Logistic Regression from scratch.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import make_classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# set the dimensions\n",
    "N = 100\n",
    "D = 2\n",
    "K = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# set the initial weights\n",
    "W = np.random.randn(D,K)\n",
    "b = np.zeros(K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2, 1)\n",
      "(1,)\n",
      "[[0.]\n",
      " [0.]]\n",
      "[0.]\n"
     ]
    }
   ],
   "source": [
    "print(W.shape)\n",
    "print(b.shape)\n",
    "print(W)\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, t = make_classification(n_samples=N, n_features=D, n_redundant=0, n_informative=1, n_clusters_per_class=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100, 2)\n",
      "(100,)\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "print(t.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X1 = pd.DataFrame(X, columns=['f1', 'f2'])\n",
    "t1 = pd.DataFrame(t, columns=['target'])\n",
    "df = pd.concat([X1, t1], axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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u5oUXVK7Y2CA4cvRd/O6dKQDV8+4PPhc8Q3zwudes2/jjXMVUrSAW2A9dcUpwDxucXVjQ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\nPzfkZSKtZ0w5AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11181c320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df.loc[df['target']==0, 'f1'], df.loc[df['target']==0, 'f2'],\n",
    "           label = 't1')\n",
    "plt.scatter(df.loc[df['target']==1, 'f1'], df.loc[df['target']==1, 'f2'],\n",
    "            label = 't2')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Log reg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Z(X, W, b):\n",
    "    return np.dot(X, W) + b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z1 = Z(X, W, b)\n",
    "Z1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sig(Z):\n",
    "    return 1/(1+np.exp(-Z))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1)"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = sig(Z1)\n",
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def cost(t, y):\n",
    "    return -t.reshape(N,-1)*np.log(y)-(1-t.reshape(N,-1))*(1-np.log(y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 1)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost1 = cost(t, y)\n",
    "cost1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def error(cost):\n",
    "    return cost.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-47.61370563888012"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error1 = error(cost1)\n",
    "error1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial error: -47.61370563888012\n",
      "error: -47.61370563888012\n",
      "accuracy: 49\n",
      "error: -137.29577651122946\n",
      "accuracy: 94\n",
      "error: -167.8656621178128\n",
      "accuracy: 94\n",
      "error: -186.44720515814248\n",
      "accuracy: 94\n",
      "error: -199.68355477175592\n",
      "accuracy: 94\n",
      "error: -209.8611133518849\n",
      "accuracy: 94\n",
      "error: -218.04989146836598\n",
      "accuracy: 94\n",
      "error: -224.840212769165\n",
      "accuracy: 93\n",
      "error: -230.5936205772634\n",
      "accuracy: 92\n",
      "error: -235.5482448529621\n",
      "accuracy: 92\n",
      "error: -239.86958118128814\n",
      "accuracy: 92\n",
      "error: -243.67749504132277\n",
      "accuracy: 92\n",
      "error: -247.0616917825795\n",
      "accuracy: 92\n",
      "error: -250.09111192192609\n",
      "accuracy: 92\n",
      "error: -252.8199128171935\n",
      "accuracy: 92\n",
      "error: -255.29142837504563\n",
      "accuracy: 92\n",
      "error: -257.5408776193257\n",
      "accuracy: 92\n",
