simple_lr_with_gradient_descent.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from numpy import *\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "points = genfromtxt(\"data/gradient_descent_example_data.csv\", delimiter=\",\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "df.columns = ['X','y']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>32.502345</td>\n",
       "      <td>31.707006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>53.426804</td>\n",
       "      <td>68.777596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>61.530358</td>\n",
       "      <td>62.562382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>47.475640</td>\n",
       "      <td>71.546632</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>59.813208</td>\n",
       "      <td>87.230925</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>55.142188</td>\n",
       "      <td>78.211518</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>52.211797</td>\n",
       "      <td>79.641973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>39.299567</td>\n",
       "      <td>59.171489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>48.105042</td>\n",
       "      <td>75.331242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>52.550014</td>\n",
       "      <td>71.300880</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>45.419730</td>\n",
       "      <td>55.165677</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>54.351635</td>\n",
       "      <td>82.478847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>44.164049</td>\n",
       "      <td>62.008923</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>58.168471</td>\n",
       "      <td>75.392870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>56.727208</td>\n",
       "      <td>81.436192</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>48.955889</td>\n",
       "      <td>60.723602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>44.687196</td>\n",
       "      <td>82.892504</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>60.297327</td>\n",
       "      <td>97.379897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>45.618644</td>\n",
       "      <td>48.847153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>38.816818</td>\n",
       "      <td>56.877213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>66.189817</td>\n",
       "      <td>83.878565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>65.416052</td>\n",
       "      <td>118.591217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>47.481209</td>\n",
       "      <td>57.251819</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>41.575643</td>\n",
       "      <td>51.391744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>51.845187</td>\n",
       "      <td>75.380652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>59.370822</td>\n",
       "      <td>74.765564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>57.310003</td>\n",
       "      <td>95.455053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>63.615561</td>\n",
       "      <td>95.229366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>46.737619</td>\n",
       "      <td>79.052406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>50.556760</td>\n",
       "      <td>83.432071</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>31.588117</td>\n",
       "      <td>50.392670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>53.660932</td>\n",
       "      <td>63.642399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>46.682229</td>\n",
       "      <td>72.247251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>43.107820</td>\n",
       "      <td>57.812513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>70.346076</td>\n",
       "      <td>104.257102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>44.492856</td>\n",
       "      <td>86.642020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>57.504533</td>\n",
       "      <td>91.486778</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>36.930077</td>\n",
       "      <td>55.231661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>55.805733</td>\n",
       "      <td>79.550437</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>38.954769</td>\n",
       "      <td>44.847124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>56.901215</td>\n",
       "      <td>80.207523</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>56.868901</td>\n",
       "      <td>83.142750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>34.333125</td>\n",
       "      <td>55.723489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>59.049741</td>\n",
       "      <td>77.634183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>57.788224</td>\n",
       "      <td>99.051415</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>54.282329</td>\n",
       "      <td>79.120646</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>51.088720</td>\n",
       "      <td>69.588898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>50.282836</td>\n",
       "      <td>69.510503</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>44.211742</td>\n",
       "      <td>73.687564</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>38.005488</td>\n",
       "      <td>61.366905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>32.940480</td>\n",
       "      <td>67.170656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>53.691640</td>\n",
       "      <td>85.668203</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>68.765734</td>\n",
       "      <td>114.853871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>46.230966</td>\n",
       "      <td>90.123572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>68.319361</td>\n",
       "      <td>97.919821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>50.030174</td>\n",
       "      <td>81.536991</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>49.239765</td>\n",
       "      <td>72.111832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>50.039576</td>\n",
       "      <td>85.232007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>48.149859</td>\n",
       "      <td>66.224958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>25.128485</td>\n",
       "      <td>53.454394</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            X           y\n",
       "0   32.502345   31.707006\n",
       "1   53.426804   68.777596\n",
       "2   61.530358   62.562382\n",
       "3   47.475640   71.546632\n",
       "4   59.813208   87.230925\n",
       "5   55.142188   78.211518\n",
       "6   52.211797   79.641973\n",
       "7   39.299567   59.171489\n",
       "8   48.105042   75.331242\n",
       "9   52.550014   71.300880\n",
