GradientDescent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementing the Gradient Descent Algorithm\n",
    "\n",
    "In this lab, we'll implement the basic functions of the Gradient Descent algorithm to find the boundary in a small dataset. First, we'll start with some functions that will help us plot and visualize the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "#Some helper functions for plotting and drawing lines\n",
    "\n",
    "def plot_points(X, y):\n",
    "    admitted = X[np.argwhere(y==1)]\n",
    "    rejected = X[np.argwhere(y==0)]\n",
    "    plt.scatter([s[0][0] for s in rejected], [s[0][1] for s in rejected], s = 25, color = 'blue', edgecolor = 'k')\n",
    "    plt.scatter([s[0][0] for s in admitted], [s[0][1] for s in admitted], s = 25, color = 'red', edgecolor = 'k')\n",
    "\n",
    "def display(m, b, color='g--'):\n",
    "    plt.xlim(-0.05,1.05)\n",
    "    plt.ylim(-0.05,1.05)\n",
    "    x = np.arange(-10, 10, 0.1)\n",
    "    plt.plot(x, m*x+b, color)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reading and plotting the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         0         1  2\n",
      "0  0.78051 -0.063669  1\n",
      "1  0.28774  0.291390  1\n",
      "2  0.40714  0.178780  1\n",
      "3  0.29230  0.421700  1\n",
      "4  0.50922  0.352560  1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = pd.read_csv('data.csv', header=None)\n",
    "print(data.head())\n",
    "X = np.array(data[[0,1]])\n",
    "y = np.array(data[2])\n",
    "plot_points(X,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "        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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.780510</td>\n",
       "      <td>-0.063669</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.287740</td>\n",
       "      <td>0.291390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.407140</td>\n",
       "      <td>0.178780</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.292300</td>\n",
       "      <td>0.421700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.509220</td>\n",
       "      <td>0.352560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.277850</td>\n",
       "      <td>0.108020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.275270</td>\n",
       "      <td>0.332230</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.439990</td>\n",
       "      <td>0.312450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.335570</td>\n",
       "      <td>0.429840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.234480</td>\n",
       "      <td>0.249860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.008449</td>\n",
       "      <td>0.136580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.124190</td>\n",
       "      <td>0.335950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.256440</td>\n",
       "      <td>0.426240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.459100</td>\n",
       "      <td>0.404260</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.445470</td>\n",
       "      <td>0.451170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.422180</td>\n",
       "      <td>0.201180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.495630</td>\n",
       "      <td>0.214450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.308480</td>\n",
       "      <td>0.243060</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.397070</td>\n",
       "      <td>0.444380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.329450</td>\n",
       "      <td>0.392170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.407390</td>\n",
       "      <td>0.402710</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.310600</td>\n",
       "      <td>0.507020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.496380</td>\n",
       "      <td>0.453840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.100730</td>\n",
       "      <td>0.320530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.699070</td>\n",
       "      <td>0.373070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.297670</td>\n",
       "      <td>0.696480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.150990</td>\n",
       "      <td>0.573410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.164270</td>\n",
       "      <td>0.277590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.332590</td>\n",
       "      <td>0.055964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.537410</td>\n",
       "      <td>0.286370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>70</th>\n",
       "      <td>0.708760</td>\n",
       "      <td>0.967640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>71</th>\n",
       "      <td>0.691760</td>\n",
       "      <td>0.608650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>72</th>\n",
       "      <td>0.664080</td>\n",
       "      <td>0.920750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73</th>\n",
       "      <td>0.659730</td>\n",
       "      <td>0.666660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74</th>\n",
       "      <td>0.645740</td>\n",
       "      <td>0.568450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75</th>\n",
       "      <td>0.896390</td>\n",
       "      <td>0.708500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>76</th>\n",
       "      <td>0.854760</td>\n",
       "      <td>0.631670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>77</th>\n",
       "      <td>0.620910</td>\n",