      "error: -259.5972699970772\n",
      "accuracy: 92\n",
      "error: -261.4847784190762\n",
      "accuracy: 92\n",
      "error: -263.22374981660613\n",
      "accuracy: 92\n",
      "error: -264.8314628520341\n",
      "accuracy: 93\n",
      "error: -266.3227054877766\n",
      "accuracy: 93\n",
      "error: -267.71022177341007\n",
      "accuracy: 93\n",
      "error: -269.0050620714186\n",
      "accuracy: 93\n",
      "error: -270.2168608966049\n",
      "accuracy: 93\n",
      "error: -271.35405973989555\n",
      "accuracy: 93\n",
      "error: -272.42408755172846\n",
      "accuracy: 93\n",
      "error: -273.4335082645823\n",
      "accuracy: 93\n",
      "error: -274.3881423851148\n",
      "accuracy: 93\n",
      "error: -275.2931679880967\n",
      "accuracy: 93\n",
      "error: -276.1532052004897\n",
      "accuracy: 93\n",
      "error: -276.972387341987\n",
      "accuracy: 93\n",
      "error: -277.75442119723397\n",
      "accuracy: 93\n",
      "error: -278.50263837156444\n",
      "accuracy: 93\n",
      "error: -279.2200392818894\n",
      "accuracy: 93\n",
      "error: -279.90933102563537\n",
      "accuracy: 93\n",
      "error: -280.57296013042014\n",
      "accuracy: 94\n",
      "error: -281.21314099881516\n",
      "accuracy: 94\n",
      "error: -281.8318807137614\n",
      "accuracy: 94\n",
      "error: -282.4310007518683\n",
      "accuracy: 94\n",
      "error: -283.012156057081\n",
      "accuracy: 94\n",
      "error: -283.5768518508625\n",
      "accuracy: 94\n",
      "error: -284.1264584931944\n",
      "accuracy: 95\n",
      "error: -284.662224658283\n",
      "accuracy: 95\n",
      "error: -285.1852890475809\n",
      "accuracy: 95\n",
      "error: -285.6966908287274\n",
      "accuracy: 95\n",
      "error: -286.19737896088935\n",
      "accuracy: 95\n",
      "error: -286.68822054360646\n",
      "accuracy: 95\n",
      "error: -287.17000830672697\n",
      "accuracy: 95\n",
      "error: -287.643467342662\n",
      "accuracy: 95\n",
      "error: -288.10926116840983\n",
      "accuracy: 95\n",
      "error: -288.56799719316183\n",
      "accuracy: 95\n",
      "error: -289.02023165742844\n",
      "accuracy: 95\n",
      "error: -289.46647410121267\n",
      "accuracy: 95\n",
      "error: -289.90719141157996\n",
      "accuracy: 95\n",
      "error: -290.34281149380416\n",
      "accuracy: 95\n",
      "error: -290.7737266049843\n",
      "accuracy: 95\n",
      "error: -291.2002963844374\n",
      "accuracy: 95\n",
      "error: -291.62285061123146\n",
      "accuracy: 95\n",
      "error: -292.0416917157731\n",
      "accuracy: 95\n",
      "error: -292.45709706937555\n",
      "accuracy: 95\n",
      "error: -292.86932107312003\n",
      "accuracy: 95\n",
      "error: -293.2785970650368\n",
      "accuracy: 95\n",
      "error: -293.685139062617\n",
      "accuracy: 95\n",
      "error: -294.08914335590214\n",
      "accuracy: 95\n",
      "error: -294.49078996483996\n",
      "accuracy: 95\n",
      "error: -294.89024397320946\n",
      "accuracy: 95\n",
      "error: -295.2876567502004\n",
      "accuracy: 95\n",
      "error: -295.68316706964197\n",
      "accuracy: 95\n",
      "error: -296.0769021359123\n",
      "accuracy: 95\n",
      "error: -296.4689785246922\n",
      "accuracy: 95\n",
      "error: -296.85950304596014\n",
      "accuracy: 95\n",
      "error: -297.2485735359353\n",
      "accuracy: 95\n",
      "error: -297.6362795840498\n",
      "accuracy: 95\n",
      "error: -298.022703200488\n",
      "accuracy: 95\n",
      "error: -298.40791942931367\n",
      "accuracy: 95\n",
      "error: -298.7919969117681\n",
      "accuracy: 95\n",
      "error: -299.174998403912\n",
      "accuracy: 95\n",
      "error: -299.5569812524134\n",
      "accuracy: 95\n",
