CH08-Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 回归的一般方法\n",
    "#### （1）收集数据：可以使用任何方法收集数据\n",
    "#### （2）准备数据：回归需要数值型数据，标称型数据将被转换成二值型数据\n",
    "#### （3）分析数据： 绘出数据的可视化二维图将有助于对数据做出理解和分析，在采用缩减法求得新回归系数之后，可以将新拟合线绘再图上作为对比 \n",
    "#### （4）训练算法：找到回归系数\n",
    "#### （5）测试算法：使用$R^2$ 或者预测值和数据的拟合度，来分析模型的效果\n",
    "#### （6）使用算法：使用回归，可以在给定输入的时候预测出一个数值，这是对分类方法的提升，因为这样可以预测连续型数据而不仅仅是离散的类别标签"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 程序清单8-1 标准回归函数和数据导入函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "def loadDataSet(fileName):    \n",
    "    numFeat = len(open(fileName).readline().split('\\t')) - 1 #特征值个数\n",
    "    dataMat = []; labelMat = []\n",
    "    fr = open(fileName)\n",
    "    for line in fr.readlines():\n",
    "        lineArr =[]\n",
    "        curLine = line.strip().split('\\t')\n",
    "        for i in range(numFeat):\n",
    "            lineArr.append(float(curLine[i]))\n",
    "        dataMat.append(lineArr)\n",
    "        labelMat.append(float(curLine[-1]))\n",
    "    return dataMat,labelMat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def standRegres(xArr,yArr):\n",
    "    xMat = mat(xArr);yMat = mat(yArr).T #xMat:200*2, yMat:1*200\n",
    "    xTx = xMat.T*xMat #xTx:2*2\n",
    "    #print(xTx)\n",
    "    if linalg.det(xTx) == 0.0:  # 判断行列式是否为0 linalg.det()计算行列式，，需要判断矩阵行列式不为零，否则不能直接求逆。\n",
    "        print(\"This matrix is singular,cannot do inverse\") #这个矩阵是奇异的，不能做逆矩阵\n",
    "        return\n",
    "    ws = xTx.I * (xMat.T * yMat)  #xTx.I,矩阵的逆矩阵，也可以写成 ws = linalg.solve(xTx,xMat.T * yMat)\n",
    "    #np.linalg.inv()：矩阵求逆\n",
    "    #np.linalg.det()：矩阵求行列式（标量）\n",
    "    #solve函数可以求解多元一次方程组\n",
    "    return ws \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xArr,yArr = loadDataSet('ex0.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 2)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#print(xArr)\n",
    "shape(xArr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200,)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#print(yArr)\n",
    "shape(yArr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ws=standRegres(xArr,yArr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3.00774324]\n",
      " [ 1.69532264]]\n"
     ]
    }
   ],
   "source": [
    "print(ws)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "xMat = mat(xArr)\n",
    "#print(xMat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "yMat = mat(yArr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "yHat = xMat * ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x93cea20>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt #--绘图\n",
    "fig=plt.figure()\n",
    "ax=fig.add_subplot(111)\n",
    "#print(xMat[:,1].flatten())  #flatten是numpy.ndarray.flatten的一个函数，即返回一个一维数组。\n",
    "#print(yMat.A[0])\n",
    "#print(yMat.T[:,0].flatten().A[0])\n",
    "ax.scatter(xMat[:,1].flatten().A[0],yMat.T[:,0].flatten().A[0]) #绘--原始数据\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x5a3a9b0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xCopy = xMat.copy()\n",
    "xCopy.sort(0) #将点按照feature2升序排列,all featrue1=1.0\n",
    "#print(xCopy)\n",
    "yHat = xCopy * ws\n",
    "ax.plot(xCopy[:,1],yHat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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dMb2HBX3To1XXnmDBM1tZ8Q8/I0/uR1Mgh0M1DTHPtZJMYxKzoG96rFVb9nNv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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5a3a9e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "yHat = xMat * ws\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.98647356],\n",
       "       [ 0.98647356,  1.        ]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corrcoef(yHat.T,yMat) #numpy的corrcoef (yEstimate , yActual) 来计算预测值和真实值的相关性。yHat和yMat的相关系数是0.98"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### 局部加权线性回归（Locally Weighted Linear Regression,LWLR）\n",
