webinar-regression-code.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data (X) - Acidity of Milk  Data(Y) - Density of Milk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def readData(filename):\n",
    "    df = pd.read_csv(filename)\n",
    "    return df.values\n",
    "\n",
    "x = readData('./data/linearX.csv')\n",
    "y = readData('./data/linearY.csv') \n",
    "x = x.reshape((99,))\n",
    "y = y.reshape((99,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 8.   9.1  8.4  6.9  7.7 15.6  7.3  7.   7.2 10.1 11.5  7.1 10.   8.9\n",
      "  7.9  5.6  6.3  6.7 10.4  8.5  7.4  6.3  5.4  8.9  9.4  7.5 11.9  7.8\n",
      "  7.4 10.8 10.2  6.2  7.7 13.7  8.   6.7  6.7  7.   8.3  7.4  9.9  6.1\n",
      "  7.   5.4 10.7  7.6  8.9  9.2  6.6  7.2  8.   7.8  7.9  7.   7.   7.6\n",
      "  9.1  9.   7.9  6.6 11.9  6.5  7.1  8.8  7.5  7.7  6.  10.6  6.6  8.2\n",
      "  7.9  7.1  5.6  6.4  7.5  9.8  7.  10.5  7.1  6.2  6.5  7.7  7.2  9.3\n",
      "  8.5  7.7  6.8  7.8  8.7  9.6  7.2  9.3  8.1  6.6  7.8 10.2  6.1  7.3\n",
      "  7.3]\n",
      "[0.99007 0.99769 0.99386 0.99508 0.9963  1.0032  0.99768 0.99584 0.99609\n",
      " 0.99774 1.0003  0.99694 0.99965 0.99549 0.99364 0.99378 0.99379 0.99524\n",
      " 0.9988  0.99733 0.9966  0.9955  0.99471 0.99354 0.99786 0.9965  0.9988\n",
      " 0.9964  0.99713 0.9985  0.99565 0.99578 0.9976  1.0014  0.99685 0.99648\n",
      " 0.99472 0.99914 0.99408 0.9974  1.0002  0.99402 0.9966  0.99402 1.0029\n",
      " 0.99718 0.9986  0.9952  0.9952  0.9972  0.9976  0.9968  0.9978  0.9951\n",
      " 0.99629 0.99656 0.999   0.99836 0.99396 0.99387 1.0004  0.9972  0.9972\n",
      " 0.99546 0.9978  0.99596 0.99572 0.9992  0.99544 0.99747 0.99668 0.9962\n",
      " 0.99346 0.99514 0.99476 1.001   0.9961  0.99598 0.99608 0.9966  0.99732\n",
      " 0.9962  0.99546 0.99738 0.99456 0.9966  0.99553 0.9984  0.9952  0.997\n",
      " 0.99586 0.9984  0.99542 0.99655 0.9962  0.9976  0.99464 0.9983  0.9967 ]\n"
     ]
    }
   ],
   "source": [
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3587c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "### Plot the Data\n",
    "plt.scatter(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x366d390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Normalisation (Optional Skip)\n",
    "x = x - x.mean()/(x.std())\n",
    "plt.scatter(x,y)\n",
    "plt.show()\n",
    "\n",
    "X = x\n",
    "Y = y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Algorithm - Linear Regression !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "49.16754909500004\n",
      "39.91425870950065\n",
      "32.40244285994534\n",
      "26.304350450600904\n",
      "21.353916509321465\n",
      "17.335151057914185\n",
      "14.0727141246352\n",
      "11.42426499559236\n",
      "9.27425156029656\n",
      "7.528868610670295\n",
      "6.111965039917162\n",
      "4.9617213306243775\n",
      "4.027952350241778\n",
      "3.269917764676601\n",
      "2.654544533292575\n",
      "2.1549839302746774\n",
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      "0.07678496536993273\n",
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      "0.05064279941459262\n",
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      "0.027148003775004804\n",
      "0.022060801782502176\n",
      "0.017931006117786866\n",
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      "0.006397741326517033\n",
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      "0.0034771721901506506\n",
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      "0.0015763690342342279\n",
      "0.0013017231283102663\n",
      "0.0010787653072352552\n",
      "0.0008977679251287347\n",
      "0.0007508340693373046\n",
      "0.0006315530182719487\n",
      "0.0005347205417360589\n",
      "0.0004561118404517466\n",
      "0.0003922972181404403\n",
      "0.0003404924439334936\n",
      "0.0002984372764275282\n",
      "0.00026429684939100856\n",
      "0.00023658161658232993\n",
      "0.00021408236287302404\n",
      "0.0001958174462125481\n",
      "0.00018098996860265853\n",
      "0.00016895300745146821\n",
      "0.00015918139035197483\n",
      "0.00015124878181898866\n",
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      "0.00012909541585996105\n",
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      "0.00012498179738729413\n",
      "0.00012348551805066796\n",
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      "0.00011983441069371721\n",
      "0.00011930686438543476\n",
      "0.00011887860176482418\n",
      "0.00011853093774115193\n",
      "0.00011824870373906992\n",
      "0.00011801958589394475\n",
      "0.00011783358779815536\n",
      "0.00011768259435799526\n",
      "0.00011756001773228056\n",
      "0.00011746050990494763\n",
      "0.0001173797293512119\n",
      "0.00011731415161690825\n",
      "0.0001172609155466222\n",
      "0.00011721769845152848\n",
      "0.00011718261477051407\n",
      "0.00011715413380318278\n",
      "0.00011713101292542242\n",
      "0.00011711224337373604\n",
      "0.00011709700623290716\n",
      "0.00011708463670674526\n",
      "0.9966045602774349 0.0007855593456460089\n"
     ]
    }
   ],
   "source": [
    "def hypothesis(theta,x):\n",
    "    return theta[0] + theta[1]*x\n",
    "\n",
    "def error(X,Y,theta):\n",
    "    total_error = 0\n",
    "    m = X.shape[0]\n",
    "    \n",
    "    for i in range(m):\n",
    "        total_error += (Y[i] - hypothesis(theta,X[i]))**2\n",
    "    \n",
    "    return 0.5*total_error\n",
    "\n",
    "def gradient(Y,X,theta):\n",
    "    grad = np.array([0.0,0.0])\n",
    "    m = X.shape[0]\n",
    "    for i in range(m):\n",
    "        grad[0] += -1*(Y[i] - hypothesis(theta,X[i]))\n",
    "        grad[1] += -1*(Y[i] - hypothesis(theta,X[i]))*X[i]        \n",
    "    return grad\n",
    "\n",
    "def gradientDescent(X,Y,learning_rate,maxItr):\n",
    "    grad = np.array([0.0,0.0])\n",
    "    theta = np.array([0.0,0.0])\n",
    "    e = []\n",
    "    \n",
    "    for i in range(maxItr):\n",
    "        grad = gradient(Y,X,theta)\n",
    "        ce = error(X,Y,theta)\n",
    "        print(ce)\n",
    "        theta[0] = theta[0] - learning_rate*grad[0]\n",
    "        theta[1] = theta[1] - learning_rate*grad[1]\n",
    "        e.append(ce)\n",
    "        \n",
    "    return theta,e\n",
    "                \n",
    "theta,e = gradientDescent(X,Y,learning_rate=0.001,maxItr=100)\n",
    "print(theta[0],theta[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf864110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X,Y)\n",
    "plt.plot(X,hypothesis(theta,X),color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf794af0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(e)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0019146858211364333\n"
     ]
    }
   ],
   "source": [
    "print(e[49])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}