      "error: -299.93799783194976\n",
      "accuracy: 95\n",
      "error: -300.31809594740025\n",
      "accuracy: 95\n",
      "error: -300.6973192037201\n",
      "accuracy: 96\n",
      "error: -301.0757073461475\n",
      "accuracy: 96\n",
      "error: -301.45329657316597\n",
      "accuracy: 96\n",
      "error: -301.83011982443855\n",
      "accuracy: 96\n",
      "error: -302.20620704574674\n",
      "accuracy: 96\n",
      "error: -302.58158543279717\n",
      "accuracy: 96\n",
      "error: -302.9562796555945\n",
      "accuracy: 96\n",
      "error: -303.33031206495576\n",
      "accuracy: 96\n",
      "error: -303.70370288259085\n",
      "accuracy: 96\n",
      "error: -304.0764703760734\n",
      "accuracy: 96\n",
      "error: -304.44863101990853\n",
      "accuracy: 96\n",
      "error: -304.82019964380567\n",
      "accuracy: 96\n",
      "error: -305.19118956918055\n",
      "accuracy: 96\n",
      "error: -305.561612734819\n",
      "accuracy: 96\n",
      "error: -305.93147981256703\n",
      "accuracy: 96\n",
      "error: -306.3008003138363\n",
      "accuracy: 96\n",
      "error: -306.66958268765404\n",
      "accuracy: 96\n",
      "error: -307.0378344109258\n",
      "accuracy: 96\n",
      "error: -307.4055620715287\n",
      "accuracy: 96\n",
      "error: -307.7727714447984\n",
      "accuracy: 96\n",
      "error: -308.13946756393324\n",
      "accuracy: 96\n",
      "error: -308.505654784795\n",
      "accuracy: 96\n",
      "error: -308.8713368455452\n",
      "accuracy: 96\n",
      "error: -309.2365169215283\n",
      "accuracy: 96\n",
      "error: -309.6011976757686\n",
      "accuracy: 96\n",
      "error: -309.96538130543433\n",
      "accuracy: 96\n",
      "error: -310.32906958457744\n",
      "accuracy: 96\n",
      "error: -310.6922639034468\n",
      "accuracy: 96\n",
      "error: -311.0549653046422\n",
      "accuracy: 96\n",
      "error: -311.41717451635634\n",
      "accuracy: 96\n",
      "error: -311.77889198293616\n",
      "accuracy: 96\n",
      "error: -312.1401178929677\n",
      "accuracy: 96\n",
      "error: -312.5008522050863\n",
      "accuracy: 96\n",
      "error: -312.8610946716849\n",
      "accuracy: 96\n",
      "error: -313.22084486068746\n",
      "accuracy: 96\n",
      "error: -313.58010217553965\n",
      "accuracy: 96\n",
      "error: -313.93886587355377\n",
      "accuracy: 96\n",
      "error: -314.2971350827413\n",
      "accuracy: 96\n",
      "error: -314.654908817249\n",
      "accuracy: 96\n",
      "error: -315.01218599150724\n",
      "accuracy: 96\n",
      "error: -315.36896543319483\n",
      "accuracy: 96\n",
      "error: -315.72524589511096\n",
      "accuracy: 96\n",
      "error: -316.0810260660401\n",
      "accuracy: 96\n",
      "error: -316.4363045806913\n",
      "accuracy: 96\n",
      "error: -316.79108002878155\n",
      "accuracy: 96\n",
      "error: -317.14535096333344\n",
      "accuracy: 96\n",
      "error: -317.4991159082475\n",
      "accuracy: 96\n",
      "error: -317.85237336520714\n",
      "accuracy: 96\n",
      "error: -318.2051218199692\n",
      "accuracy: 96\n",
      "error: -318.557359748087\n",
      "accuracy: 96\n",
      "error: -318.90908562011396\n",
      "accuracy: 96\n",
      "error: -319.2602979063263\n",
      "accuracy: 96\n",
      "error: -319.6109950810031\n",
      "accuracy: 96\n",
      "error: -319.96117562630343\n",
      "accuracy: 96\n",
      "error: -320.310838035766\n",
      "accuracy: 96\n",
      "error: -320.6599808174654\n",
      "accuracy: 96\n",
      "error: -321.0086024968544\n",
      "accuracy: 96\n",
      "error: -321.3567016193122\n",
      "accuracy: 96\n",
      "error: -321.7042767524271\n",
      "accuracy: 96\n",
      "error: -322.0513264880339\n",
