Implement_SGD.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "REYPoTJ1Af7u"
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "from sklearn.datasets import load_boston\n",
    "from random import seed\n",
    "from random import randrange\n",
    "from csv import reader\n",
    "from math import sqrt\n",
    "from sklearn import preprocessing\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from prettytable import PrettyTable\n",
    "from sklearn.linear_model import SGDRegressor\n",
    "from sklearn import preprocessing\n",
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "NTQ2iH-kAwbo"
   },
   "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>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = load_boston().data\n",
    "Y = load_boston().target\n",
    "# data overview\n",
    "boston_data=pd.DataFrame(load_boston().data,columns=load_boston().feature_names)\n",
    "# data overview\n",
    "boston_data.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(354, 13)\n",
      "(152, 13)\n",
      "(354,)\n",
      "(152,)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.3, random_state=5)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "print(Y_train.shape)\n",
    "print(Y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# standardizing data\n",
    "from sklearn import preprocessing\n",
    "scaler = preprocessing.StandardScaler().fit(X_train)\n",
    "X_train = scaler.transform(X_train)\n",
    "X_test=scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(354, 13)\n",
      "(152, 13)\n",
      "(354,)\n",
      "(152,)\n"
     ]
    }
   ],
   "source": [
    "X_test=np.array(X_test)\n",
    "Y_test=np.array(Y_test)\n",
    "# shape of test and train data matxis\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "print(Y_train.shape)\n",
    "print(Y_test.shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Training and testing the model\n",
    "scikit-learn’s LinearRegression to train our model on both the training and test\n",
    "sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean Squared Error : 30.697037704088565\n",
      "Mean Absolute Error : 3.557668475650041\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import mean_absolute_error\n",
    "lin_model = LinearRegression()\n",
    "lin_model.fit(X_train, Y_train)\n",
    "\n",
    "plt.scatter(Y_test,lin_model.predict(X_test))\n",
    "plt.grid()\n",
    "plt.xlabel('Actual house price')\n",
    "plt.ylabel('Predicted house price')\n",
    "plt.title('scatter plot between actual house price and predicted house price')\n",
    "plt.show()\n",
    "print('Mean Squared Error :',mean_squared_error(Y_test, lin_model.predict(X_test)))\n",
    "print('Mean Absolute Error :',mean_absolute_error(Y_test, lin_model.predict(X_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model evaluation\n",
    "We will evaluate our model using RMSE and R2-score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The model performance for training set\n",
      "--------------------------------------\n",
      "RMSE is 4.366731254717563\n",
      "R2 score is 0.7611598772034454\n",
      "\n",
      "\n",
      "The model performance for testing set\n",
      "--------------------------------------\n",
      "RMSE is 5.540490745781331\n",
      "R2 score is 0.6771696999851694\n"
     ]
    }
   ],
   "source": [
    "# model evaluation for training set\n",
    "from sklearn.metrics import r2_score\n",
    "y_train_predict = lin_model.predict(X_train)\n",
    "rmse = (np.sqrt(mean_squared_error(Y_train, y_train_predict)))\n",
    "r2 = r2_score(Y_train, y_train_predict)\n",
    "print(\"The model performance for training set\")\n",
    "print(\"--------------------------------------\")\n",
    "print('RMSE is {}'.format(rmse))\n",
    "print('R2 score is {}'.format(r2))\n",
    "print(\"\\n\")\n",
    "# model evaluation for testing set\n",
    "y_test_predict = lin_model.predict(X_test)\n",
    "rmse = (np.sqrt(mean_squared_error(Y_test, y_test_predict)))\n",
    "r2 = r2_score(Y_test, y_test_predict)\n",
    "print(\"The model performance for testing set\")\n",
    "print(\"--------------------------------------\")\n",
    "print('RMSE is {}'.format(rmse))\n",
    "print('R2 score is {}'.format(r2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(x,w,b):\n",
    "    y_pred=[]\n",
