模型树

模型树是将叶节点设置为分段线性函数，具体代码如下：

def loadDataSet(fileName):      #general function to parse tab -delimited floats
    dataMat = []                #assume last column is target value
    fr = open(fileName)
    for line in fr.readlines():
        curLine = line.strip().split('\t')
        fltLine = map(float,curLine) #map all elements to float()
        dataMat.append(fltLine)
    return dataMat

def binSplitDataSet(dataSet, feature, value):
    mat0 = dataSet[nonzero(dataSet[:,feature] > value)[0],:][0]
    mat1 = dataSet[nonzero(dataSet[:,feature] <= value)[0],:][0]
    return mat0,mat1
def modelLeaf(dataSet):#create linear model and return coeficients
    ws,X,Y = linearSolve(dataSet)
    return ws


def modelErr(dataSet):
    ws,X,Y = linearSolve(dataSet)
    yHat = X * ws
    return sum(power(Y - yHat,2))

def chooseBestSplit(dataSet, leafType=regLeaf, errType=regErr, ops=(1,4)):
    tolS = ops[0]; tolN = ops[1]
    #if all the target variables are the same value: quit and return value
    if len(set(dataSet[:,-1].T.tolist()[0])) == 1: #exit cond 1
        return None, leafType(dataSet)
    m,n = shape(dataSet)
    #the choice of the best feature is driven by Reduction in RSS error from mean
    S = errType(dataSet)
    bestS = inf; bestIndex = 0; bestValue = 0
    for featIndex in range(n-1):
        for splitVal in set(dataSet[:,featIndex]):
            mat0, mat1 = binSplitDataSet(dataSet, featIndex, splitVal)
            if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN): continue
            newS = errType(mat0) + errType(mat1)
            if newS < bestS: 
                bestIndex = featIndex
                bestValue = splitVal
                bestS = newS
    #if the decrease (S-bestS) is less than a threshold don't do the split
    if (S - bestS) < tolS: 
        return None, leafType(dataSet) #exit cond 2
    mat0, mat1 = binSplitDataSet(dataSet, bestIndex, bestValue)
    if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN):  #exit cond 3
        return None, leafType(dataSet)
    return bestIndex,bestValue#returns the best feature to split on
                              #and the value used for that split

def createTree(dataSet, leafType=regLeaf, errType=regErr, ops=(1,4)):#assume dataSet is NumPy Mat so we can array filtering
    feat, val = chooseBestSplit(dataSet, leafType, errType, ops)#choose the best split
    if feat == None: return val #if the splitting hit a stop condition return val
    retTree = {}
    retTree['spInd'] = feat
    retTree['spVal'] = val
    lSet, rSet = binSplitDataSet(dataSet, feat, val)
    retTree['left'] = createTree(lSet, leafType, errType, ops)
    retTree['right'] = createTree(rSet, leafType, errType, ops)
    return retTree  

输出结果

>>> data=mat(regTrees.loadDataSet('C:\\Users\\WM\\Desktop\\python\\exp2.txt'))
>>> regTrees.createTree(data,regTrees.modelLeaf,regTrees.modelErr,(1,10))
{'spInd': 0, 'spVal': matrix([[ 0.285477]]), 'right': matrix([[ 3.46877936],
        [ 1.18521743]]), 'left': matrix([[  1.69855694e-03],
        [  1.19647739e+01]])}
>>> 

 每个节点的分割本质上也是为了使预测误差最小，如观察分割后的子集的方差，方差小意味着这个子集中的数据具有比较相近的目标值，因此可以用他们的均值作为预测值