       "      <td>0.804240</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>78</th>\n",
       "      <td>0.790570</td>\n",
       "      <td>0.561080</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79</th>\n",
       "      <td>0.589350</td>\n",
       "      <td>0.715820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>0.568460</td>\n",
       "      <td>0.740600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>0.659120</td>\n",
       "      <td>0.715480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>0.709380</td>\n",
       "      <td>0.740410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>0.591540</td>\n",
       "      <td>0.629270</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>0.458290</td>\n",
       "      <td>0.464100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>0.799820</td>\n",
       "      <td>0.748470</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>0.609740</td>\n",
       "      <td>0.547570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>0.681270</td>\n",
       "      <td>0.869850</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>0.766940</td>\n",
       "      <td>0.647360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>0.690480</td>\n",
       "      <td>0.830580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>0.681220</td>\n",
       "      <td>0.965410</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>0.732290</td>\n",
       "      <td>0.642450</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>0.761450</td>\n",
       "      <td>0.601380</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>0.589850</td>\n",
       "      <td>0.869550</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>0.731450</td>\n",
       "      <td>0.745160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>0.770290</td>\n",
       "      <td>0.701400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.731560</td>\n",
       "      <td>0.717820</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.445560</td>\n",
       "      <td>0.579910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.852750</td>\n",
       "      <td>0.859870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>0.519120</td>\n",
       "      <td>0.623590</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           0         1\n",
       "0   0.780510 -0.063669\n",
       "1   0.287740  0.291390\n",
       "2   0.407140  0.178780\n",
       "3   0.292300  0.421700\n",
       "4   0.509220  0.352560\n",
       "5   0.277850  0.108020\n",
       "6   0.275270  0.332230\n",
       "7   0.439990  0.312450\n",
       "8   0.335570  0.429840\n",
       "9   0.234480  0.249860\n",
       "10  0.008449  0.136580\n",
       "11  0.124190  0.335950\n",
       "12  0.256440  0.426240\n",
       "13  0.459100  0.404260\n",
       "14  0.445470  0.451170\n",
       "15  0.422180  0.201180\n",
       "16  0.495630  0.214450\n",
       "17  0.308480  0.243060\n",
       "18  0.397070  0.444380\n",
       "19  0.329450  0.392170\n",
       "20  0.407390  0.402710\n",
       "21  0.310600  0.507020\n",
       "22  0.496380  0.453840\n",
       "23  0.100730  0.320530\n",
       "24  0.699070  0.373070\n",
       "25  0.297670  0.696480\n",
       "26  0.150990  0.573410\n",
       "27  0.164270  0.277590\n",
       "28  0.332590  0.055964\n",
       "29  0.537410  0.286370\n",
       "..       ...       ...\n",
       "70  0.708760  0.967640\n",
       "71  0.691760  0.608650\n",
       "72  0.664080  0.920750\n",
       "73  0.659730  0.666660\n",
       "74  0.645740  0.568450\n",
       "75  0.896390  0.708500\n",
       "76  0.854760  0.631670\n",
       "77  0.620910  0.804240\n",
       "78  0.790570  0.561080\n",
       "79  0.589350  0.715820\n",
       "80  0.568460  0.740600\n",
       "81  0.659120  0.715480\n",
       "82  0.709380  0.740410\n",
       "83  0.591540  0.629270\n",
       "84  0.458290  0.464100\n",
       "85  0.799820  0.748470\n",
       "86  0.609740  0.547570\n",
       "87  0.681270  0.869850\n",
       "88  0.766940  0.647360\n",
       "89  0.690480  0.830580\n",
       "90  0.681220  0.965410\n",
       "91  0.732290  0.642450\n",
       "92  0.761450  0.601380\n",
       "93  0.589850  0.869550\n",
       "94  0.731450  0.745160\n",
       "95  0.770290  0.701400\n",
       "96  0.731560  0.717820\n",
       "97  0.445560  0.579910\n",
       "98  0.852750  0.859870\n",
       "99  0.519120  0.623590\n",
       "\n",
       "[100 rows x 2 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[[0,1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>2</th>\n",
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       "    <tr>\n",
       "      <th>95</th>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>96</th>\n",
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       "      <th>97</th>\n",
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       "      <th>98</th>\n",
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       "          0        1  2\n",
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   "source": [
    "data.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## TODO: Implementing the basic functions\n",
    "Here is your turn to shine. Implement the following formulas, as explained in the text.\n",
    "- Sigmoid activation function\n",
    "\n",
    "$$\\sigma(x) = \\frac{1}{1+e^{-x}}$$\n",
    "\n",
    "- Output (prediction) formula\n",
    "\n",
    "$$\\hat{y} = \\sigma(w_1 x_1 + w_2 x_2 + b)$$\n",
    "\n",