    "    for i in range(len(x)):\n",
    "        y=np.asscalar(np.dot(w,x[i])+b)\n",
    "        y_pred.append(y)\n",
    "    return np.array(y_pred)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_(test_data,y_pred):\n",
    "    #scatter plot\n",
    "    plt.scatter(test_data,y_pred)\n",
    "    plt.grid()\n",
    "    plt.title('scatter plot between actual house price and predicted house price')\n",
    "    plt.xlabel('actual house price')\n",
    "    plt.ylabel('predicted house price')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def CustomGradientDescentRegressor(train_data,learning_rate=0.001,n_itr=1000,k=10):\n",
    "    w_cur=np.zeros(shape=(1,train_data.shape[1]-1))\n",
    "    b_cur=0\n",
    "    cur_itr=1\n",
    "    while(cur_itr<=n_itr):\n",
    "        w_old=w_cur\n",
    "        b_old=b_cur\n",
    "        w_temp=np.zeros(shape=(1,train_data.shape[1]-1))\n",
    "        b_temp=0\n",
    "        temp=train_data.sample(k)\n",
    "        #print(temp.head(3))\n",
    "        y=np.array(temp['price'])\n",
    "        x=np.array(temp.drop('price',axis=1))\n",
    "        for i in range(k):\n",
    "            w_temp+=x[i]*(y[i]-(np.dot(w_old,x[i])+b_old))*(-2/k)\n",
    "            b_temp+=(y[i]-(np.dot(w_old,x[i])+b_old))*(-2/k)\n",
    "        w_cur=w_old-learning_rate*w_temp/k\n",
    "        b_cur=b_old-learning_rate*b_temp/k\n",
    "        if(w_old==w_cur).all():\n",
    "            break\n",
    "        cur_itr+=1\n",
    "    return w_cur,b_cur"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Funtion to get optimal learning rate on the implemented SGD Classifier\n",
    "from math import log\n",
    "from sklearn.preprocessing import Normalizer\n",
    "normalizer = Normalizer()\n",
    "\n",
    "x1_train,x1_test,y1_train,y1_test=train_test_split(X,Y,test_size=0.3)\n",
    "x1_train,x1_cv,y1_train_,y1_cv_=train_test_split(x1_train,y1_train,test_size=0.3)\n",
    "x1_train = normalizer.transform(x1_train)\n",
    "x1_cv=normalizer.transform(x1_cv)\n",
    "x1_train_=np.array(x1_train)\n",
    "x1_train_data=pd.DataFrame(x1_train)\n",
    "x1_train_data['price']=y1_train_\n",
    "x1_cv_data=pd.DataFrame(x1_cv)\n",
    "x1_cv_data['price']=y1_cv_\n",
    "y1_train_=np.array(y1_train_)\n",
    "y1_cv_=np.array(y1_cv_)\n",
    "#print(y1_cv_.shape)\n",
    "\n",
    "def tuneParams_learning_rate():\n",
    "    train_error=[]\n",
    "    cv_error=[]\n",
    "    r=[0.00001,0.0001,0.001,0.01,0.1]\n",
    "    for itr in r:\n",
    "        w,b=CustomGradientDescentRegressor(x1_train_data,learning_rate=itr,n_itr=1000)\n",
    "        # print(w.shape,b.shape,x1_train_.shape)\n",
    "        y1_pred_train=predict(x1_train_,w,b)\n",
    "        train_error.append(mean_squared_error(y1_train_,y1_pred_train))\n",
    "        w,b=CustomGradientDescentRegressor(x1_cv_data,learning_rate=itr,n_itr=1000)\n",
    "        y1_pred_cv=predict(x1_cv,w,b)\n",
    "        cv_error.append(mean_squared_error(y1_cv_,y1_pred_cv))\n",
    "    return train_error,cv_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_error,cv_error=tuneParams_learning_rate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SGD with optimal learning rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Mean Squared Error')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting obtained values\n",
    "import math\n",
    "r=[0.00001,0.0001,0.001,0.01,0.1]\n",
    "x1=[math.log10(i) for i in r]\n",
    "plt.plot(x1,train_error,label='train MSE')\n",
    "plt.plot(x1,cv_error,label='CV MSE')\n",
    "plt.scatter(x1,train_error)\n",
    "plt.scatter(x1,cv_error)\n",
    "plt.legend()\n",
    "plt.xlabel('log of learning rate')\n",
    "plt.ylabel('Mean Squared Error')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "407.0897448317865\n",
      "18.72037628266577\n"
     ]
    }
   ],
   "source": [
    "# running implemented SGD Classifier with obtained optimal learning rate\n",
    "\n",
    "# standardizing data\n",
    "scaler = preprocessing.StandardScaler().fit(X_train)\n",
    "X_train = scaler.transform(X_train)\n",
    "X_test=scaler.transform(X_test)\n",
    "\n",
    "train_data=pd.DataFrame(X_train)\n",
    "train_data['price']=Y_train\n",
    "train_data.head(3)\n",
    "\n",
    "w,b=CustomGradientDescentRegressor(train_data,learning_rate=0.001,n_itr=1000)\n",