    "#### 给待预测点附近的每个点赋予一定的权重，该算法解出回归系数w的形式如下：\n",
    "#### &emsp;&emsp;&emsp;&emsp; $ \\hat{\\omega}=（X^{T}WX）^{-1}X^{T}Wy $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### LWLR 使用“核”（与支持向量机中的核类似）来对附近点赋予更高的权重。最常用高斯核，对用权重如下：\n",
    "#### &emsp;&emsp;&emsp;&emsp; $ \\omega (i,i)=exp\\left ( \\frac{\\left | x^{^{(i)}}-x \\right |}{-2k^{^{2}}} \\right )$\n",
    "#### k=0.5 时，大部分的数据都用于训练回归模型，k=0.01,仅有很少数的局部点被用于训练回归模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 程序清单8-2 局部加权线性回归函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def lwlr(testPoint,xArr,yArr,k=1.0):\n",
    "    xMat = mat(xArr);yMat=mat(yArr).T\n",
    "    m = shape(xMat)[0]  #200 行\n",
    "    weights = mat(eye((m))) #创建1对角阵\n",
    "    for j in range(m):\n",
    "        diffMat = testPoint - xMat[j,:]\n",
    "        weights[j,j] = exp(diffMat*diffMat.T/(-2.0*k**2)) #权重大小以指数级衰减\n",
    "    xTx = xMat.T * (weights * xMat)\n",
    "    if linalg.det(xTx) == 0.0:  # 判断行列式是否为0 linalg.det()计算行列式，，需要判断矩阵行列式不为零，否则不能直接求逆。\n",
    "        print(\"This matrix is singular,cannot do inverse\") #这个矩阵是奇异的，不能做逆矩阵\n",
    "        return\n",
    "    ws = xTx.I * (xMat.T * (weights*yMat))\n",
    "    return testPoint * ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def lwlrTest(testArr,xArr,yArr,k=1.0):\n",
    "    m = shape(testArr)[0]\n",
    "    yHat = zeros(m)\n",
    "    for i in range(m):\n",
    "        yHat[i] = lwlr(testArr[i],xArr,yArr,k)\n",
    "    return yHat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 0.067732]\n",
      "[[ 3.12204471]]\n"
     ]
    }
   ],
   "source": [
    "lwlr(xArr[0],xArr,yArr,1.0)  # 对单点进行估计\n",
    "print(xArr[0])\n",
    "print(lwlr(xArr[0],xArr,yArr,1.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.176513"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yArr[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3.20175729]]\n"
     ]
    }
   ],
   "source": [
    "print(lwlr(xArr[0],xArr,yArr,0.001)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "yHat = lwlrTest(xArr,xArr,yArr,0.003) #k = 0.003"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true,
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "xMat = mat(xArr)\n",
    "srtInd = xMat[:,1].argsort(0) #rgsort函数返回的是数组值从小到大的索引值, #等价于argsort(xMat[:,1],0)\n",
    "#print(srtInd)\n",
    "xSort = xMat[srtInd][:,0,:] #200*2 #等价于xMat[srtInd.flatten().A[0]] \n",
    "#print(xSort)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dFbNARKYAMcaYecBTwKciMgHrxdV7bRdilXIoi8Xw9OzNnM7M5ftHr6Fdw6E8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\n8TsXTOjh4fYPVSyml//OV0t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      "text/plain": [
       "<matplotlib.figure.Figure at 0x9429b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt #--绘图\n",
    "fig=plt.figure()\n",
    "ax=fig.add_subplot(111)\n",
    "ax.plot(xSort[:,1],yHat[srtInd]) #绘--预测数据\n",
    "ax.scatter(xMat[:,1].flatten().A[0],mat(yArr).T.flatten().A[0],s=2,c='red')#绘--原始数据\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "yHat = lwlrTest(xArr,xArr,yArr,0.01)#k = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xMat = mat(xArr)\n",
    "srtInd = xMat[:,1].argsort(0) #rgsort函数返回的是数组值从小到大的索引值, #等价于argsort(xMat[:,1],0)\n",
    "#print(srtInd)\n",
    "xSort = xMat[srtInd][:,0,:] #200*2 #等价于xMat[srtInd.flatten().A[0]] \n",
    "#print(xSort)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v+v4JqhqrqrHR0dGnGLIpE3fJ2eGAjAzo3BkdOZID2bnk5uW7b1/OF1t3Z2bz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\nGOsS0gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x946d240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt #--绘图\n",
