3. Logistic Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"https://raw.githubusercontent.com/DataForScience/DeepLearning/master/data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\"> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> <h1>Deep Learning From Scratch</h1>\n",
    "<h1>Logistic Regression</h1>\n",
    "        <p>Bruno Gonçalves<br/>\n",
    "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
    "            @bgoncalves, @data4sci</p></div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "import watermark\n",
    "\n",
    "%load_ext watermark\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.10.9\n",
      "IPython version      : 8.10.0\n",
      "\n",
      "Compiler    : Clang 14.0.6 \n",
      "OS          : Darwin\n",
      "Release     : 22.5.0\n",
      "Machine     : x86_64\n",
      "Processor   : i386\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: 03a6cf9c5faed1d6e551b54357ff497cfa569fb9\n",
      "\n",
      "pandas    : 1.5.3\n",
      "matplotlib: 3.7.0\n",
      "numpy     : 1.23.5\n",
      "seaborn   : 0.12.2\n",
      "watermark : 2.4.2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -i -n -v -m -g -iv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('d4sci.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('data/iris.csv', delimiter=',', header=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quick visualization of the data. Always a good way to make sure we have what we expect"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>virginica</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>150 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal_length  sepal_width  petal_length  petal_width    species\n",
       "0             5.1          3.5           1.4          0.2     setosa\n",
       "1             4.9          3.0           1.4          0.2     setosa\n",
       "2             4.7          3.2           1.3          0.2     setosa\n",
       "3             4.6          3.1           1.5          0.2     setosa\n",
       "4             5.0          3.6           1.4          0.2     setosa\n",
       "..            ...          ...           ...          ...        ...\n",
       "145           6.7          3.0           5.2          2.3  virginica\n",
       "146           6.3          2.5           5.0          1.9  virginica\n",
       "147           6.5          3.0           5.2          2.0  virginica\n",
       "148           6.2          3.4           5.4          2.3  virginica\n",
       "149           5.9          3.0           5.1          1.8  virginica\n",
       "\n",
       "[150 rows x 5 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the labels. We will try to predict the 'virginica' label"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "data['y'] = 0\n",
    "data.loc[data['species'] == 'virginica', 'y'] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extract the data as arrays"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>6.7</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.3</td>\n",
       "      <td>virginica</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>146</th>\n",
       "      <td>6.3</td>\n",
       "      <td>2.5</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.9</td>\n",
       "      <td>virginica</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>147</th>\n",
       "      <td>6.5</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.2</td>\n",
       "      <td>2.0</td>\n",
       "      <td>virginica</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>148</th>\n",
       "      <td>6.2</td>\n",
       "      <td>3.4</td>\n",
       "      <td>5.4</td>\n",
       "      <td>2.3</td>\n",
       "      <td>virginica</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149</th>\n",
       "      <td>5.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.1</td>\n",
       "      <td>1.8</td>\n",
       "      <td>virginica</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     sepal_length  sepal_width  petal_length  petal_width    species  y\n",
       "145           6.7          3.0           5.2          2.3  virginica  1\n",
       "146           6.3          2.5           5.0          1.9  virginica  1\n",
       "147           6.5          3.0           5.2          2.0  virginica  1\n",
       "148           6.2          3.4           5.4          2.3  virginica  1\n",
       "149           5.9          3.0           5.1          1.8  virginica  1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data[['sepal_length','sepal_width','petal_length','petal_width']].values\n",
    "y = data['y'].values.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Utility functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logistic function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logistic(z):\n",
    "    return 1./(1+np.exp(-z))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Get matrix dimensions and add the bias column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "M, N = X.shape\n",
    "X = np.concatenate((np.ones((M, 1)), X), axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have a few more features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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      " [1.  6.3 2.7 4.9 1.8]\n",
      " [1.  6.7 3.3 5.7 2.1]\n",
      " [1.  7.2 3.2 6.  1.8]\n",
      " [1.  6.2 2.8 4.8 1.8]\n",
      " [1.  6.1 3.  4.9 1.8]\n",
      " [1.  6.4 2.8 5.6 2.1]\n",
      " [1.  7.2 3.  5.8 1.6]\n",
      " [1.  7.4 2.8 6.1 1.9]\n",
      " [1.  7.9 3.8 6.4 2. ]\n",
      " [1.  6.4 2.8 5.6 2.2]\n",
      " [1.  6.3 2.8 5.1 1.5]\n",
      " [1.  6.1 2.6 5.6 1.4]\n",
