Logistic Regression Gradient Descent.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "from builtins import range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 100\n",
    "D = 2\n",
    "\n",
    "N_per_class = N//2\n",
    "\n",
    "\n",
    "X = np.random.randn(N,D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# center the first 50 points at (-2,-2)\n",
    "X[:N_per_class,:] = X[:N_per_class,:] - 2*np.ones((N_per_class,D))\n",
    "\n",
    "# center the last 50 points at (2, 2)\n",
    "X[N_per_class:,:] = X[N_per_class:,:] + 2*np.ones((N_per_class,D))\n",
    "\n",
    "# labels: first N_per_class are 0, last N_per_class are 1\n",
    "T = np.array([0]*N_per_class + [1]*N_per_class)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 3)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ones = np.ones((N, 1))\n",
    "Xb = np.concatenate((ones, X), axis=1)\n",
    "Xb.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# randomly initialize the weights\n",
    "w = np.random.randn(D + 1)\n",
    "\n",
    "# calculate the model output\n",
    "z = Xb.dot(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    return 1/(1 + np.exp(-z))\n",
    "\n",
    "\n",
    "Y = sigmoid(z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.19986264, 0.01466494, 0.02243806, 0.17169344, 0.02878246,\n",
       "       0.56026925, 0.02555837, 0.04816325, 0.13108552, 0.13228684,\n",
       "       0.02907388, 0.06458564, 0.05342666, 0.2004559 , 0.09692951,\n",
       "       0.03697502, 0.31113768, 0.12279073, 0.12956663, 0.19747155,\n",
       "       0.09686029, 0.07358954, 0.05519872, 0.04275713, 0.08857767,\n",
       "       0.08016758, 0.04374457, 0.08884786, 0.08061072, 0.06216873,\n",
       "       0.19463228, 0.07631153, 0.10861772, 0.30520841, 0.06580548,\n",
       "       0.0172835 , 0.0730741 , 0.06067123, 0.00253463, 0.03845631,\n",
       "       0.54932522, 0.18901762, 0.03468397, 0.00989757, 0.33070212,\n",
       "       0.10536651, 0.03344796, 0.06923682, 0.02676635, 0.2199454 ,\n",
       "       0.116663  , 0.92114812, 0.81160941, 0.26792235, 0.68405904,\n",
       "       0.78059895, 0.56476345, 0.4023627 , 0.47643886, 0.31760335,\n",
       "       0.18462815, 0.42056847, 0.23078222, 0.93227674, 0.89136549,\n",
       "       0.39241565, 0.97015513, 0.86467661, 0.51199004, 0.40542274,\n",
       "       0.40891724, 0.44444777, 0.82516786, 0.59169501, 0.98184576,\n",
       "       0.16627896, 0.85391623, 0.6488083 , 0.74173267, 0.33814512,\n",
       "       0.23336023, 0.74651084, 0.27179737, 0.22001316, 0.96954556,\n",
       "       0.88218845, 0.70565247, 0.92295899, 0.9609166 , 0.2262016 ,\n",
       "       0.4089794 , 0.65503537, 0.75607993, 0.76069127, 0.86737802,\n",
       "       0.88406329, 0.44369755, 0.7157497 , 0.86283098, 0.51308805])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate the cross-entropy error\n",
    "def cross_entropy(T, Y):\n",
    "    E = 0\n",
    "    for i in range(len(T)):\n",
    "        if T[i] == 1:\n",
    "            E -= np.log(Y[i])\n",
    "        else:\n",
    "            E -= np.log(1 - Y[i])\n",
    "    return E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.18449741994076\n",
      "weight for 0 iteration is [1.19695117 4.90536621 4.856356  ]\n",
      "(100,)\n",
      "____________\n",
      "1.1120310062604726\n",
      "weight for 1 iteration is [1.26377397 4.86055112 4.87641137]\n",
      "(100,)\n",
      "____________\n",
      "1.0444861089172024\n",
      "weight for 2 iteration is [1.32822466 4.81734673 4.89579375]\n",
      "(100,)\n",
      "____________\n",
      "0.9816902614540176\n",
      "weight for 3 iteration is [1.39031682 4.77574767 4.9145082 ]\n",
      "(100,)\n",
      "____________\n",
      "0.9234400902338126\n",
      "weight for 4 iteration is [1.45007913 4.73573841 4.9325641 ]\n",
      "(100,)\n",
      "____________\n",
      "0.8695089811845138\n",
      "weight for 5 iteration is [1.50755356 4.69729448 4.94997464]\n",
      "(100,)\n",
      "____________\n",
      "0.8196545686823292\n",
      "weight for 6 iteration is [1.56279329 4.66038387 4.96675624]\n",
      "(100,)\n",
      "____________\n",
      "0.773625653583338\n",
      "weight for 7 iteration is [1.61586062 4.62496842 4.98292786]\n",
      "(100,)\n",
      "____________\n",
      "0.7311682821944305\n",
      "weight for 8 iteration is [1.66682488 4.59100524 4.99851048]\n",
      "(100,)\n",
      "____________\n",
      "0.6920308397999164\n",
      "weight for 9 iteration is [1.71576055 4.55844796 5.01352648]\n",
      "(100,)\n",
      "____________\n"
     ]
    }
   ],
   "source": [
    "learning_rate = 0.1\n",
    "for i in range(10):\n",
    "    if i % 1 == 0:\n",
    "        print(cross_entropy(T, Y))\n",
    "\n",
    "    # gradient descent weight udpate\n",
    "    w += learning_rate * Xb.T.dot(T - Y)\n",
    "    print(\"weight for\", i, \"iteration is\", w)\n",
    "\n",
    "    # recalculate Y\n",
    "    Y = sigmoid(Xb.dot(w))\n",
    "    print(Y.shape)\n",
    "    print(\"____________\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Final w: [1.71576055 4.55844796 5.01352648]\n"
     ]
    }
   ],
   "source": [
    "print(\"Final w:\", w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the data and separating line\n",
    "plt.scatter(X[:,0], X[:,1], c=T, s=100, alpha=0.5)\n",
    "x_axis = np.linspace(-6, 6, 100)\n",
    "y_axis = -(w[0] + x_axis*w[1]) / w[2]\n",
    "plt.plot(x_axis, y_axis)\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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}