    "fig=plt.figure()\n",
    "ax=fig.add_subplot(111)\n",
    "ax.plot(xSort[:,1],yHat[srtInd]) #绘--预测数据\n",
    "ax.scatter(xMat[:,1].flatten().A[0],mat(yArr).T.flatten().A[0],s=2,c='red')#绘--原始数据\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "yHat = lwlrTest(xArr,xArr,yArr,1.0)#k = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xMat = mat(xArr)\n",
    "srtInd = xMat[:,1].argsort(0) #rgsort函数返回的是数组值从小到大的索引值, #等价于argsort(xMat[:,1],0)\n",
    "#print(srtInd)\n",
    "xSort = xMat[srtInd][:,0,:] #200*2 #等价于xMat[srtInd.flatten().A[0]] \n",
    "#print(xSort)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WziO/1POf+lz/Nnu9nvzmuzPrAwX4YMepXdvZJiamiE7cmLLFgr5xxz8gB2uB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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x941e4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt #--绘图\n",
    "fig=plt.figure()\n",
    "ax=fig.add_subplot(111)\n",
    "ax.plot(xSort[:,1],yHat[srtInd]) #绘--预测数据\n",
    "ax.scatter(xMat[:,1].flatten().A[0],mat(yArr).T.flatten().A[0],s=2,c='red')#绘--原始数据\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 预测鲍鱼年龄"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rssError(yArr,yHatArr):\n",
    "    return((yArr-yHatArr)**2).sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "abX,abY = loadDataSet('abalone.txt')\n",
    "yHat01 = lwlrTest(abX[0:99],abX[0:99],abY[0:99],0.1)\n",
    "yHat1 = lwlrTest(abX[0:99],abX[0:99],abY[0:99],1)\n",
    "yHat10 = lwlrTest(abX[0:99],abX[0:99],abY[0:99],10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "56.825235689728842"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rssError(abY[0:99],yHat01.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "429.89056187006514"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rssError(abY[0:99],yHat1.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "549.11817088264513"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rssError(abY[0:99],yHat10.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "yHat01 = lwlrTest(abX[100:199],abX[0:99],abY[0:99],0.1)\n",
    "yHat1 = lwlrTest(abX[100:199],abX[0:99],abY[0:99],1)\n",
    "yHat10 = lwlrTest(abX[100:199],abX[0:99],abY[0:99],10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "41317.161723642595"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rssError(abY[100:199],yHat01.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "573.52614418976702"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rssError(abY[100:199],yHat1.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "517.57119053875977"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rssError(abY[100:199],yHat10.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "518.63631532496379"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ws = standRegres(abX[0:99],abY[0:99])\n",
    "yHat = mat(abX[100:199])*ws\n",
    "rssError(abY[100:199],yHat.T.A) # .A将矩阵转化为数组"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 岭回归使用了单位矩阵乘以常量$\\lambda $,其中单位矩阵I，可以看到值1贯穿整个对角线，其余元素全是0，形象地在0构成的平面上有一天1组成的岭，回归系数计算公式\n",
    "#### &emsp;&emsp;&emsp;&emsp; $ \\hat{\\omega}=（X^{T}X+\\lambda I）^{-1}X^{T}y $\n",
    "#### 岭回归最先用来处理特征数多于样本的情况，现在也用于再估计总加入偏差，从而得到更好的估计，这里通过引入$\\lambda $来限制所有$\\omega$之和，通过引入惩罚项，能够减少不重要的参数，这个技术在统计学中也叫做缩减（shrinkage）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 程序清单8-3 岭回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def ridgeRegres(xMat,yMat,lam = 0.2):\n",
    "    xTx = xMat.T*xMat #xTx:2*2\n",
    "    denom = xTx + eye(shape(xMat)[1])*lam    \n",
    "    if linalg.det(xTx) == 0.0:  \n",
    "        print(\"This matrix is singular,cannot do inverse\") \n",
    "        return\n",
    "    ws = denom.I * (xMat.T * yMat)\n",
    "    return ws "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def ridgeTest(xArr,yArr):\n",
