2018/07/05/logistic-regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import log_loss\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((6, 1), (6,))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.array([1,2,3,4,5,6]).reshape(6,1)\n",
    "y = np.array([0,0,1,0,1,1])\n",
    "x.shape, y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = LogisticRegression().fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.28663014626267075, -0.5850076540365196)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slope = m.coef_[0][0]\n",
    "b = m.intercept_[0]\n",
    "slope,b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "colors = ListedColormap(['#FF0000', '#0000FF'])\n",
    "plt.scatter(x,y, c=y, cmap=colors);\n",
    "fx = slope*x+b\n",
    "plt.plot(x,fx, color='#ff33cc');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.55504603, -0.85342354],\n",
       "       [-0.68729075, -0.69903811],\n",
       "       [-0.84000405, -0.56512127],\n",
       "       [-1.0128086 , -0.45129567],\n",
       "       [-1.20456453, -0.35642145],\n",
       "       [-1.41353691, -0.27876369]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m.predict_log_proba(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x, fn):\n",
    "    return 1 / (1+np.exp(-fn(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: 1 p: 0.43 log(p): -0.85\n",
      "x: 2 p: 0.50 log(p): -0.70\n",
      "x: 3 p: 0.57 log(p): -0.57\n",
      "x: 4 p: 0.64 log(p): -0.45\n",
      "x: 5 p: 0.70 log(p): -0.36\n",
      "x: 6 p: 0.76 log(p): -0.28\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, 7):\n",
    "    p = sigmoid(i, lambda x: slope*x + b)\n",
    "    print(\"x: {} p: {:.2f} log(p): {:.2f}\".format(i, p, np.log(p)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, 0, 1, 1])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.42595416, 0.49706319, 0.56829123, 0.63680253, 0.70017747,\n",
       "       0.7567187 ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat = m.predict_proba(x)[:,1]\n",
    "y_hat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def my_log_loss(y, y_hat):\n",
    "    ll = (y*np.log(y_hat)) + ((1-y)*np.log(1-y_hat))\n",
    "    return -ll.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5759086317357319"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_loss(y, m.predict_proba(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5759086317357319"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_log_loss(y, y_hat)"
   ]
  },
  {
   "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
}