       "10  45.419730   55.165677\n",
       "11  54.351635   82.478847\n",
       "12  44.164049   62.008923\n",
       "13  58.168471   75.392870\n",
       "14  56.727208   81.436192\n",
       "15  48.955889   60.723602\n",
       "16  44.687196   82.892504\n",
       "17  60.297327   97.379897\n",
       "18  45.618644   48.847153\n",
       "19  38.816818   56.877213\n",
       "20  66.189817   83.878565\n",
       "21  65.416052  118.591217\n",
       "22  47.481209   57.251819\n",
       "23  41.575643   51.391744\n",
       "24  51.845187   75.380652\n",
       "25  59.370822   74.765564\n",
       "26  57.310003   95.455053\n",
       "27  63.615561   95.229366\n",
       "28  46.737619   79.052406\n",
       "29  50.556760   83.432071\n",
       "..        ...         ...\n",
       "70  31.588117   50.392670\n",
       "71  53.660932   63.642399\n",
       "72  46.682229   72.247251\n",
       "73  43.107820   57.812513\n",
       "74  70.346076  104.257102\n",
       "75  44.492856   86.642020\n",
       "76  57.504533   91.486778\n",
       "77  36.930077   55.231661\n",
       "78  55.805733   79.550437\n",
       "79  38.954769   44.847124\n",
       "80  56.901215   80.207523\n",
       "81  56.868901   83.142750\n",
       "82  34.333125   55.723489\n",
       "83  59.049741   77.634183\n",
       "84  57.788224   99.051415\n",
       "85  54.282329   79.120646\n",
       "86  51.088720   69.588898\n",
       "87  50.282836   69.510503\n",
       "88  44.211742   73.687564\n",
       "89  38.005488   61.366905\n",
       "90  32.940480   67.170656\n",
       "91  53.691640   85.668203\n",
       "92  68.765734  114.853871\n",
       "93  46.230966   90.123572\n",
       "94  68.319361   97.919821\n",
       "95  50.030174   81.536991\n",
       "96  49.239765   72.111832\n",
       "97  50.039576   85.232007\n",
       "98  48.149859   66.224958\n",
       "99  25.128485   53.454394\n",
       "\n",
       "[100 rows x 2 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<matplotlib.text.Text at 0x112651510>"
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     "execution_count": 6,
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7WIrFYt0xIJq3Y75BDVSSTHGO+bgC+Bzw/NC65wP/SDD/Ry8X4FzgORpMHgZM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ff05310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df.X, df.y, 'kx')\n",
    "plt.xlabel('independent')\n",
    "plt.ylabel('depend')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1128d9a50>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SjoKISAQoKChgwoQJ9OnThwkTJlBQUBCSdhxqbuay/HxWn3028Y2NJN5xBz8eOJCndEdC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\ngCQUAIC0ecBMUUJXwZoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1126b7090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df.X, df.y, 'k.')\n",
    "plt.plot([0, 70], [60,60], '-')\n",
    "plt.plot([0, 70], [0,70], '-')\n",
    "plt.plot([0, 70], [0,70], '-')\n",
    "plt.plot([5, 80], [5,120], '-')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#https://www.google.co.in/search?q=rmse+error+actual+and+predicted&rlz=1C5CHFA_enIN727IN727&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjA1um577fWAhXIxLwKHTNaDCUQ_AUICigB&biw=1152&bih=626#imgrc=eOhzl5tO3VhMaM:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMSE \n",
    "<img src=\"data/images/error_compute.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# y = mx + b\n",
    "# m is slope, b is y-intercept\n",
    "def compute_error_for_line_given_points(b, m, points):\n",
    "    totalError = 0\n",
    "    for i in range(0, len(points)):\n",
    "        x = points[i, 0]\n",
    "        y = points[i, 1]\n",
    "        totalError += (y - (m * x + b)) ** 2\n",
    "    return totalError / float(len(points))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11297a2d0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Ekccff1zvvvuu3nrrLSUlJfmOA1Q7RpgAAABQLgUFBRoyZIhuvPFGXXjhhb7j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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112798c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "x_quad = [n/10 for n in range(0, 100)]\n",
    "y_quad = [(n-4)**2+5 for n in x_quad]\n",
    "plt.figure(figsize = (10,7))\n",
    "plt.plot(x_quad, y_quad, 'k--')\n",
    "plt.axis([0,10,0,30])\n",
    "plt.plot([1, 2, 3], [14, 9, 6], 'ro')\n",
    "plt.plot([5, 7, 8],[6, 14, 21], 'bo')\n",
    "plt.plot(4, 5, 'ko')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.title('Quadratic Equation')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gradient Descent \n",
    "<img src=\"data/images/gradient_de_image.png\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def step_gradient(b_current, m_current, points, learningRate):\n",
    "    b_gradient = 0\n",
    "    m_gradient = 0\n",
    "    N = float(len(points))\n",
    "    for i in range(0, len(points)):\n",
    "        x = points[i, 0]\n",
    "        y = points[i, 1]\n",
    "        b_gradient += -(2/N) * (y - ((m_current * x) + b_current))\n",
    "        m_gradient += -(2/N) * x * (y - ((m_current * x) + b_current))\n",
    "    new_b = b_current - (learningRate * b_gradient)\n",
    "    new_m = m_current - (learningRate * m_gradient)\n",
    "    return [new_b, new_m]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def gradient_descent_runner(points, starting_b, starting_m, learning_rate, num_iterations):\n",
    "    b = starting_b\n",
    "    m = starting_m\n",
    "    for i in range(num_iterations):\n",
    "        b, m = step_gradient(b, m, array(points), learning_rate)\n",
    "    return [b, m]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "learning_rate = 0.0001\n",
    "initial_b = 0 # initial y-intercept guess\n",
    "initial_m = 0 # initial slope guess\n",
    "num_iterations = 1000\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5565.1078344832113"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Starting error\n",
    "compute_error_for_line_given_points(initial_b, initial_m, points)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "[b, m] = gradient_descent_runner(points, initial_b, initial_m, learning_rate, num_iterations)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "After 1000 iterations b = 0.0889365199374, m = 1.47774408519, error = 112.614810116\n"
     ]
    }
   ],
   "source": [
    "print \"After {0} iterations b = {1}, m = {2}, error = {3}\".format(num_iterations, b, m, compute_error_for_line_given_points(b, m, points))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"data/images/gradient_descent_example.gif\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML('<img src=\"data/images/gradient_descent_example.gif\">')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
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