    "    xMat = mat(xArr);yMat=mat(yArr).T\n",
    "    yMean = mean(yMat,0)  #数据标准化\n",
    "    yMat = yMat - yMean\n",
    "    xMeans = mean(xMat,0)\n",
    "    xVar = var(xMat,0)\n",
    "    xMat = (xMat-xMeans)/xVar#所有特征减去各自的均值并除以方差\n",
    "    numTestPts = 30#取30个不同的lambda调用函数,30个不同的lambda值进行测试，选最优\n",
    "    wMat = zeros((numTestPts,shape(xMat)[1]))\n",
    "    for i in range(numTestPts):\n",
    "        ws = ridgeRegres(xMat,yMat,exp(i-10))\n",
    "        wMat[i,:] = ws.T\n",
    "    return wMat\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ridgeWeights = ridgeTest(abX,abY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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APRN3pKoPAg9C8gvfyyqNejDUdVkvNTNoyi1+k7xe9cx1kzb6nxnGlzRO7+pc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\nAfr/AfEvICh2KzpGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x951b8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    " #缩减效果图\n",
    "import matplotlib.pyplot as plt\n",
    "fig=plt.figure()\n",
    "ax=fig.add_subplot(111)\n",
    "ax.plot(ridgeWeights)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 前向逐步回归算法的伪代码\n",
    "####  数据标准化，使其分布满足0均值和单位方差\n",
    "####  在每轮迭代过程中：\n",
    "####  &emsp;&emsp;设置当前最小误差lowestError为正无穷：\n",
    "#### &emsp;&emsp; 对每个特征：\n",
    "#### &emsp;&emsp; &emsp;&emsp; 增大或缩小：\n",
    "#### &emsp;&emsp; &emsp;&emsp;&emsp;&emsp; 改变一个系数得到一个新的W\n",
    "#### &emsp;&emsp; &emsp;&emsp;&emsp;&emsp; 计算新W小的误差\n",
    "#### &emsp;&emsp; &emsp;&emsp;&emsp;&emsp; 如果误差Error小于当前最小误差lowestError：设置Wbest等于当前的W\n",
    "#### &emsp;&emsp; 如果所有向量都没被优化，增加迭代数目，继续下一次循环"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 程序清单8-4 前向逐步线性回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def regularize(xMat):#regularize 标准化\n",
    "    inMat = xMat.copy()\n",
    "    inMeans= mean(inMat,0)\n",
    "    inVar = var(inMat,0)\n",
    "    inMat = (inMat - inMeans)/inVar\n",
    "    return inMat\n",
    "\n",
    "def stageWise(xArr,yArr,eps = 0.01,numIt=100):\n",
    "    xMat = mat(xArr);yMat=mat(yArr).T\n",
    "    yMean = mean(yMat,0)  #数据标准化\n",
    "    yMat = yMat - yMean\n",
    "    xMat = regularize(xMat)\n",
    "    m,n = shape(xMat)\n",
    "    returnMat = zeros((numIt,n))\n",
    "    ws = zeros((n,1))\n",
    "    wsTest = ws.copy()\n",
    "    wsMax = ws.copy()\n",
    "    for i in range(numIt):\n",
    "        print(ws.T)\n",
    "        lowestError = inf;\n",
    "        for j in range(n):\n",
    "            for sign in [-1,1]:\n",
    "                wsTest = ws.copy()\n",
    "                wsTest[j]+=eps*sign\n",
    "                yTest = xMat*wsTest\n",
    "                rssE = rssError(yMat.A,yTest.A)\n",
    "                if rssE < lowestError:\n",
    "                    lowestError = rssE\n",
    "                    wsMax = wsTest\n",
    "        ws = wsMax.copy()\n",
    "        returnMat[i,:] = ws.T\n",
    "    return returnMat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xArr, yArr = loadDataSet('abalone.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "#stageWeights=stageWise(xArr,yArr,0.001,5000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Z7mtGa4GZ4W9ruvt7ZXs6j37zQuxz2BqXya5Cm3QDInZgH3Ax0ARsAT5tjNkV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9578358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "fig=plt.figure()\n",
    "ax=fig.add_subplot(111)\n",
    "ax.plot(stageWeights)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 用回归法预测乐高套装的价格\n",
    "#### （1）收集数据：用Google Shopping的API收集数据\n",
    "#### （2）准备数据：返回的JSON数据中抽取价格\n",
    "#### （3）分析数据： 可视化并观察数据\n",
    "#### （4）训练算法：构建不同的模型，采用逐步线性回归和直接的线性回归模型\n",
    "#### （5）测试算法：使用交叉验证测试不同的模型，来分析哪个效果最好\n",
