sample/logistic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn import datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "iris = datasets.load_iris()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = iris.data[:, :2]\n",
    "y = (iris.target != 0) * 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Wa/MTnEYjWa/KwO6qnx8wQgxeBwAA6IHB6wAAADkjsAIAAAiEwAoAACAQAisAAIBACKw6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\nAiGwAgAACOT/A1flvRpe7BsWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12cb3f99b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[y == 0][:, 0], X[y == 0][:, 1], color='b', label='0')\n",
    "plt.scatter(X[y == 1][:, 0], X[y == 1][:, 1], color='r', label='1')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class LogisticRegression:\n",
    "    def __init__(self, lr=0.01, num_iter=100000, fit_intercept=True, verbose=False):\n",
    "        self.lr = lr\n",
    "        self.num_iter = num_iter\n",
    "        self.fit_intercept = fit_intercept\n",
    "        self.verbose = verbose\n",
    "    \n",
    "    def __add_intercept(self, X):\n",
    "        intercept = np.ones((X.shape[0], 1))\n",
    "        return np.concatenate((intercept, X), axis=1)\n",
    "    \n",
    "    def __sigmoid(self, z):\n",
    "        return 1 / (1 + np.exp(-z))\n",
    "    def __loss(self, h, y):\n",
    "        return (-y * np.log(h) - (1 - y) * np.log(1 - h)).mean()\n",
    "    \n",
    "    def fit(self, X, y):\n",
    "        if self.fit_intercept:\n",
    "            X = self.__add_intercept(X)\n",
    "        \n",
    "        # weights initialization\n",
    "        self.theta = np.zeros(X.shape[1])\n",
    "        \n",
    "        for i in range(self.num_iter):\n",
    "            z = np.dot(X, self.theta)\n",
    "            h = self.__sigmoid(z)\n",
    "            gradient = np.dot(X.T, (h - y)) / y.size\n",
    "            self.theta -= self.lr * gradient\n",
    "            \n",
    "            z = np.dot(X, self.theta)\n",
    "            h = self.__sigmoid(z)\n",
    "            loss = self.__loss(h, y)\n",
    "                \n",
    "            if(self.verbose ==True and i % 10000 == 0):\n",
    "                print(f'loss: {loss} \\t')\n",
    "    \n",
    "    def predict_prob(self, X):\n",
    "        if self.fit_intercept:\n",
    "            X = self.__add_intercept(X)\n",
    "    \n",
    "        return self.__sigmoid(np.dot(X, self.theta))\n",
    "    \n",
    "    def predict(self, X):\n",
    "        return self.predict_prob(X).round()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "model = LogisticRegression(lr=0.1, num_iter=300000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 14.3 s, sys: 12 ms, total: 14.3 s\n",
      "Wall time: 14.3 s\n"
     ]
    }
   ],
   "source": [
    "%time model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = model.predict(X)\n",
    "(preds == y).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-25.96818124,  12.56179068, -13.44549335])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PPfWUbrvtNj333HP67W9/63Y4AAAHkVgBCVJSUqIRI0bopZde0sqVK9WyZUu3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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f12c754be80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 6))\n",
    "plt.scatter(X[y == 0][:, 0], X[y == 0][:, 1], color='b', label='0')\n",
    "plt.scatter(X[y == 1][:, 0], X[y == 1][:, 1], color='r', label='1')\n",
    "plt.legend()\n",
    "x1_min, x1_max = X[:,0].min(), X[:,0].max(),\n",
    "x2_min, x2_max = X[:,1].min(), X[:,1].max(),\n",
    "xx1, xx2 = np.meshgrid(np.linspace(x1_min, x1_max), np.linspace(x2_min, x2_max))\n",
    "grid = np.c_[xx1.ravel(), xx2.ravel()]\n",
    "probs = model.predict_prob(grid).reshape(xx1.shape)\n",
    "plt.contour(xx1, xx2, probs, [0.5], linewidths=1, colors='black');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LogisticRegression(C=1e20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
      "Wall time: 855 µs\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1e+20, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%time model.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "preds = model.predict(X)\n",
    "(preds == y).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([-80.62725491]), array([[ 31.61988897, -28.31500665]]))"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_, model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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