      "accuracy: 96\n",
      "error: -322.3978494440237\n",
      "accuracy: 96\n",
      "error: -322.74384426594855\n",
      "accuracy: 96\n",
      "error: -323.0893096284343\n",
      "accuracy: 96\n",
      "error: -323.43424423641926\n",
      "accuracy: 96\n",
      "error: -323.7786468262331\n",
      "accuracy: 96\n",
      "error: -324.12251616652907\n",
      "accuracy: 96\n",
      "error: -324.4658510590811\n",
      "accuracy: 96\n",
      "error: -324.8086503394574\n",
      "accuracy: 96\n",
      "error: -325.15091287758304\n",
      "accuracy: 96\n"
     ]
    }
   ],
   "source": [
    "error_list = []\n",
    "acc_list = []\n",
    "W0_list = []\n",
    "W1_list = []\n",
    "b_list = []\n",
    "lr = 0.001\n",
    "print('initial error: {}'.format(error1))\n",
    "\n",
    "for e in range(15000):\n",
    "    \n",
    "    Z1 = Z(X, W, b)\n",
    "    y = sig(Z1)\n",
    "    cost1 = cost(t, y)\n",
    "    error1 = error(cost1)\n",
    "    \n",
    "    dw = np.dot(X.T,(y - t.reshape(N,-1)))\n",
    "    db = ((y - t.reshape(N,-1)).sum())/N\n",
    "    \n",
    "    W -= lr*dw\n",
    "    b -= lr*db\n",
    "    \n",
    "    acc_list.append(((np.round(y.T))==t).sum())\n",
    "    error_list.append(error1)\n",
    "    W0_list.append(list(W[0]))\n",
    "    W1_list.append(list(W[1]))\n",
    "    b_list.append(list(b))\n",
    "    \n",
    "    if e % 100 == 0:\n",
    "        print('error: {}'.format(error1))\n",
    "        print('accuracy: {}'.format(((np.round(y.T))==t).sum()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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37a2l1nrAHyZNxYLXX0zXSUou5MS5WZg1rIqh2KVpUbXWesCbp01D8dj/peskJb/VLnHi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\nOioAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1117e4940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ex1 = np.linspace(-3, 3, 100)\n",
    "ex2 = -(W[0]*ex1 + b)/W[1]\n",
    "\n",
    "plt.axes(xlim=(-3,3), ylim=(-3,3))\n",
    "plt.scatter(df.loc[df['target']==0, 'f1'], df.loc[df['target']==0, 'f2'],\n",
    "           label = 't1')\n",
    "plt.scatter(df.loc[df['target']==1, 'f1'], df.loc[df['target']==1, 'f2'],\n",
    "            label = 't2')\n",
    "plt.plot(ex1, ex2, color='r')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WWAtkAi8Bly3i5y8H3uwf5wHHgMuAvwU+6bd/Evgb//gyv8YsYI1fe9jvewG4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\nEBERFAYpjHeRAAAACUlEQVQiIgL8fxaPWH5i7R6RAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11181fa20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(error_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3AJ8HngG2Ai9m5n1NyTdJNzO9uk9mjgMvAid0Oe8f0jqjbUzGiFgKbMnM709a1Yh8h6sf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\nhIUuSYWw0CWpEBa6JBXi/wHDWUvmuFZcqgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110566080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(acc_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x111199cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(W0_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IhPuZgRQdvcOsXzon6FJERGZcZMJ9X0cfAJctUc9dRMIvMuG+v6MXgMuXqOcuIuEXmXDf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\nSAgp3EVEQkjhLiISQgp3EZEQ+v+ulzSuqwM03wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110ee8b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(W1_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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bw9TFBMAFp4N2zrU+z4F2mllimi6gXek02wJscc7N9e9/QcZjBSIimWZmdKiR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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110d535c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(b_list)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}