    "#### （6）使用算法：这次练习的目标就是生成数据模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "#原文中通过Google提供的API来抓取价格，但由于现在访问不了Google,所以，直接通过文本给的html文件直接读取价格信息。然后进一步进行分析预测。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 程序清单8-5 购物信息的获取函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "from bs4 import BeautifulSoup\n",
    "import numpy as np\n",
    "import random\n",
    "def scrapePage(retX, retY, inFile, yr, numPce, origPrc):\n",
    "    # 打开并读取HTML文件\n",
    "    with open(inFile, encoding='utf-8') as f:\n",
    "        html = f.read()\n",
    "        soup = BeautifulSoup(html)\n",
    "        i = 1\n",
    "        # 根据HTML页面结构进行解析\n",
    "        currentRow = soup.find_all('table', r = \"%d\" % i)\n",
    "    while(len(currentRow) != 0):\n",
    "        currentRow = soup.find_all('table', r = \"%d\" % i)\n",
    "        title = currentRow[0].find_all('a')[1].text\n",
    "        lwrTitle = title.lower()\n",
    "        # 查找是否有全新标签\n",
    "        if (lwrTitle.find('new') > -1) or (lwrTitle.find('nisb') > -1):\n",
    "            newFlag = 1.0\n",
    "        else:\n",
    "            newFlag = 0.0\n",
    "        # 查找是否已经标志出售，我们只收集已出售的数据\n",
    "        soldUnicde = currentRow[0].find_all('td')[3].find_all('span')\n",
    "        if len(soldUnicde) == 0:\n",
    "            print(\"商品 #%d 没有出售\" % i)\n",
    "        else:\n",
    "            # 解析页面获取当前价格\n",
    "            soldPrice = currentRow[0].find_all('td')[4]\n",
    "            priceStr = soldPrice.text\n",
    "            priceStr = priceStr.replace('$','')\n",
    "            priceStr = priceStr.replace(',','')\n",
    "            if len(soldPrice) > 1:\n",
    "                priceStr = priceStr.replace('Free shipping', '')\n",
    "            sellingPrice = float(priceStr)\n",
    "            # 去掉不完整的套装价格\n",
    "            if  sellingPrice > origPrc * 0.5:\n",
    "                print(\"%d\\t%d\\t%d\\t%f\\t%f\" % (yr, numPce, newFlag, origPrc, sellingPrice))\n",
    "                retX.append([yr, numPce, newFlag, origPrc])\n",
    "                retY.append(sellingPrice)\n",
    "        i += 1\n",
    "        currentRow = soup.find_all('table', r = \"%d\" % i)\n",
    "     \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "#分别抓取各网页数据\n",
    "def setDataCollect(retX, retY):\n",
    "    scrapePage(retX, retY, 'lego8288.html', 2006, 800, 49.99)             \n",
    "    scrapePage(retX, retY, 'lego10030.html', 2002, 3096, 269.99)          \n",
    "    scrapePage(retX, retY, 'lego10179.html', 2007, 5195, 499.99)             \n",
    "    scrapePage(retX, retY, 'lego10181.html', 2007, 3428, 199.99)               \n",
    "    scrapePage(retX, retY, 'lego10189.html', 2008, 5922, 299.99)                \n",
    "    scrapePage(retX, retY, 'lego10196.html', 2009, 3263, 249.99)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\Anaconda3\\lib\\site-packages\\bs4\\__init__.py:181: UserWarning: No parser was explicitly specified, so I'm using the best available HTML parser for this system (\"lxml\"). This usually isn't a problem, but if you run this code on another system, or in a different virtual environment, it may use a different parser and behave differently.\n",
      "\n",
      "The code that caused this warning is on line 193 of the file E:\\Anaconda3\\lib\\runpy.py. To get rid of this warning, change code that looks like this:\n",
      "\n",
      " BeautifulSoup(YOUR_MARKUP})\n",
      "\n",
      "to this:\n",
      "\n",
      " BeautifulSoup(YOUR_MARKUP, \"lxml\")\n",
      "\n",
      "  markup_type=markup_type))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2006\t800\t0\t49.990000\t85.000000\n",
      "2006\t800\t0\t49.990000\t102.500000\n",
      "2006\t800\t0\t49.990000\t77.000000\n",
      "商品 #4 没有出售\n",