    "- Error function\n",
    "\n",
    "$$Error(y, \\hat{y}) = - y \\log(\\hat{y}) - (1-y) \\log(1-\\hat{y})$$\n",
    "\n",
    "- The function that updates the weights\n",
    "\n",
    "$$ w_i \\longrightarrow w_i + \\alpha (y - \\hat{y}) x_i$$\n",
    "\n",
    "$$ b \\longrightarrow b + \\alpha (y - \\hat{y})$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Implement the following functions\n",
    "\n",
    "# Activation (sigmoid) function\n",
    "def sigmoid(x):\n",
    "    return (1/(1+np.exp(-x)))\n",
    "\n",
    "# Output (prediction) formula\n",
    "def output_formula(features, weights, bias):\n",
    "    return (sigmoid(np.dot(features, weights) + bias))\n",
    "\n",
    "# Error (log-loss) formula\n",
    "def error_formula(y, output):\n",
    "    return (-y*(np.log(output)-(1-y)*np.log(1-output)))\n",
    "\n",
    "# Gradient descent step\n",
    "def update_weights(x, y, weights, bias, learnrate):\n",
    "    output = output_formula(x, weights, bias)\n",
    "    d_error = y - output\n",
    "    weights += learnrate * d_error * x\n",
    "    bias += learnrate * d_error\n",
    "    return weights, bias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training function\n",
    "This function will help us iterate the gradient descent algorithm through all the data, for a number of epochs. It will also plot the data, and some of the boundary lines obtained as we run the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(44)\n",
    "\n",
    "epochs = 100\n",
    "learnrate = 0.01\n",
    "\n",
    "def train(features, targets, epochs, learnrate, graph_lines=False):\n",
    "    \n",
    "    errors = []\n",
    "    n_records, n_features = features.shape\n",
    "    last_loss = None\n",
    "    weights = np.random.normal(scale=1 / n_features**.5, size=n_features)\n",
    "    bias = 0\n",
    "    for e in range(epochs):\n",
    "        del_w = np.zeros(weights.shape)\n",
    "        for x, y in zip(features, targets):\n",
    "            output = output_formula(x, weights, bias)\n",
    "            error = error_formula(y, output)\n",
    "            weights, bias = update_weights(x, y, weights, bias, learnrate)\n",
    "        \n",
    "        # Printing out the log-loss error on the training set\n",
    "        out = output_formula(features, weights, bias)\n",
    "        loss = np.mean(error_formula(targets, out))\n",
    "        errors.append(loss)\n",
    "        if e % (epochs / 10) == 0:\n",
    "            print(\"\\n========== Epoch\", e,\"==========\")\n",
    "            if last_loss and last_loss < loss:\n",
    "                print(\"Train loss: \", loss, \"  WARNING - Loss Increasing\")\n",
    "            else:\n",
    "                print(\"Train loss: \", loss)\n",
    "            last_loss = loss\n",
    "            predictions = out > 0.5\n",
    "            accuracy = np.mean(predictions == targets)\n",
    "            print(\"Accuracy: \", accuracy)\n",
    "        if graph_lines and e % (epochs / 100) == 0:\n",
    "            display(-weights[0]/weights[1], -bias/weights[1])\n",
    "            \n",
    "\n",
    "    # Plotting the solution boundary\n",
    "    plt.title(\"Solution boundary\")\n",
    "    display(-weights[0]/weights[1], -bias/weights[1], 'black')\n",
    "\n",
    "    # Plotting the data\n",
    "    plot_points(features, targets)\n",
    "    plt.show()\n",
    "\n",
    "    # Plotting the error\n",
    "    plt.title(\"Error Plot\")\n",
    "    plt.xlabel('Number of epochs')\n",
    "    plt.ylabel('Error')\n",
    "    plt.plot(errors)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time to train the algorithm!\n",
    "When we run the function, we'll obtain the following:\n",
    "- 10 updates with the current training loss and accuracy\n",
    "- A plot of the data and some of the boundary lines obtained. The final one is in black. Notice how the lines get closer and closer to the best fit, as we go through more epochs.\n",
    "- A plot of the error function. Notice how it decreases as we go through more epochs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "========== Epoch 0 ==========\n",
      "Train loss:  0.3559743168670997\n",
      "Accuracy:  0.4\n",
      "\n",
      "========== Epoch 10 ==========\n",
      "Train loss:  0.39784566173456015   WARNING - Loss Increasing\n",
      "Accuracy:  0.59\n",
      "\n",
      "========== Epoch 20 ==========\n",
      "Train loss:  0.351463297289164\n",
      "Accuracy:  0.74\n",
      "\n",
      "========== Epoch 30 ==========\n",
      "Train loss:  0.31394715089105796\n",
      "Accuracy:  0.84\n",
      "\n",
      "========== Epoch 40 ==========\n",
      "Train loss:  0.2844523616008021\n",
      "Accuracy:  0.86\n",
      "\n",
      "========== Epoch 50 ==========\n",
      "Train loss:  0.26088612330447836\n",
      "Accuracy:  0.93\n",
      "\n",
      "========== Epoch 60 ==========\n",
      "Train loss:  0.2417349668527042\n",
      "Accuracy:  0.93\n",
      "\n",
      "========== Epoch 70 ==========\n",
      "Train loss:  0.22592385204759333\n",
      "Accuracy:  0.93\n",
      "\n",
      "========== Epoch 80 ==========\n",
      "Train loss:  0.21268177075617678\n",
      "Accuracy:  0.94\n",
      "\n",
      "========== Epoch 90 ==========\n",
      "Train loss:  0.2014479211910581\n",
      "Accuracy:  0.94\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train(X, y, epochs, learnrate, True)"
   ]
  }
 ],
 "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}