对数几率回归.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 对数几率回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 考虑二分类问题，对于二分类问题只有0和1，因此需要将结果映射为0和1即可，常用的函数为sigmoid函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import load_iris,make_classification\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sigmoid = lambda x:1./(1+np.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x113ae8438>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ys9GpLMrda9x9ZezxIeADotcjzhS9vs06uBTY7O49PUDyhLj7q8DeDrMTyaKk\nfx7TNtyPoauLcXc00j+6GlQtMDKFNV0E1Ln7pi6WO/BHM3svdh3Z3nB77M/ih7v4MzDR7ZgqXyXa\nw+tMb2yvRH7+QLeRmU0AZgNvd7L4gtj7+7yZnd5bNdH9exP079VCuu5kBbXNEsmipG+3Xr1Adkdm\n9kdgVCeL/s7dn03WetzdzaxHuwUlWOONHLvXfqG7V5vZCOBFM/sw9j98jx2rLuB+4G6iH8S7iQ4Z\nffVE1peMuo5sLzP7O6Ad+E0XL5P07ZVpzGwg8BTwTXc/2GHxSmC8uzfEvk95BpjSS6Wl7Xtj0cuA\nXg3c1cniILfZUSeSRccr0HB398t68LSELsYN1JnZaHevif1ZuCsVNZpZLnAdcPYxXqM6dr/LzP6N\n6J9gJ/SBSHTbmdkDwHOdLEp0Oya1LjP7MvBZ4FKPDTZ28hpJ316dSNqF35PNzPKIBvtv3P3pjsvj\nw97dl5nZL82s2N1Tfg6VBN6bQLZZzJXASnev67ggyG1GYlmU9O2WicMyS4GFZlZgZhOJ/u/7Thft\nboo9vglI2l8CHVwGfOjuVZ0tNLMBZjboyGOiXyq+31nbZOkwxnltF+tL5MLnya5rHvBd4Gp3b+yi\nTW9tr7S88Hvs+5uHgA/c/addtBkVa4eZzSH6Od6Tyrpi60rkven1bRany7+gg9pmMYlkUfI/j6n+\n9rinN6KhVAW0AHXA8rhlf0f0m+UNwJVx8x8ktmcNMAx4CdgE/BEYmqI6HwFu7TBvDLAs9ngS0W++\n1wDlRIcnUr3tfg2sA9bGfkFGd6wrNj2f6N4Ym3uprgqi44qrY7dFQW6vzn5+4NYj7yfRPT7uiy1f\nR9xeWyms6UKiw2lr47bT/A513RbbNmuIfjF9QarrOtZ7E/Q2i613ANGwHhI3r9e3GdH/XGqAtlh+\nfa2rLEr151FHqIqIZKFMHJYREZFuKNxFRLKQwl1EJAsp3EVEspDCXUQkCyncRUSykMJdRCQLKdxF\nRLLQfwAQyl4UsTc3ggAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113be8eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-10,10,10000)\n",
    "y = sigmoid(x)\n",
    "plt.plot(x,y)\n",
    "plt.scatter(0,sigmoid(0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 上述就是sigmoid函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 读取数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = load_iris()\n",
    "X = data.data[data.target != 0]\n",
    "y = data.target[data.target != 0]\n",
    "y[y == 1] = 0\n",
    "y[y == 2] = 1\n",
    "Y = y.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[ 7. ,  3.2,  4.7,  1.4],\n",
       "        [ 6.4,  3.2,  4.5,  1.5],\n",
       "        [ 6.9,  3.1,  4.9,  1.5],\n",
       "        [ 5.5,  2.3,  4. ,  1.3],\n",
       "        [ 6.5,  2.8,  4.6,  1.5]]), array([[0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0],\n",
       "        [0]]))"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:5],Y[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 定义对数几率回归的梯度下降解法\n",
    "\n",
    "* 根据西瓜书中的说法，逻辑回归是不怎么准确的，应该使用对数几率回归，简称对数回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class LogisticRegression(object):\n",
    "    def __init__(self):\n",
    "        self.sigmoid = lambda x:1./(1+np.exp(-x))\n",
    "    def fit(self, X, y):\n",
    "        self.w = np.random.randn(X.shape[1],1)\n",
    "        for _ in range(1000):\n",
    "            y_pred = self.sigmoid(X @ self.w)\n",
    "            self.w -= 0.01 * X.T @ (y_pred - y) #梯度下降\n",
    "            print(np.mean(0.5*(y_pred- y)**2))\n",
    "    def predict(self,X):\n",
    "        y_pred = np.round(self.sigmoid(X.dot(self.w)))\n",
    "        return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lr = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "0.249999999846\n",
      "0.249999874152\n",
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      "0.249973057264\n",
      "0.249999999984\n",
      "0.233347132686\n",
      "0.249999999999\n",
      "0.0654220716453\n",
      "0.133225655915\n",
      "0.249999992943\n",
      "0.24998527144\n",
      "0.249999999914\n",
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     ]
    }
   ],
   "source": [
    "lr.fit(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = lr.predict(X)\n",
    "accuracy = np.sum(Y == y_pred, axis=0) / len(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predict acc 0.96\n"
     ]
    }
   ],
   "source": [
    "print('predict acc %s'%accuracy[0])"
   ]
  }
 ],
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   "language": "python",
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