Implement SGD for linear regression [M].ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pdb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 596,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class LinearRegression():\n",
    "    \n",
    "    def __init__(self, fit_intercept=True, copy_X=True):\n",
    "        self.params = {\"fit_intercept\" : fit_intercept, \"copy_X\" : copy_X}\n",
    "        \n",
    "    def fit(self, X, y, n_ite):\n",
    "        \"\"\"Fit model to training data\"\"\"\n",
    "        n_samples = X.shape[0]\n",
    "        n_features = X.shape[1]\n",
    "        y=np.reshape(y, (-1,1))\n",
    "        self.coef_ = np.zeros((n_features,1), dtype=float)\n",
    "        self.intercept_ = 0\n",
    "        \n",
    "        if self.params['copy_X']:\n",
    "            copy_x = np.copy(X)\n",
    "            \n",
    "        r=.0001\n",
    "        batch_size=int(n_samples/100)\n",
    "        \n",
    "        i=0\n",
    "        while i<n_ite:\n",
    "            #r=float(r0/np.power(3,i))\n",
    "            indices=np.random.randint(n_samples, size=batch_size)\n",
    "            \n",
    "            term1=y[indices]*copy_x[indices]\n",
    "            term2=np.dot(copy_x[indices], self.coef_)*copy_x[indices]\n",
    "            term3=self.intercept_*copy_x[indices]\n",
    "\n",
    "            gradient_w=np.reshape(np.sum(2*(term1-term2-term3), axis=0), (n_features, 1))/n_samples\n",
    "            #pdb.set_trace()\n",
    "\n",
    "            coef_prev=self.coef_\n",
    "            self.coef_=self.coef_ + r*gradient_w\n",
    "            \n",
    "            \n",
    "            term1=y[indices]\n",
    "            term2=np.dot(copy_x[indices], coef_prev)\n",
    "            term3=self.intercept_\n",
    "\n",
    "            gradient_b=np.sum(2*(term1-term2-term3))/n_samples\n",
    "\n",
    "            intercept_prev=self.intercept_\n",
    "            self.intercept_=self.intercept_ + r * gradient_b\n",
    "            \n",
    "            i+=1\n",
    "        \n",
    "        self.i_=i\n",
    "        return self\n",
    "    \n",
    "    def predict(self, X):\n",
    "        return np.dot(X, self.coef_)+self.intercept_\n",
    "    \n",
    "    def get_params(self):\n",
    "        return self.params\n",
    "    \n",
    "    def score(self, X, y):\n",
    "        \"\"\"Calculate coefficient of determination R^2\"\"\"\n",
    "        predictions = self.predict(X)\n",
    "        u = np.sum((y-predictions)**2)\n",
    "        mean=np.mean(y)\n",
    "        v=np.sum((y-mean)**2)\n",
    "        return 1-float(u/v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "boston = load_boston()\n",
    "import pandas as pd\n",
    "bos = pd.DataFrame(boston.data)\n",
    "bos['PRICE'] = boston.target\n",
    "\n",
    "X = bos.drop('PRICE', axis = 1)\n",
    "Y = bos['PRICE']\n",
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.33, random_state = 5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 615,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/vishal/anaconda3/lib/python3.6/site-packages/numpy/core/fromnumeric.py:57: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "  return getattr(obj, method)(*args, **kwds)\n"
     ]
    }
   ],
   "source": [
    "lm = LinearRegression()\n",
    "lm.fit(X_train, Y_train, 150000)\n",
    "\n",
    "Y_pred = lm.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 616,
   "metadata": {},
   "outputs": [
    {
     "data": {
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BjcAIuYYSe5C4NieJ/Nyc5CIV8f1K7HsqL2D18x9jyDa6j7vV7sDhc+NPw7ikJfHx1Ztm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\nfqichfv3HsffT1zGpltzJ/TaR+va4WC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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd691ee6e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delta_y = np.array(Y_test) - Y_pred.ravel();\n",
    "\n",
    "import seaborn as sns;\n",
    "import numpy as np;\n",
    "sns.set_style('whitegrid')\n",
    "sns.kdeplot(np.array(delta_y), bw=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 617,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/vishal/anaconda3/lib/python3.6/site-packages/numpy/core/fromnumeric.py:57: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "  return getattr(obj, method)(*args, **kwds)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.49608642392756375"
      ]
     },
     "execution_count": 617,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.score(X_test, np.reshape(Y_test, (-1,1)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "Most of the errors are distributed around 0. R^2 score is close to 0.5 which is a good enough value"
   ]
  }
 ],
 "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
}