前向逐步线性回归

加载数据集
数据标准化，使其分布满足0均值和单位方差。
初始回归系数全部设为1
在每轮迭代过程中：
    设置当前最小误差lowestError为正无穷
    对每个特征的权重系数：
        增大或者缩小一个步长
        计算新回归系数W下的误差
        如果误差小于当前最小误差:
            设置最佳回归系数 Wbest = W
返回最终的最佳回归系数Wbest

from numpy import *
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]))
    return dataMat,labelMat

def regularize(xMat):#regularize by columns
    inMat = xMat.copy()
    inMeans = mean(inMat,0)   #calc mean then subtract it off
    inVar = var(inMat,0)      #calc variance of Xi then divide by it
    inMat = (inMat - inMeans)/inVar
    return inMat
def rssError(yArr,yHatArr): #yArr and yHatArr both need to be arrays
    return ((yArr-yHatArr)**2).sum()
def stageWise(xArr,yArr,eps=0.01,numIt=100):
    xMat = mat(xArr)
    yMat=mat(yArr).T
    yMean = mean(yMat,0)
    yMat = yMat - yMean     #can also regularize ys but will get smaller coef
    xMat = regularize(xMat)
    m,n=shape(xMat)
    #returnMat = zeros((numIt,n)) #testing code remove
    #ws = zeros((n,1)) #初始所有权重为0
    ws = ones((n,1)) #初始所有权重为1
    #wsMax = ws.copy()
    Mat = zeros((numIt, n))
    for i in range(numIt):
        if i%1000 ==0 : #每迭代1000次，打印归回系数
            print ("第%d次迭代后回归系数为："%i,end ="")
            print(ws.T)
        lowestError = inf #初始误差设为正无穷大
        for j in range(n):
            for sign in [-1,1]: # 贪心算法，左右试探
                wsTest = ws.copy() # 初始化
                wsTest[j] += eps*sign #eps 为步长
                yTest = xMat*wsTest #预测值
                rssE = rssError(yMat.A,yTest.A)
                if rssE < lowestError:
                    lowestError = rssE
                    wsMax = wsTest
        ws = wsMax.copy()
        Mat[i,:]=ws.T
    return Mat
xArr,yArr = loadDataSet("abalone.txt")
numIt = 20000
Wmat = stageWise(xArr,yArr,eps=0.001, numIt=numIt)
print(Wmat.shape)
import matplotlib.pyplot as plt
n = Wmat.shape[1]#特征数，即回归系数个数
for i in range(n):
    plt.plot(arange(numIt), Wmat[:,i], label = "W(%s)"%i)
plt.legend(loc="upper right")
plt.title(r"前向逐步回归""\n基于数据集'abalone.txt'", fontsize=16)
plt.xlabel(r"迭代次数")
plt.grid(ls="--",lw =1)
plt.show()