Logistic Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Hypothesis which uses the following sigmoid function </h2>\n",
    "<h1> $$ \\frac{1}{(1 + e^{-\\theta^\\intercal X})} $$ </h1>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(theta, X):\n",
    "    return 1 / (1 + np.exp((-np.matmul(X,theta.transpose()))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Calculates cost with regularization </h2>\n",
    "<h2> Note that $ \\theta_{0} $ is not included in the calculation of cost </h2>\n",
    "<h1> $$ \\frac{1}{m} \\sum_{i=1}^m (-y^{(i)}*ln(h_{\\theta}(x^{(i)}))-(1-y^{(i)})ln(1-h_{\\theta}(x^{(i)}))) + \\frac{\\lambda}{2m} \\sum_{j=1}^n \\theta_j^2 $$ </h1>\n",
    "<h3> where m = number of training examples, and $y^{(i)}$ and $x^{(i)}$ is training example i </h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_cost(theta, X, y, lbda): # theta is dimensions n x 1, X is dimensions m x n, y is dimensions m x 1, lbda is regularization constant\n",
    "    m = X.shape[0]\n",
    "    h = sigmoid(theta, X)\n",
    "    cost = (1/m)*(-y*np.log(h)-(1-y)*np.log(1-h)).sum() + (lbda / (2*m))*np.square(theta).sum()\n",
    "    cost -= (lbda / (2*m)) * theta[0]**2 # remove contribution of theta_zero as it should not be included in cost\n",
    "    return cost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2> Vectorized implementation gradient calculation together with regularization </h2>\n",
    "<h2> Note that for $\\theta_{0}$, regularization is not needed </h2>\n",
    "<h1> $$ \\frac{\\partial J}{\\partial \\theta_{j}} = \\frac{1}{m} \\sum_{i=1}^m (h_{\\theta}(x^{(i)})-y^{(i)})x_{j}^{(i)} + \\frac{\\lambda}{m} \\theta_{j}$$ </h1>\n",
    "<h3> for j = 1,2,...,n where n is the number of weights theta, and m is the number of training examples </h3>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_grad(theta, X, y, lbda):\n",
    "    m = X.shape[0]\n",
    "    h = sigmoid(theta, X)\n",
    "    grad = np.matmul(X.transpose(),h - y) # vectorized implementation of gradient\n",
    "    grad += (lbda/m) * theta\n",
    "    grad[0] -= (lbda/m) * theta[0] # remove contribution of theta_zero as it should not be included in grad calculation\n",
    "    return grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def logistic_regression(X, y, alpha, iterations, test_X, test_y):\n",
    "    theta = np.random.rand(X.shape[1]) # randomly initiates weights\n",
    "    m = X.shape[0]\n",
    "    costs_train = []\n",
    "    costs_test = []\n",
    "    for i in range(iterations):\n",
    "        costs_train.append(calculate_cost(theta, X, y, 1))\n",
    "        theta -= alpha * (1/m)*calculate_grad(theta, X ,y, 1)\n",
    "        costs_test.append(calculate_cost(theta, test_X, test_y, 1))\n",
    "    x_graph = np.arange(0,iterations,1);    \n",
    "    plt.plot(x_graph,costs_train, label='train') \n",
    "    plt.plot(x_graph,costs_test, label='test')\n",
    "    plt.legend()\n",
    "    return theta   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(theta, X, threshold):\n",
    "    pred = sigmoid(theta, X)\n",
    "    pred_result = (pred>=threshold).astype(int) # those above threshold = 1, 0 otherwise\n",
    "    return pred_result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize(X, mean, std):\n",
    "    return (X-mean) / std"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pregnancies                 0\n",
      "Glucose                     0\n",
      "BloodPressure               0\n",
      "SkinThickness               0\n",
      "Insulin                     0\n",
      "BMI                         0\n",
      "DiabetesPedigreeFunction    0\n",
      "Age                         0\n",
      "Outcome                     0\n",
      "dtype: int64\n",
      "268\n",
      "500\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv(\"data/logistic_diabetes.csv\")\n",
    "print(df.isnull().sum())\n",
    "print(len(df[df['Outcome']==1]))\n",
    "print(len(df[df['Outcome']==0])) # making sure data is balanced, a bit of imbalance but should be okay\n",
    "train=df.sample(frac=0.75,random_state=150) #random state is a seed value\n",
    "test=df.drop(train.index)\n",
    "\n",
    "train_x = train.loc[:,train.columns != \"Outcome\"] # splitting dependent and independent variables\n",
    "test_x = test.loc[:,test.columns != \"Outcome\"]\n",
    "train_y = train['Outcome'].values\n",
    "test_y = test['Outcome'].values\n",
    "\n",
    "train_mean = train_x.mean(axis=0) # mean normalization\n",
    "train_std = train_x.std(axis=0)\n",
    "train_x = normalize(train_x,train_mean ,train_std)\n",
    "test_x = normalize(test_x,train_mean ,train_std )\n",
    "\n",
    "train_x.insert(0, 'One', 1) # adding column of ones for theta that is independent of features\n",
    "test_x.insert(0, 'One', 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "theta = logistic_regression(train_x.values, train_y, 0.05, 500, test_x.values, test_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'predict' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-1-f003e8dd03cb>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mpred_y\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtest_x\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      2\u001b[0m \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpred_y\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mtest_y\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[0mpred_train_y\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mtrain_x\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m0.6\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mresult_train\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpred_train_y\u001b[0m \u001b[1;33m==\u001b[0m \u001b[0mtrain_y\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msum\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m/\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNameError\u001b[0m: name 'predict' is not defined"
     ]
    }
   ],
   "source": [
    "pred_y = predict(theta, test_x.values, 0.6)\n",
    "result = pred_y == test_y\n",
    "pred_train_y = predict(theta, train_x.values, 0.6)\n",
    "result_train = pred_train_y == train_y\n",
    "print(sum(result) / len(result))"
   ]
  }
 ],
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