Default_CV.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Default Data set - Comparison of Validation set approach, Leave One Out CV and K Fold CV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import sklearn.linear_model as skl_lm\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split, LeaveOneOut, KFold, cross_val_score\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "default = pd.read_csv('C:\\\\Users\\\\Paaru\\\\Desktop\\\\SJSU MSEE\\\\2nd sem - Spring 2018\\\\EE 259 - Intro to statistical learning\\\\data sets\\\\Default.csv', na_values='?').dropna()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Int64Index: 10000 entries, 0 to 9999\n",
      "Data columns (total 5 columns):\n",
      "Unnamed: 0    10000 non-null int64\n",
      "default       10000 non-null object\n",
      "student       10000 non-null object\n",
      "balance       10000 non-null float64\n",
      "income        10000 non-null float64\n",
      "dtypes: float64(2), int64(1), object(2)\n",
      "memory usage: 468.8+ KB\n"
     ]
    }
   ],
   "source": [
    "default.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>default</th>\n",
       "      <th>student</th>\n",
       "      <th>balance</th>\n",
       "      <th>income</th>\n",
       "      <th>default_value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>729.526495</td>\n",
       "      <td>44361.625074</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>No</td>\n",
       "      <td>Yes</td>\n",
       "      <td>817.180407</td>\n",
       "      <td>12106.134700</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>1073.549164</td>\n",
       "      <td>31767.138947</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>529.250605</td>\n",
       "      <td>35704.493935</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>No</td>\n",
       "      <td>No</td>\n",
       "      <td>785.655883</td>\n",
       "      <td>38463.495879</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0 default student      balance        income  default_value\n",
       "0           1      No      No   729.526495  44361.625074              0\n",
       "1           2      No     Yes   817.180407  12106.134700              0\n",
       "2           3      No      No  1073.549164  31767.138947              0\n",
       "3           4      No      No   529.250605  35704.493935              0\n",
       "4           5      No      No   785.655883  38463.495879              0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "default['default_value']=default.default.factorize()[0]\n",
    "default.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Validation set approach - Using 3 random splits of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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hiCRL+VFkfyyaBr3HQLcBUUfSQNnKMvJz8jmhzwmRfL67c9Pz86ipq+P2Cw7T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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14124df9320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "'''Splitting the data set into 2 equal parts randomly and verifying the \n",
    "        results using validation set approach '''\n",
    "\n",
    "t_prop = 0.5 #dividing ratio\n",
    "\n",
    "p_order = np.arange(1,11) #Considering 10 degrees of polynomial\n",
    "r_state = np.arange(0,3) #Considering 3 random states\n",
    "\n",
    "X, Y = np.meshgrid(p_order, r_state, indexing='ij')\n",
    "Z = np.zeros((p_order.size,r_state.size))\n",
    "regr = skl_lm.LogisticRegression()\n",
    "\n",
    "# Generate 3 random splits of the dataset\n",
    "\n",
    "for (i,j),v in np.ndenumerate(Z):\n",
    "    poly = PolynomialFeatures(int(X[i,j]))\n",
    "    X_poly = poly.fit_transform(default[['income','balance']])\n",
    "    #Dividing into training and test set\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X_poly, \n",
    "                                    default.default_value.ravel(),\n",
    "                                    test_size=t_prop, random_state=Y[i,j])\n",
    "\n",
    "    pred = regr.fit(X_train, y_train).predict(X_test)\n",
    "    #Calculating the test error for each split and each degree\n",
    "    Z[i,j]= mean_squared_error(y_test, pred) \n",
    "    \n",
    "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(15,4))\n",
    "\n",
    "# Left plot : Considering only first split\n",
    "ax1.plot(X.T[0],Z.T[0], '-o')\n",
    "ax1.set_title('Random split of the data set')\n",
    "\n",
    "# Right plot : Considering all 3 random splits\n",
    "ax2.plot(X,Z, '-o')\n",
    "ax2.set_title('3 random splits of the data set')\n",
    "\n",
    "for ax in fig.axes:\n",
    "    ax.set_ylabel('MSE')\n",
    "    ax.set_ylim(0,0.05)\n",
    "    ax.set_xlabel('Degree of Polynomial')\n",
    "    ax.set_xlim(0.5,10.5)\n",
    "    ax.set_xticks(range(2,11,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LOOCV and K Fold CV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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khjbcOYIbRcQBVJrFScXjKH68o7MkqZlZIyVJDW24RvBRoO9GKX/p97jv+Ygi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\nK+YqpgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14125475c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "p_order = np.arange(1,9) #Considering 8 degrees of polynomial\n",
    "r_state = np.arange(0,3) #Considering 3 random states\n",
    "\n",
    "regr = LogisticRegression()\n",
    "loo  = LeaveOneOut() # LeaveOneOut CV - LOOCV\n",
    "loo.get_n_splits(default)\n",
    "scores = list()\n",
    "\n",
    "for i in p_order:\n",
    "    poly   = PolynomialFeatures(i)\n",
    "    X_poly = poly.fit_transform(default[['income','balance']])\n",
    "    score  = cross_val_score(regr, X_poly, default.default_value, \n",
    "                                 cv=loo, scoring='neg_mean_squared_error')\n",
    "    scores.append(score.mean())\n",
    "    \n",
    "\n",
    "# k-fold CV with k = 5\n",
    "\n",
    "folds    = 5\n",
    "elements = len(default.index)\n",
    "\n",
    "X, Y = np.meshgrid(p_order, r_state, indexing='ij')\n",
    "Z    = np.zeros((p_order.size,r_state.size))\n",
    "\n",
    "regr = LogisticRegression()\n",
    "\n",
    "for (i,j),v in np.ndenumerate(Z):\n",
    "    poly   = PolynomialFeatures(X[i,j])\n",
    "    X_poly = poly.fit_transform(default[['income','balance']])\n",
    "    kfold_5   = KFold(n_splits=folds, random_state=Y[i,j])\n",
    "    Z[i,j] = cross_val_score(regr, X_poly, default.default_value,\n",
    "                             cv=kfold_5, scoring='neg_mean_squared_error').mean()\n",
    "    \n",
    "fig, (ax1, ax2) = plt.subplots(1,2, figsize=(15,4))\n",
    "\n",
    "\n",
    "\n",
    "# Left plot - LOOCV\n",
    "ax1.plot(p_order, np.array(scores)*-1, '-o') \n",
    "# cross_val_score() method return negative values for the scores.\n",
    "ax1.set_title('LOOCV')\n",
    "\n",
    "# Right plot - KFold\n",
    "ax2.plot(X,Z*-1, '-o') \n",
    "ax2.set_title('5-fold CV')\n",
    "\n",
    "for ax in fig.axes:\n",
    "    ax.set_ylabel('Mean Squared Error')\n",
    "    ax.set_ylim(0,0.05)\n",
    "    ax.set_xlabel('Degree of Polynomial')\n",
    "    ax.set_xlim(0.5,10.5)\n",
    "    ax.set_xticks(range(2,11,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}