      " [1.  7.7 3.  6.1 2.3]\n",
      " [1.  6.3 3.4 5.6 2.4]\n",
      " [1.  6.4 3.1 5.5 1.8]\n",
      " [1.  6.  3.  4.8 1.8]\n",
      " [1.  6.9 3.1 5.4 2.1]\n",
      " [1.  6.7 3.1 5.6 2.4]\n",
      " [1.  6.9 3.1 5.1 2.3]\n",
      " [1.  5.8 2.7 5.1 1.9]\n",
      " [1.  6.8 3.2 5.9 2.3]\n",
      " [1.  6.7 3.3 5.7 2.5]\n",
      " [1.  6.7 3.  5.2 2.3]\n",
      " [1.  6.3 2.5 5.  1.9]\n",
      " [1.  6.5 3.  5.2 2. ]\n",
      " [1.  6.2 3.4 5.4 2.3]\n",
      " [1.  5.9 3.  5.1 1.8]]\n"
     ]
    }
   ],
   "source": [
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Set the training parameters and initialize the weight matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.5\n",
    "epsilon = 0.12\n",
    "\n",
    "weights = 2*np.random.rand(N+1, 1)*epsilon - epsilon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training procedure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10 [[0.87954698]] [[2.93006119]] [-0.34314497 -1.29165108 -1.22127792  0.62755594  0.65882767]\n",
      "20 [[2.13792469]] [[0.24787749]] [-0.48787471 -1.46428705 -1.53686588  1.49113637  1.20653653]\n",
      "30 [[2.11603014]] [[0.6285851]] [-0.62121528 -1.68484204 -1.77581826  2.08123533  1.63090281]\n",
      "40 [[1.90152414]] [[0.60777197]] [-0.75243005 -1.9772651  -1.98736327  2.46092051  1.96175993]\n",
      "50 [[1.72338991]] [[0.56780944]] [-0.87969725 -2.26267897 -2.1863898   2.8158872   2.27881575]\n",
      "60 [[1.54770906]] [[0.51920483]] [-1.00398288 -2.53946765 -2.3787765   3.1612999   2.588942  ]\n",
      "70 [[1.36864556]] [[0.46478692]] [-1.12426442 -2.80326922 -2.5632658   3.49801597  2.8917121 ]\n",
      "80 [[1.183359]] [[0.406757]] [-1.2386744  -3.04753333 -2.73635913  3.82290241  3.18406325]\n",
      "90 [[0.98503946]] [[0.34612357]] [-1.34447126 -3.26220279 -2.89250141  4.13075148  3.46067812]\n",
      "100 [[0.74921182]] [[0.27869814]] [-1.43628099 -3.425522   -3.02006301  4.41502909  3.71242191]\n",
      "110 [[0.37907567]] [[0.13947505]] [-1.4949371  -3.45419654 -3.07510029  4.67867635  3.92102075]\n",
      "120 [[0.09674833]] [[0.02390147]] [-1.49947292 -3.31136174 -3.02440953  4.86255218  4.03197971]\n",
      "129 [[0.0909446]] [[0.00091514]] [-1.51329806 -3.29036512 -3.0214449   4.90214079  4.07273283]\n"
     ]
    }
   ],
   "source": [
    "oldJ = 0\n",
    "err = 1\n",
    "\n",
    "Js = []\n",
    "count = 0\n",
    "\n",
    "# Stop when the relative change in error is sufficiently small\n",
    "while err > 0.001:\n",
    "    Zs = np.dot(X, weights)\n",
    "    Hs = logistic(Zs) # phi(z)\n",
    "    \n",
    "    deltas = alpha/M*np.dot(X.T, (Hs-y))\n",
    "    weights -= deltas\n",
    "\n",
    "    count += 1\n",
    "\n",
    "    # Cross Entropy\n",
    "    J = -1/M*(np.dot(y.T, np.log(Hs)) + np.dot(1-y.T, np.log(1-Hs)))\n",
    "    \n",
    "    Js.append(float(J))\n",
    "    \n",
    "    # Relative change in error\n",
    "    err = np.abs((oldJ-J)/J)\n",
    "    oldJ = J\n",
    "    \n",
    "    if count % 10 == 0:\n",
    "        print(count, J, err, weights.flatten())\n",
    "\n",
    "print(count, J, err, weights.flatten())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution exploration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_boundary(Zs, Hs, y):\n",
    "    data_fit = np.concatenate((Zs, Hs), axis=1)\n",
    "    data_fit.sort(axis = 0)\n",
    "\n",
    "    z = np.linspace(Zs.min(), Zs.max(), 100)\n",
    "\n",
    "    plt.plot(z, logistic(z), 'r-', label='Theory')\n",
    "    plt.plot(Zs, Hs, 'X', label='empirical', markersize=8)\n",
    "    plt.plot(Zs, y, 'd', label = 'data', markersize=8)\n",
    "    plt.xlabel('z')\n",
    "    plt.ylabel('h(z)')\n",
    "    #plt.title('Logistic Regression')\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary(Zs, Hs, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utility function to plot labeled points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_points(data, features, weights, label='y'):\n",
    "    plt.plot(data[features[0]][data[label]==0], \n",
    "             data[features[1]][data[label]==0], '*', label='y=0', markersize=8)\n",
    "    \n",
    "    plt.plot(data[features[0]][data[label]==1], \n",
    "             data[features[1]][data[label]==1], 'd', label='y=1', markersize=8)\n",
    "\n",
    "    plt.xlabel(features[0])\n",
    "    plt.ylabel(features[1])\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_points(data, ['petal_width', 'petal_length'], weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The separation bounday is not perfect here either"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_points(data, ['sepal_width', 'petal_length'], weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_boundary_threshold(Zs, Hs, y, threshold=0.5):\n",
    "    data_fit = np.concatenate((Zs, Hs), axis=1)\n",
    "    data_fit.sort(axis = 0)\n",
    "\n",
    "    z = np.linspace(Zs.min(), Zs.max(), 100)\n",
    "\n",
    "    plt.plot(z, logistic(z), 'r-', label='Theory')\n",
    "    plt.plot(Zs[Hs>threshold], Hs[Hs>threshold], 'X', label='empirical 1', markersize=8)\n",
    "    plt.plot(Zs[Hs<=threshold], Hs[Hs<=threshold], 's', label='empirical 0', markersize=8)\n",
    "\n",
    "    plt.plot(Zs, y, 'd', label = 'data', markersize=8)\n",
    "    plt.xlabel('z')\n",
    "    plt.ylabel('h(z)')    \n",
    "    plt.plot([Zs.min(), Zs.max()], [threshold, threshold],  lw=5, linestyle=':', color='darkgray')\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_boundary_threshold(Zs, Hs, y, 0.9)"
   ]
  },
  {
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   "metadata": {},
   "source": [
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