i,feature in enumerate(total_predictors):\n",
    "    print('Subset of size {} is'.format(i), feature)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Choosing the best model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "score_dict = {}\n",
    "for i,feature in enumerate(total_predictors[1:]):\n",
    "    X = data[feature]\n",
    "    y = data['Balance']\n",
    "    X = sm.add_constant(X)\n",
    "    result = sm.OLS(y, X).fit()\n",
    "    score_dict[i+1] = result.rsquared_adj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1, 'Chossing the best model')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 864x432 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "temp = pd.DataFrame({'Number of predictors':list(score_dict.keys()),'Adjusted_R2_Score':list(score_dict.values())})\n",
    "plt.figure(figsize = (12,6))\n",
    "g = sns.FacetGrid(data = temp,size=5)\n",
    "g.map(plt.scatter, 'Number of predictors' , 'Adjusted_R2_Score')\n",
    "g.map(plt.plot, 'Number of predictors', 'Adjusted_R2_Score')\n",
    "plt.title('Chossing the best model')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: 0.7452098462445803,\n",
       " 2: 0.8744888189724805,\n",
       " 3: 0.9494990734177157,\n",
       " 4: 0.9517033272701592,\n",
       " 5: 0.9535788787498292,\n",
       " 6: 0.9539960984035273,\n",
       " 7: 0.9540098163629883,\n",
       " 8: 0.9539649480880468,\n",
       " 9: 0.9539242850304841,\n",
       " 10: 0.9538912342742093,\n",
       " 11: 0.9538286695430547}"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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