線性回歸(Linear Regression).ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  線性回歸(Linear Regression)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 先引入我們需要的packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os \n",
    "import numpy as np\n",
    "import random\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 產生100組資料"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 分別對y和x建立一個長度100的向量\n",
    "x=np.zeros(100)\n",
    "y=np.zeros(100)\n",
    "# 這裡我們設立我們的斜率為m截距為b\n",
    "# d為資料點的離散程度\n",
    "m=25\n",
    "b=20\n",
    "d=1\n",
    "# 這裡我們設x=1~100\n",
    "# y=mx+b加上一個-1~1的隨機值\n",
    "for i in range(0,100):\n",
    "    x[i]=i/100\n",
    "    y[i]=m*x[i]+b+d*random.uniform(-1,1)\n",
    "# 設定我們輸出圖片的大小\n",
    "plt.rcParams[\"figure.figsize\"] = (18,18)\n",
    "#畫出圈圈的點，bo：b代表藍色、o代表圈圈、marksize為大小\n",
    "plt.plot(x,y,\"bo\",markersize=10)\n",
    "# 設定x和y軸座標的字體大小\n",
    "plt.xticks(fontsize=30)\n",
    "plt.yticks(fontsize=30)\n",
    "#畫出來\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 這裡進行線性回歸"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25.01894989754612\n",
      "19.98672904783176\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 初始畫我們的權重\n",
    "w=np.zeros(2)\n",
    "# 分別算出x、y、x^2、x*y的平均值\n",
    "x_mean=np.mean(x)\n",
    "y_mean=np.mean(y)\n",
    "x2_mean=np.mean(x**2)\n",
    "xy_mean=np.mean(x*y)\n",
    "# 設我們的學習參數為1\n",
    "a=1\n",
    "# 我們讓他跑100次迴圈\n",
    "T=100\n",
    "for t in range(0,T):\n",
    "    #更新我們權重w\n",
    "    w[0]=w[0]-a*(w[0]+w[1]*x_mean-y_mean)\n",
    "    w[1]=w[1]-a*(w[0]*x_mean+w[1]*x2_mean-xy_mean)\n",
    "print(w[1])\n",
    "print(w[0])\n",
    "# 設定我們輸出圖片的大小\n",
    "plt.rcParams[\"figure.figsize\"] = (18,18)\n",
    "#畫出圈圈的點，bo：b代表藍色、o代表圈圈、marksize為大小\n",
    "plt.plot([0,1],[w[0],w[1]+w[0]],\"r-\",linewidth=6)\n",
    "plt.plot(x,y,\"bo\",markersize=10)\n",
    "# 設定x和y軸座標的字體大小\n",
    "plt.xticks(fontsize=30)\n",
    "plt.yticks(fontsize=30)\n",
    "#畫出來\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 梯度消失(Gradient Vanishing)\n",
    "##### 我們可以看到，當學習速度設很小的時候，同樣的步數下，會產生梯度消失，收斂的速度會非常慢"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.214960533447175\n",
      "5.719618471508153\n"
     ]
    }
   ],
   "source": [
    "w=np.zeros(2)\n",
    "x_mean=np.mean(x)\n",
    "y_mean=np.mean(y)\n",
    "x2_mean=np.mean(x**2)\n",
    "xy_mean=np.mean(x*y)\n",
    "a=0.002\n",
    "T=100\n",
    "for t in range(0,T):\n",
    "    w[0]=w[0]-a*(w[0]+w[1]*x_mean-y_mean)\n",
    "    w[1]=w[1]-a*(w[0]*x_mean+w[1]*x2_mean-xy_mean)\n",
    "print(w[1])\n",
    "print(w[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 梯度爆炸(Gradient Exploding)\n",
    "##### 我們可以看到，當學習速度設很大的時候，同樣的步數下，會產生梯度爆炸，我們的權重會衝到很大的值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-4.324156864266374e+275\n",
      "1.796399352357865e+274\n"
     ]
    }
   ],
   "source": [
    "w=np.zeros(2)\n",
    "x_mean=np.mean(x)\n",
    "y_mean=np.mean(y)\n",
    "x2_mean=np.mean(x**2)\n",
    "xy_mean=np.mean(x*y)\n",
    "a=50\n",
    "T=100\n",
    "for t in range(0,T):\n",
    "    w[0]=w[0]-a*(w[0]+w[1]*x_mean-y_mean)\n",
    "    w[1]=w[1]-a*(w[0]*x_mean+w[1]*x2_mean-xy_mean)\n",
    "print(w[1])\n",
    "print(w[0])"
   ]
  },
  {
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}