    "y_pred=predict(X_test,w,b)\n",
    "plot_(Y_test,y_pred)\n",
    "\n",
    "# Errors in implemeted model\n",
    "print(mean_squared_error(Y_test,y_pred))\n",
    "print(mean_absolute_error(Y_test,y_pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+---------------------------------------------------------------------------+--------------------+--------------------+\n",
      "|  Model  |                               Weight Vector                               |        MSE         |        MAE         |\n",
      "+---------+---------------------------------------------------------------------------+--------------------+--------------------+\n",
      "| sklearn |  [-1.27363359  0.94438381 -0.17050408  0.18568703 -1.48334986  2.80195533 | 30.697037704088523 | 3.5576684756500456 |\n",
      "|         |   -0.29987372 -2.72418289  2.77088061 -2.13961719 -2.08896111  1.15085564 |                    |                    |\n",
      "|         |                                -3.28764536]                               |                    |                    |\n",
      "|  custom | [[-0.44221964  0.41906133 -0.53858802  0.06924496 -0.42845355  1.01871314 | 407.0897448317865  | 18.72037628266577  |\n",
      "|         |   -0.42427858  0.20557453 -0.38055787 -0.49631308 -0.67312195  0.36036467 |                    |                    |\n",
      "|         |                                -0.96236716]]                              |                    |                    |\n",
      "+---------+---------------------------------------------------------------------------+--------------------+--------------------+\n"
     ]
    }
   ],
   "source": [
    "from prettytable import PrettyTable\n",
    "# MSE = mean squared error\n",
    "# MAE =mean absolute error\n",
    "\n",
    "# SkLearn SGD classifier predicted weight matrix\n",
    "sklearn_w=lin_model.coef_\n",
    "sklearn_w\n",
    "\n",
    "# weight vector obtained from impemented SGD Classifier\n",
    "custom_w=w\n",
    "custom_w\n",
    "\n",
    "x=PrettyTable()\n",
    "x.field_names=['Model','Weight Vector','MSE','MAE']\n",
    "x.add_row(['sklearn',sklearn_w,mean_squared_error(Y_test, lin_model.predict(X_test)),mean_absolute_error(Y_test, lin_model.predict(X_test))])\n",
    "x.add_row(['custom',custom_w,mean_squared_error(Y_test,y_pred),(mean_absolute_error(Y_test,y_pred))])\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+--------------------------------+---------------------------------+\n",
      "| SKLearn Linear predicted value | Implemented SGD predicted value |\n",
      "+--------------------------------+---------------------------------+\n",
      "|       37.38997665507024        |        8.887231945314387        |\n",
      "|       31.567941925266958       |        9.499527309732441        |\n",
      "|       27.133738856870593       |        6.588559580441435        |\n",
      "|       6.551176248190249        |        -5.140072254048163       |\n",
      "|       33.69310848335396        |        9.399331030047158        |\n",
      "|       5.549193679561011        |        -5.151965111419517       |\n",
      "|       27.10005629259134        |        5.422311635158753        |\n",
      "|       29.829809857410336       |        6.8045855572056375       |\n",
      "|       26.446224206063096       |        5.185713147592359        |\n",
      "|       22.388735254918274       |        1.1343460206951623       |\n",
      "|       32.24739998445638        |         8.64744075139054        |\n",
      "|       21.74892355880308        |        5.336577443413589        |\n",
      "|       23.42369575482934        |        4.519186179828747        |\n",
      "|       33.57974606716836        |        9.019029641966544        |\n",
      "|       28.31450393032138        |         7.13159084083202        |\n",
      "+--------------------------------+---------------------------------+\n"
     ]
    }
   ],
   "source": [
    "sklearn_pred=lin_model.predict(X_test)\n",
    "implemented_pred=y_pred\n",
    "x=PrettyTable()\n",
    "x.field_names=['SKLearn Linear predicted value','Implemented SGD predicted value']\n",
    "for itr in range(15):\n",
    "    x.add_row([sklearn_pred[itr],implemented_pred[itr]])\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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