gradientdescent.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 读取数据，载入所需要的库"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>population</th>\n",
       "      <th>profit</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>6.1101</td>\n",
       "      <td>17.5920</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.5277</td>\n",
       "      <td>9.1302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>8.5186</td>\n",
       "      <td>13.6620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>7.0032</td>\n",
       "      <td>11.8540</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.8598</td>\n",
       "      <td>6.8233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   population   profit\n",
       "0      6.1101  17.5920\n",
       "1      5.5277   9.1302\n",
       "2      8.5186  13.6620\n",
       "3      7.0032  11.8540\n",
       "4      5.8598   6.8233"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "path = r'data1.txt'\n",
    "data  = pd.read_csv(path, header=None, sep=\",\",names=['population','profit'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 对初始数据进行可视化操作"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x234ca55d518>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x234c8d30f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data.population, data.profit, c=\"DarkBlue\", alpha = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ML kernels---Univariable Linear Regression---Gradient Descent(简易版)\n",
    "$\\theta_{j}=\\theta_{j}-\\alpha \\frac{\\partial}{\\partial \\theta_{j}}J(\\theta_0 , \\theta_1)$ 其中j在0，1中取值\n",
    "此法适用于凸函数，凸函数必有全局最优解，不会令梯度下降法陷入到局部最优解中"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(length, x_list, y_list,steps,theta0,theta1,alpha):\n",
    "    sum1=0\n",
    "    sum2=0\n",
    "    for j in range(steps):\n",
    "        for i in range(length):\n",
    "            sum1+=x_list[i]*theta1+theta0-y_list[i]\n",
    "            sum2+=x_list[i]*(x_list[i]*theta1+theta0-y_list[i])\n",
    "        temp0 = theta0 - alpha/length*sum1\n",
    "        temp1 = theta1 - alpha/length*sum2\n",
    "        theta0 = temp0\n",
    "        theta1 = temp1\n",
    "    return theta0, theta1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上述编写的函数，要注意$\\theta_0 , \\theta_1$同时更新，每一次求偏导都是用到了全部的数据集"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "根据要求，我们设置学习速率$\\alpha=0.01$，学习次数steps=1500，$\\theta_0 , \\theta_1$的初始值均设置为0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-1.361798403450554 0.9315919943225802\n"
     ]
    }
   ],
   "source": [
    "x=data.iloc[:,0].values\n",
    "y=data.iloc[:,1].values\n",
    "a,b=gradientDescent(len(x),x,y,1500,0,0,0.01)\n",
    "print(a,b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x234cab56438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,a+b*x,color=\"green\")\n",
    "plt.scatter(x,y, c=\"DarkBlue\",alpha=1)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最终的可视化结果如上图所示，散点为数据集，直线为Prediction"
   ]
  },
  {
   "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}