11 ML ridge regression

ridge regression(岭回归) 数据缩减(shrinkage)的一种方法。

from numpy import *
import matplotlib.pyplot as plt

def loadDataSet(fileName):      #general function to parse tab -delimited floats
    numFeat = len(open(fileName).readline().split('\t')) - 1 #get number of fields 
    dataMat = []
    labelMat = []

    fr = open(fileName)
    for line in fr.readlines():
        lineArr =[]
        curLine = line.strip().split('\t')
        for i in range(numFeat):
            lineArr.append(float(curLine[i]))
        dataMat.append(lineArr)
        labelMat.append(float(curLine[-1])) # last is label
    return dataMat,labelMat

def ridgeRegres(xMat,yMat,lam=0.2):
    xTx = xMat.T*xMat
    denom = xTx + eye(shape(xMat)[1])*lam
    if linalg.det(denom) == 0.0:
        print "This matrix is singular, cannot do inverse"
        return
    ws = denom.I * (xMat.T*yMat)
    return ws
    
def ridgeTest(xArr,yArr):
    xMat = mat(xArr);
    yMat = mat(yArr).T
    
    yMean = mean(yMat,0)
    yMat = yMat - yMean     #to eliminate X0 take mean off of Y

    #regularize X's
    xMeans = mean(xMat,0)   #calc mean then subtract it off
    xVar = var(xMat,0)      #calc variance of Xi then divide by it
    xMat = (xMat - xMeans)/xVar
    numTestPts = 30

    wMat = zeros((numTestPts,shape(xMat)[1]))
    for i in range(numTestPts):
        ws = ridgeRegres(xMat,yMat,exp(i-10))
        wMat[i,:]=ws.T
    return wMat

abX, abY = loadDataSet('abalone.txt')
ridgeWeights = ridgeTest(abX, abY)
print('ridgeWeights', ridgeWeights[0:5])

fig = plt.figure()
ax = fig.add_subplot(111)

ax.plot(ridgeWeights)
plt.show()

1.png