      "2006\t800\t0\t49.990000\t162.500000\n",
      "2002\t3096\t0\t269.990000\t699.990000\n",
      "2002\t3096\t0\t269.990000\t602.000000\n",
      "2002\t3096\t0\t269.990000\t515.000000\n",
      "2002\t3096\t0\t269.990000\t510.000000\n",
      "2002\t3096\t0\t269.990000\t375.000000\n",
      "2002\t3096\t1\t269.990000\t1050.000000\n",
      "2002\t3096\t0\t269.990000\t740.000000\n",
      "2002\t3096\t1\t269.990000\t759.000000\n",
      "2002\t3096\t0\t269.990000\t730.000000\n",
      "2002\t3096\t1\t269.990000\t750.000000\n",
      "商品 #11 没有出售\n",
      "2007\t5195\t0\t499.990000\t910.000000\n",
      "2007\t5195\t1\t499.990000\t1199.990000\n",
      "2007\t5195\t0\t499.990000\t811.880000\n",
      "商品 #4 没有出售\n",
      "2007\t5195\t0\t499.990000\t1324.790000\n",
      "2007\t5195\t1\t499.990000\t850.000000\n",
      "2007\t5195\t1\t499.990000\t800.000000\n",
      "2007\t5195\t0\t499.990000\t810.000000\n",
      "2007\t5195\t1\t499.990000\t1075.000000\n",
      "2007\t5195\t0\t499.990000\t1050.000000\n",
      "2007\t5195\t1\t499.990000\t1199.990000\n",
      "2007\t5195\t0\t499.990000\t1342.310000\n",
      "2007\t5195\t1\t499.990000\t1000.000000\n",
      "2007\t5195\t0\t499.990000\t1780.000000\n",
      "2007\t5195\t0\t499.990000\t750.000000\n",
      "商品 #16 没有出售\n",
      "2007\t5195\t0\t499.990000\t2204.990000\n",
      "商品 #18 没有出售\n",
      "2007\t5195\t1\t499.990000\t925.000000\n",
      "2007\t5195\t0\t499.990000\t860.000000\n",
      "商品 #21 没有出售\n",
      "商品 #22 没有出售\n",
      "2007\t5195\t1\t499.990000\t1199.990000\n",
      "2007\t5195\t1\t499.990000\t1099.990000\n",
      "2007\t5195\t1\t499.990000\t1149.990000\n",
      "2007\t5195\t1\t499.990000\t800.000000\n",
      "2007\t5195\t1\t499.990000\t850.000000\n",
      "2007\t3428\t0\t199.990000\t469.950000\n",
      "2007\t3428\t0\t199.990000\t479.000000\n",
      "2007\t3428\t0\t199.990000\t299.990000\n",
      "2007\t3428\t0\t199.990000\t369.000000\n",
      "2007\t3428\t1\t199.990000\t424.950000\n",
      "2007\t3428\t1\t199.990000\t380.000000\n",
      "2007\t3428\t0\t199.990000\t305.000000\n",
      "2008\t5922\t1\t299.990000\t530.000000\n",
      "商品 #2 没有出售\n",
      "2008\t5922\t1\t299.990000\t599.950000\n",
      "2008\t5922\t0\t299.990000\t510.000000\n",
      "2008\t5922\t0\t299.990000\t423.000000\n",
      "商品 #6 没有出售\n",
      "商品 #7 没有出售\n",
      "2008\t5922\t1\t299.990000\t599.990000\n",
      "商品 #9 没有出售\n",
      "2008\t5922\t1\t299.990000\t589.990000\n",
      "2008\t5922\t1\t299.990000\t569.990000\n",
      "2008\t5922\t1\t299.990000\t529.990000\n",
      "2008\t5922\t0\t299.990000\t500.000000\n",
      "2008\t5922\t1\t299.990000\t549.950000\n",
      "2008\t5922\t0\t299.990000\t300.000000\n",
      "商品 #16 没有出售\n",
      "2009\t3263\t1\t249.990000\t380.000000\n",
      "2009\t3263\t1\t249.990000\t399.000000\n",
      "2009\t3263\t1\t249.990000\t427.990000\n",
      "2009\t3263\t0\t249.990000\t360.000000\n",
      "商品 #5 没有出售\n",
      "商品 #6 没有出售\n",
      "2009\t3263\t1\t249.990000\t399.000000\n",
      "2009\t3263\t1\t249.990000\t399.950000\n",
      "2009\t3263\t1\t249.990000\t499.990000\n",
      "商品 #10 没有出售\n",
      "2009\t3263\t0\t249.990000\t399.950000\n",
      "商品 #12 没有出售\n",
      "2009\t3263\t1\t249.990000\t331.510000\n"
     ]
    }
   ],
   "source": [
    "lgX = [];lgY=[]\n",
    "setDataCollect(lgX,lgY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(63, 4)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "shape(lgX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "#print(lgX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lgX1 = mat(ones((63,5)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgX1[:,1:5] = mat(lgX)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2006, 800, 0.0, 49.99]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgX[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[  1.00000000e+00,   2.00600000e+03,   8.00000000e+02,\n",
