2-logistic-regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setup "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = datasets.load_iris()\n",
    "X = data[\"data\"][:,3:]\n",
    "y = (data[\"target\"] == 2).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X[y==0], y[y==0], \"bs\")\n",
    "plt.plot(X[y==1], y[y==1], \"g^\")\n",
    "plt.legend([\"Not iris virginica\",\"Iris virginica\"])\n",
    "plt.xlabel(\"Petal width  (cm)\")\n",
    "plt.title(\"Data to be used\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Logistic regression "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Trying to find a decision boundary that seperates the two classes best. For this we are going to use the logistic (sigmoid) function to estimate probabilities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sigmoid function\n",
    "\n",
    "$$\n",
    "\\sigma(z) = \\frac{1}{1+e^{(-z)}}\n",
    "$$\n",
    "\n",
    "Loss function\n",
    "\n",
    "$$\n",
    "L(\\theta) = - y^{(i)} \\log(\\sigma (\\theta^{T}x^{(i)})) - (1 - y^{(i)}) \\log (1 - (\\sigma (\\theta^{T}x^{(i)})))\n",
    "$$\n",
    "\n",
    "Error\n",
    "\n",
    "$$\n",
    "E = \\sigma(Xw + b) - y  \n",
    "$$\n",
    "\n",
    "Partial derivatives\n",
    "\n",
    "$$\n",
    "\\frac{\\partial}{\\partial \\theta_{w}} = \\frac{1}{m}X^{T}E \\\\\n",
    "\\frac{\\partial}{\\partial \\theta_{b}} = \\frac{1}{m}\\sum_{i = 1}^{m} E \\\\\n",
    "$$\n",
    "\n",
    "Step function\n",
    "\n",
    "$$\n",
    "\\theta_{w,b} = \\theta_{w,b} - \\alpha \\frac{\\partial}{\\partial \\theta_{w,b}}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1 / (1 + np.exp(-z)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = [1.2]\n",
    "b = -5\n",
    "iterations = 10000\n",
    "alpha = 0.003\n",
    "m = len(X)\n",
    "J_hist = []\n",
    "\n",
    "#full algorithm\n",
    "for i in range(iterations):\n",
    "    \n",
    "    #calculate cost - just for plotting\n",
    "    total_cost = 0\n",
    "    for i in range(m):\n",
    "        pred = sigmoid(np.dot(w, X[i])+ b)\n",
    "        total_cost += (-y[i] * np.log(pred)) - (1 - y[i]) * np.log(1 - pred)\n",
    "    total_cost /= m\n",
    "    J_hist.append(total_cost)\n",
    "    \n",
    "    #get partial derivatives\n",
    "    error = sigmoid(np.dot(X, w) + b) - y\n",
    "    dj_dw = (1/m)*np.dot(X.T, error)\n",
    "    dj_db = (1/m)*np.sum(error)\n",
    "    \n",
    "    # Update Parameters using w, b, alpha and gradient\n",
    "    w = w - alpha * dj_dw               \n",
    "    b = b - alpha * dj_db   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min loss: 0.23554544405993208\n"
     ]
    }
   ],
   "source": [
    "plt.plot(J_hist)\n",
    "plt.xlabel(\"Epochs\")\n",
    "plt.ylabel(\"Loss\")\n",
    "plt.title(\"Training\")\n",
    "plt.show()\n",
    "\n",
    "print(f\"Min loss: {min(J_hist)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "preds = []\n",
    "threshold = 0.5\n",
    "\n",
    "for i in range(len(X)):\n",
    "    res = sigmoid(w[0] * X[i] + b)\n",
    "    if res > threshold:\n",
    "        preds.append(X[i])\n",
    "        \n",
    "thresh = min(preds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X[y==0], y[y==0], \"bs\")\n",
    "plt.plot(X[y==1], y[y==1], \"g^\")\n",
    "plt.axvline(x=thresh, c = \"y\")\n",
    "plt.axvspan(0, thresh, facecolor='purple', alpha=0.1)\n",
    "plt.axvspan(thresh, max(X), facecolor='red', alpha=0.1)\n",
    "\n",
    "plt.legend([\"Not iris virginica\",\"Iris virginica\", \"Decision boundary\"])\n",
    "plt.xlabel(\"Petal width  (cm)\")\n",
    "plt.title(f\"Decision boundary with threshold: {threshold}\")\n",
    "plt.show()"
   ]
  },
  {
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}