Logistic_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2 align=\"center\"> Logistic Regression </h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2: Load the Data and Libraries\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "plt.style.use(\"ggplot\")\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pylab import rcParams\n",
    "rcParams['figure.figsize'] = 12, 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        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>DMV_Test_1</th>\n",
       "      <th>DMV_Test_2</th>\n",
       "      <th>Results</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>34.623660</td>\n",
       "      <td>78.024693</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>30.286711</td>\n",
       "      <td>43.894998</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>35.847409</td>\n",
       "      <td>72.902198</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60.182599</td>\n",
       "      <td>86.308552</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>79.032736</td>\n",
       "      <td>75.344376</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   DMV_Test_1  DMV_Test_2  Results\n",
       "0   34.623660   78.024693        0\n",
       "1   30.286711   43.894998        0\n",
       "2   35.847409   72.902198        0\n",
       "3   60.182599   86.308552        1\n",
       "4   79.032736   75.344376        1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('DMV_Written_Tests.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 100 entries, 0 to 99\n",
      "Data columns (total 3 columns):\n",
      "DMV_Test_1    100 non-null float64\n",
      "DMV_Test_2    100 non-null float64\n",
      "Results       100 non-null int64\n",
      "dtypes: float64(2), int64(1)\n",
      "memory usage: 2.4 KB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "scores = df[['DMV_Test_1', 'DMV_Test_2']].values\n",
    "results = df['Results'].values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 3: Visualize the Data\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "passed = (results == 1).reshape(100,1)\n",
    "failed = (results == 0).reshape(100, 1)\n",
    "ax = sns.scatterplot(x = scores[passed[:,0], 0], y = scores[passed[:,0], 1], marker = \"^\", color='green', s=60)\n",
    "sns.scatterplot(x = scores[failed[:,0], 0], y = scores[failed[:,0], 1], marker = \"X\", color='red', s=60)\n",
    "ax.set(xlabel = 'DMV Written Test 1 scores', ylabel = 'DMV Written Test 2 scores')\n",
    "ax.legend(['passed', 'failed'])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 4: Define the Logistic Sigmoid Function $\\sigma(z)$\n",
    "---\n",
    "\n",
    "$$ \\sigma(z) = \\frac{1}{1+e^{-z}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid_function(x):\n",
    "    return 1/(1 + np.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sigmoid_function(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 5: Compute the Cost Function $J(\\theta)$ and Gradient\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The objective of logistic regression is to minimize the cost function\n",
    "\n",
    "$$J(\\theta) = -\\frac{1}{m} \\sum_{i=1}^{m} [ y^{(i)}log(h_{\\theta}(x^{(i)})) + (1 - y^{(i)})log(1 - (h_{\\theta}(x^{(i)}))]$$\n",
    "\n",
    "where the gradient of the cost function is given by\n",
    "\n",
    "$$ \\frac{\\partial J(\\theta)}{\\partial \\theta_j} = \\frac{1}{m} \\sum_{i=1}^{m} (h_{\\theta}(x^{(i)}) - y^{(i)})x_j^{(i)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_cost(theta, x, y):\n",
    "    m=len(y)\n",
    "    y_pred = sigmoid_function(np.dot(x, theta))\n",
    "    error = (y * np.log(y_pred)) + (1 -y) * (np.log(1-y_pred))\n",
    "    cost = -1/m * sum(error)\n",
    "    gradient = 1/m * np.dot(x.transpose(), (y_pred - y))\n",
    "    \n",
    "    return cost[0], gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 6: Cost and Gradient at Initialization\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at initialization 0.693147180559946\n",
      "Gradient at initialization [[-0.1       ]\n",
      " [-0.28122914]\n",
      " [-0.25098615]]\n"
     ]
    }
   ],
   "source": [
    "mean_scores = np.mean(scores, axis = 0)\n",
    "std_scores = np.std(scores, axis = 0)\n",
    "scores = (scores - mean_scores) / std_scores\n",
    "\n",
    "rows = scores.shape[0]\n",
    "cols = scores.shape[1]\n",
    " \n",
    "X = np.append(np.ones((rows, 1)), scores, axis = 1)\n",