       "           0.00000000e+00,   4.99900000e+01]])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgX1[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ws = standRegres(lgX1,lgY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[  5.53199701e+04],\n",
       "        [ -2.75928219e+01],\n",
       "        [ -2.68392234e-02],\n",
       "        [ -1.12208481e+01],\n",
       "        [  2.57604055e+00]])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 76.07418847]])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgX1[0]*ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[  5.53199701e+04],\n",
       "        [ -2.75928219e+01],\n",
       "        [ -2.68392234e-02],\n",
       "        [ -1.12208481e+01],\n",
       "        [  2.57604055e+00]])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 431.17797665]])"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgX1[-1]*ws"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "matrix([[ 516.20733099]])"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgX1[43]*ws"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 程序清单8-6 交叉验证测试岭回归"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def crossValidation(xArr,yArr,numVal = 10):\n",
    "    m = len(yArr)\n",
    "    indexList = list(range(m))  #代码这里要修改\n",
    "    #创建numVal*30的误差矩阵\n",
    "    ##30的由来：ridgeTest()使用了30个不同的lambda值来创建不同的回归系数，即numTestPts = 30\n",
    "    errorMat = zeros((numVal,30))\n",
    "    for i in range(numVal):\n",
    "        #创建训练集和测试集容器\n",
    "        trainX = [];trainY = []\n",
    "        testX = [];testY =[]\n",
    "         #打乱索引顺序，实现随机选取训练集和测试集数据点\n",
    "        random.shuffle(indexList)\n",
    "        #数据分为训练集和测试集，#90%训练+10%测试\n",
    "        for j in range(m):\n",
    "            if j < m*0.9:\n",
    "                trainX.append(xArr[indexList[j]])\n",
    "                trainY.append(yArr[indexList[j]])\n",
    "            else:\n",
    "                testX.append(xArr[indexList[j]])\n",
    "                testY.append(yArr[indexList[j]])\n",
    "        wMat = ridgeTest(trainX,trainY)#获得30组ws向量\n",
    "        for k in range(30):\n",
    "            #用训练时的参数将测试数据标准化\n",
    "            matTestX = mat(testX);\n",
    "            matTrainX = mat(trainX)\n",
    "            meanTrain = mean(matTrainX,0)\n",
    "            varTrain = var(matTrainX,0)\n",
    "            matTestX = (matTestX - meanTrain)/varTrain\n",
    "            yEst = matTestX * mat(wMat[k,:]).T +mean(trainY)\n",
    "            errorMat[i,k]=rssError(yEst.T.A,array(testY))\n",
    "    #计算不同岭回归ws下errorMat的平均值，观察平均性能  \n",
    "    #meanErrors:1*30矩阵\n",
    "    meanErrors=mean(errorMat,0)\n",
    "    minMean = float(min(meanErrors))\n",
    "     #nonzero(meanErrors==minMean)返回的是误差最小的索引，因此bestWeights为误差最小的那个w向量\n",
    "    bestWeights = wMat[nonzero(meanErrors == minMean)]\n",
    "     #岭回归使用了数据标准化，而standRegres没有，为了比较可视化，因此需要将数据还原\n",
    "    #标准化后 Xreg = (x-meanX)/var(x)，预测y=Xreg*w+meanY\n",
    "    #因此，利用未标准化的x来计算y= x*w/var(x) - meanX*w/var(x) +meanY\n",
    "    #其中unReg=w/var\n",
    "    xMat = mat(xArr)\n",
    "    yMat = mat(yArr).T\n",
    "    meanX = mean(xMat,0)\n",
    "    varX = var(xMat,0)\n",
    "    unReg = bestWeights / varX\n",
    "    #数据还原\n",
    "    print(\"the best model from Ridge Regression is:\\n\",unReg)\n",
    "     #特别注意这里的sum函数，一定是np.sum,因为一般的sum只能对list求和，而这里的参数是matrix\n",
    "    print(\"with constant term:\",-1*sum(multiply(meanX,unReg))+mean(yMat))\n",
    "          "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the best model from Ridge Regression is:\n",
