regression.py

  1. from numpy import *
  3. def loadDataSet(fileName):      #general function to parse tab -delimited floats
  4.     numFeat = len(open(fileName).readline().split('\t')) - 1 #get number of fields 
  5.     dataMat = []; labelMat = []
  6.     fr = open(fileName)
  7.     for line in fr.readlines():
  8.         lineArr =[]
  9.         curLine = line.strip().split('\t')
  10.         for i in range(numFeat):
  11.             lineArr.append(float(curLine[i]))
  12.         dataMat.append(lineArr)
  13.         labelMat.append(float(curLine[-1]))
  14.     return dataMat,labelMat
  16. def standRegres(xArr,yArr):
  17.     xMat = mat(xArr); yMat = mat(yArr).T
  18.     xTx = xMat.T*xMat
  19.     if linalg.det(xTx) == 0.0:
  20.         print("This matrix is singular, cannot do inverse")
  21.         return
  22.     ws = xTx.I * (xMat.T*yMat)
  23.     return ws

image.png
image.png
image.png

局部加权线性回归

（根据数据来局部调整预测）

  1. def lwlr(testPoint,xArr,yArr,k=1.0):
  2.     xMat = mat(xArr); yMat = mat(yArr).T
  3.     m = shape(xMat)[0]
  4.     weights = mat(eye((m)))
  5.     for j in range(m):                      #next 2 lines create weights matrix
  6.         diffMat = testPoint - xMat[j,:]     #
  7.         weights[j,j] = exp(diffMat*diffMat.T/(-2.0*k**2))
  8.     xTx = xMat.T * (weights * xMat)
  9.     if linalg.det(xTx) == 0.0:
  10.         print("This matrix is singular, cannot do inverse")
  11.         return
  12.     ws = xTx.I * (xMat.T * (weights * yMat))
  13.     return testPoint * ws
  15. def lwlrTest(testArr,xArr,yArr,k=1.0):  #loops over all the data points and applies lwlr to each one
  16.     m = shape(testArr)[0]
  17.     yHat = zeros(m)
  18.     for i in range(m):
  19.         yHat[i] = lwlr(testArr[i],xArr,yArr,k)
  20.     return yHat

image.png

缩减系数来理解数据

当特征大于样本数量，则无法再计算，因为此时矩阵为非满秩矩阵，计算逆会出现问题

岭回归

通过加入对角线为1其余为0的单位矩阵的系数倍数使得矩阵非奇异。
能够减少不重要的参数。

  1. def ridgeRegres(xMat,yMat,lam=0.2):
  2.     xTx = xMat.T*xMat
  3.     denom = xTx + eye(shape(xMat)[1])*lam
  4.     if linalg.det(denom) == 0.0:
  5.         print("This matrix is singular, cannot do inverse")
  6.         return
  7.     ws = denom.I * (xMat.T*yMat)
  8.     return ws
  10. def ridgeTest(xArr,yArr):
  11.     xMat = mat(xArr); yMat=mat(yArr).T
  12.     yMean = mean(yMat,0)
  13.     yMat = yMat - yMean     #to eliminate X0 take mean off of Y
  14.     #regularize X's
  15.     xMeans = mean(xMat,0)   #calc mean then subtract it off
  16.     xVar = var(xMat,0)      #calc variance of Xi then divide by it
  17.     xMat = (xMat - xMeans)/xVar
  18.     numTestPts = 30
  19.     wMat = zeros((numTestPts,shape(xMat)[1]))
  20.     for i in range(numTestPts):
  21.         ws = ridgeRegres(xMat,yMat,exp(i-10))
  22.         wMat[i,:]=ws.T
  23.     return wMat

image.png
image.png

前向逐步线性回归

  1. def stageWise(xArr,yArr,eps=0.01,numIt=100):
  2.     xMat = mat(xArr); yMat=mat(yArr).T
  3.     yMean = mean(yMat,0)
  4.     yMat = yMat - yMean     #can also regularize ys but will get smaller coef
  5.     xMat = regularize(xMat)
  6.     m,n=shape(xMat)
  7.     returnMat = zeros((numIt,n)) #testing code remove
  8.     ws = zeros((n,1)); wsTest = ws.copy(); wsMax = ws.copy()
  9.     for i in range(numIt):
  10.         print(ws.T)
  11.         lowestError = inf; 
  12.         for j in range(n):
  13.             for sign in [-1,1]:
  14.                 wsTest = ws.copy()
  15.                 wsTest[j] += eps*sign
  16.                 yTest = xMat*wsTest
  17.                 rssE = rssError(yMat.A,yTest.A)
  18.                 if rssE < lowestError:
  19.                     lowestError = rssE
  20.                     wsMax = wsTest
  21.         ws = wsMax.copy()
  22.         returnMat[i,:]=ws.T
  23.     return returnMat

image.png

权衡偏差和方差

示例：预测乐高玩具套装的价格

获取数据

  1. from time import sleep
  2. import json
  3. import urllib.request
  4. def searchForSet(retX, retY, setNum, yr, numPce, origPrc):
  5.     sleep(10)
  6.     myAPIstr = 'AIzaSyD2cR2KFyx12hXu6PFU-wrWot3NXvko8vY'
  7.     searchURL = 'https://www.googleapis.com/shopping/search/v1/public/products?key=%s&country=US&q=lego+%d&alt=json' % (myAPIstr, setNum)
  8.     pg = urllib.request.urlopen(searchURL)
  9.     retDict = json.loads(pg.read())
  10.     for i in range(len(retDict['items'])):
  11.         try:
  12.             currItem = retDict['items'][i]
  13.             if currItem['product']['condition'] == 'new':
  14.                 newFlag = 1
  15.             else: newFlag = 0
  16.             listOfInv = currItem['product']['inventories']
  17.             for item in listOfInv:
  18.                 sellingPrice = item['price']
  19.                 if  sellingPrice > origPrc * 0.5:
  20.                     print("%d\t%d\t%d\t%f\t%f" % (yr,numPce,newFlag,origPrc, sellingPrice))
  21.                     retX.append([yr, numPce, newFlag, origPrc])
  22.                     retY.append(sellingPrice)
  23.         except: print('problem with item %d' % i)
  25. def setDataCollect(retX, retY):
  26.     searchForSet(retX, retY, 8288, 2006, 800, 49.99)
  27.     searchForSet(retX, retY, 10030, 2002, 3096, 269.99)
  28.     searchForSet(retX, retY, 10179, 2007, 5195, 499.99)
  29.     searchForSet(retX, retY, 10181, 2007, 3428, 199.99)
  30.     searchForSet(retX, retY, 10189, 2008, 5922, 299.99)
  31.     searchForSet(retX, retY, 10196, 2009, 3263, 249.99)