    "y = results.reshape(rows, 1)\n",
    "\n",
    "theta_int = np.zeros((cols + 1, 1))\n",
    "cost, gradient = compute_cost(theta_int, X, y)\n",
    "\n",
    "print(\"Cost at initialization\", cost)\n",
    "print(\"Gradient at initialization\", gradient)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 7: Gradient Descent\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Minimize the cost function $J(\\theta)$ by updating the below equation and repeat until convergence\n",
    "$\\theta_j := \\theta_j - \\alpha \\frac{\\partial J(\\theta)}{\\partial \\theta_j}$ (simultaneously update $\\theta_j$ for all $j$)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradient_descent(x, y, theta, alpha, iterations):\n",
    "    costs = []\n",
    "    for i in range(iterations):\n",
    "        cost, gradient = compute_cost(theta, x, y)\n",
    "        theta -= (alpha * gradient)\n",
    "        costs.append(cost)\n",
    "    return theta, costs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta after running gradient descent [[1.50850586]\n",
      " [3.5468762 ]\n",
      " [3.29383709]]\n"
     ]
    }
   ],
   "source": [
    "theta, costs = gradient_descent(X, y, theta_int, 1, 200)\n",
    "print(\"Theta after running gradient descent\", theta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resulting cost: 0.2048938203512014\n"
     ]
    }
   ],
   "source": [
    "print(\"Resulting cost:\", costs[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 8: Plotting the Convergence of $J(\\theta)$\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot $J(\\theta)$ against the number of iterations of gradient descent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(costs)\n",
    "plt.xlabel(\"Iterations\")\n",
    "plt.ylabel(\"$J(\\theta)$\")\n",
    "plt.title(\"Values of cost function over Iterations of Gradient Descent\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 9: Plotting the decision boundary\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$h_\\theta(x) = \\sigma(z)$, where $\\sigma$ is the logistic sigmoid function and $z = \\theta^Tx$\n",
    "\n",
    "When $h_\\theta(x) \\geq 0.5$ the model predicts class \"1\":\n",
    "\n",
    "$\\implies \\sigma(\\theta^Tx) \\geq 0.5$\n",
    "\n",
    "$\\implies \\theta^Tx \\geq 0$ predict class \"1\" \n",
    "\n",
    "Hence, $\\theta_1 + \\theta_2x_2 + \\theta_3x_3 = 0$ is the equation for the decision boundary, giving us \n",
    "\n",
    "$ x_3 = \\frac{-(\\theta_1+\\theta_2x_2)}{\\theta_3}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.scatterplot(x = X[passed[:, 0], 1],\n",
    "                     y = X[passed[:, 0], 2], \n",
    "                     marker = '^', \n",
    "                     color = 'green', \n",
    "                     s=60)\n",
    "\n",
    "sns.scatterplot(x = X[failed[:, 0], 1],\n",
    "                y = X[failed[:, 0], 2], \n",
    "                marker = 'x', \n",
    "                color = 'red', \n",
    "                s=60)\n",
    "\n",
    "ax.legend(['Passed', 'Failed'])\n",
    "ax.set(xlabel = \"DMV Written 1 scores\", ylabel = \"DMV Written 2 Scores\")\n",
    "\n",
    "x_boundary = np.array([np.min(X[:, 1]), np.max(X[:, 1])])\n",
    "y_boundary = -(theta[0] + theta[1] * x_boundary) / theta[2]\n",
    "\n",
    "sns.lineplot(x = x_boundary, y = y_boundary, color = 'blue')\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 10: Predictions using the optimized $\\theta$ values\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$h_\\theta(x) = x\\theta$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(theta, x):\n",
    "    results = x.dot(theta)\n",
    "    return results > 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training Accuracy: 89 %\n"
     ]
    }
   ],
   "source": [
    "p = predict(theta, X)\n",
    "print(\"Training Accuracy:\", sum(p == y)[0], \"%\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A person who scores 50 and 79 on their DMV Written test have a 0.71 proability of passing\n"
     ]
    }
   ],
   "source": [
    "test = np.array([50, 79])\n",
    "test = (test - mean_scores) / std_scores\n",
    "test = np.append(np.ones(1), test)\n",
    "probability = sigmoid_function(test.dot(theta))\n",
    "print(\"A person who scores 50 and 79 on their DMV Written test have a\", np.round(probability[0], 2), \"proability of passing\")"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}