      " [[ -3.34922409e+01   4.90836452e-04   1.90316935e+01   2.08853435e+00]]\n",
      "with constant term: 67188.4053238\n"
     ]
    }
   ],
   "source": [
    "crossValidation(lgX,lgY,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -1.45288906e+02,  -8.39360442e+03,  -3.28682450e+00,\n",
       "          4.42362406e+04],\n",
       "       [ -1.46649725e+02,  -1.89952152e+03,  -2.80638599e+00,\n",
       "          4.27891633e+04],\n",
       "       [ -1.44450432e+02,   8.55488076e+02,  -1.35089285e+00,\n",
       "          4.00885735e+04],\n",
       "       [ -1.37402474e+02,   1.64217093e+03,   1.95840783e+00,\n",
       "          3.44932120e+04],\n",
       "       [ -1.24750588e+02,   1.44326171e+03,   7.62540167e+00,\n",
       "          2.50647592e+04],\n",
       "       [ -1.10234679e+02,   8.81842164e+02,   1.40617304e+01,\n",
       "          1.43874420e+04],\n",
       "       [ -9.96484167e+01,   4.17805568e+02,   1.87140361e+01,\n",
       "          6.66770425e+03],\n",
       "       [ -9.40345090e+01,   1.71289137e+02,   2.10844952e+01,\n",
       "          2.71206176e+03],\n",
       "       [ -9.11400659e+01,   6.57287394e+01,   2.20487105e+01,\n",
       "          1.03800465e+03],\n",
       "       [ -8.86246985e+01,   2.45452725e+01,   2.23181664e+01,\n",
       "          3.87564774e+02],\n",
       "       [ -8.41447674e+01,   9.05861459e+00,   2.21495534e+01,\n",
       "          1.43313895e+02],\n",
       "       [ -7.44804291e+01,   3.31863501e+00,   2.14607512e+01,\n",
       "          5.27810178e+01],\n",
       "       [ -5.68008473e+01,   1.20770663e+00,   2.00168153e+01,\n",
       "          1.93999701e+01],\n",
       "       [ -3.43546503e+01,   4.38238026e-01,   1.77836684e+01,\n",
       "          7.12719906e+00],\n",
       "       [ -1.62951276e+01,   1.59882766e-01,   1.48514658e+01,\n",
       "          2.62234165e+00],\n",
       "       [ -6.48291858e+00,   5.89025383e-02,   1.09847950e+01,\n",
       "          9.67404902e-01],\n",
       "       [ -2.35268585e+00,   2.18391027e-02,   6.61152257e+00,\n",
       "          3.57478187e-01],\n",
       "       [ -8.35001919e-01,   8.09519290e-03,   3.19552087e+00,\n",
       "          1.32007993e-01],\n",
       "       [ -2.99711902e-01,   2.99108326e-03,   1.33043325e+00,\n",
       "          4.86659524e-02],\n",
       "       [ -1.08982743e-01,   1.10249682e-03,   5.14449554e-01,\n",
       "          1.79199150e-02],\n",
       "       [ -3.99038878e-02,   4.05898142e-04,   1.92885670e-01,\n",
       "          6.59479857e-03],\n",
       "       [ -1.46534283e-02,   1.49365062e-04,   7.14631760e-02,\n",
       "          2.42642878e-03],\n",
       "       [ -5.38707897e-03,   5.49542829e-05,   2.63587872e-02,\n",
       "          8.92679468e-04],\n",
       "       [ -1.98130399e-03,   2.02173589e-05,   9.70622185e-03,\n",
       "          3.28404700e-04],\n",
       "       [ -7.28814363e-04,   7.43766021e-06,   3.57198872e-03,\n",
       "          1.20814188e-04],\n",
       "       [ -2.68106796e-04,   2.73617711e-06,   1.31423307e-03,\n",
       "          4.44451712e-05],\n",
       "       [ -9.86297565e-05,   1.00658531e-06,   4.83502591e-04,\n",
       "          1.63504803e-05],\n",
       "       [ -3.62836944e-05,   3.70302314e-07,   1.77873811e-04,\n",
       "          6.01500768e-06],\n",
       "       [ -1.33480028e-05,   1.36226645e-07,   6.54365445e-05,\n",
       "          2.21279795e-06],\n",
       "       [ -4.91045279e-06,   5.01149871e-08,   2.40728171e-05,\n",
       "          8.14042912e-07]])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ridgeTest(lgX,lgY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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