机器学习实战-回归

from numpy import *
import matplotlib.pyplot as plt

---

def loadDataSet(filename):
    numFeat = len(open(filename).readline().split('\t')) - 1
    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

---

#最小二乘法
def standRegres(xArr, yArr):
    xMat = mat(xArr); yMat = mat(yArr).T
    xTx = xMat.T *xMat
    if linalg.det(xTx) == 0.0:
        print('This matrix is singular, cannot do inverse')
        return
    ws = xTx.I * (xMat.T * yMat)
    return ws

---

#局部加权线性回归
def lwlr(testPoint, xArr, yArr, k = 1.0):
    xMat = mat(xArr); yMat = mat(yArr).T
    m = shape(xMat)[0]
    weights = mat(eye(m))
    for j in range(m):
        diffMat = testPoint - xMat[j, :]
        weights[j,j] = exp(diffMat*diffMat.T/(-2.0 * k ** 2))
    xTx = xMat.T * (weights * xMat)
    if linalg.det(xTx) == 0.0:
        print('This matrix is singular, cannot do inverse')
        return
    ws = xTx.I * (xMat.T * (weights * yMat))
    return testPoint * ws

def lwlrTest(testArr, xArr, yArr, k=1.0):
    m = shape(testArr)[0]
    yHat = zeros(m)
    for i in range(m):
        yHat[i] = lwlr(testArr[i], xArr, yArr, k)
    return yHat

---

#预测的值与真实的值的方差
def rssError(yArr, yHatArr):
    return ((yArr-yHatArr)**2).sum()

---

#岭回归
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
    Xmeans = mean(xMat, 0)
    xVar = var(xMat, 0)
    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

def regularize(xMat):
    Xmeans = mean(xMat, 0)
    xVar = var(xMat, 0)
    xMat = (xMat - Xmeans) / xVar
    return xMat

---

#前向逐步回归
def stageWise(xArr, yArr, eps = 0.01, numIt = 100):
    xMat = mat(xArr); yMat = mat(yArr).T
    yMean = mean(yMat, 0)
    yMat = yMat - yMean
    xMat = regularize(xMat)
    m, n = shape(xMat)
    returnMat = zeros((numIt, n))
    ws = zeros((n,1)); wsTest = ws.copy(); wsMax = ws.copy()
    for i in range(numIt):
#       print(ws.T)
        lowestError = inf
        for j in range(n):
            for sign in [-1, 1]:
                wsTest = ws.copy()
                wsTest[j] += eps * sign
                yTest = xMat * wsTest
                rssE = rssError(yMat.A, yTest.A)
                if rssE < lowestError:
                    lowestError = rssE
                    wsMax = wsTest
        ws = wsMax.copy()
        returnMat[i, :] = ws.T
    return returnMat


abX, abY = loadDataSet('abalone.txt')
ridgeWeights = stageWise(abX, abY, 0.005, 1000)
fig = plt.figure()
ax = fig.add_subplot(111)

ax.plot(ridgeWeights)
plt.show()