Logistic Regression (Noman).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from sklearn.metrics import accuracy_score\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((100, 2), (100,))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris_data = datasets.load_iris()\n",
    "X = iris_data.data[:100,:2]\n",
    "y = iris_data.target[:100]\n",
    "X_full = iris_data.data[:100, :]\n",
    "X.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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DSYshsrqDRCnj9Vk9QkmPnQ9VvBBMRA4G7gMOAVqA/wAuUNX3iorKh4KW+27K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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2cec21f510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "setosa     = plt.scatter(X[:50,0], X[:50, 1], c='b')\n",
    "versicolor = plt.scatter(X[50:,0], X[50:, 1], c='r')\n",
    "\n",
    "plt.xlabel('Sepal Width')\n",
    "plt.ylabel('Sepal Length')\n",
    "\n",
    "plt.legend((setosa,versicolor), ('setosa','versicolor'))\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Ncy6RlBOORPn9GxaPB26/ejreLJ2GIalBz0SRBL3y0U4OtAa4/MwJVFcVOx1H5BAVuUgC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\n/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2cb773b710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_   = np.linspace(-5,5, num=50)\n",
    "y_   = 1.0/(1 + np.exp(-x_))\n",
    "\n",
    "plt.plot(x_,y_)\n",
    "plt.axhline(.5)\n",
    "plt.axvline(.0)\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binary Data set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "X = np.array([[0,0],[1,1],[1,0],[1,1],[0,0],[0,1],[1,0],[1,1],[0,1]]).reshape(9,2) \n",
    "y = np.array([0,1,1,1,0,1,1,1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def logistic_fuinction(theta, X):\n",
    "     return 1.0/(1 + np.exp(- X.dot(theta) ))\n",
    "    \n",
    "def log_gradient(theta, X, y):\n",
    "    output = logistic_fuinction(theta, X)- np.squeeze(y)\n",
    "    return output.T.dot(X)\n",
    "\n",
    "def costFunction(theta, X,y, reg=0.001):\n",
    "    step_1 = np.squeeze(y) * np.log(logistic_fuinction(theta, X))\n",
    "    step_2 = (1-np.squeeze(y)) * np.log(logistic_fuinction(theta, X))\n",
    "    final  = -step_1-step_2\n",
    "    \n",
    "    regulaization = 0.5 * np.mean(np.sum(theta**2) * reg)\n",
    "    return np.mean(final)+regulaization\n",
    "\n",
    "def gradient_descent(theta, X,y, lr = 0.001, convergence = 0.0001):\n",
    "    X = (X - np.mean(X, axis=0))/np.std(X, axis=0) \n",
    "    cost = costFunction(theta, X, y)\n",
    "    cost_itr = []\n",
    "    cost_itr.append([0, cost])\n",
    "    change_cost = 1\n",
    "    i = 0\n",
    "    \n",
    "    while(change_cost > convergence):\n",
    "        old_cost = cost\n",
    "        theta = theta - lr*(log_gradient(theta, X, y))\n",
    "        cost  = costFunction(theta, X, y)\n",
    "        cost_itr.append([i, cost])\n",
    "        change_cost = old_cost-cost\n",
    "        i = i+1\n",
    "    return theta, np.array(cost_itr)\n",
    "\n",
    "def perdiction(theta, X, hard=True):\n",
    "    #normalize\n",
    "    X = (X - np.mean(X, axis=0)) / np.std(X, axis=0)\n",
    "    pred_prob = logistic_fuinction(theta, X)\n",
    "    pred_value = np.where(pred_prob >= .5, 1, 0)\n",
    "    print \n",
    "    #if hard:\n",
    "    #    return pred_value\n",
    "    return pred_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "theta_dim = X.shape[1]\n",
    "theta = np.random.normal(0, 0.01, theta_dim)\n",
    "fitted_values, cost = gradient_descent(theta, X,y)\n",
    "output = perdiction(fitted_values, X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "98.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(output == y)*1.0/ len(X) * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}