经过对Logistic回归理论的学习,推导出取对数后的似然函数为

现在我们的目的是求一个向量,使得最大。其中

对这个似然函数求偏导后得到

根据梯度上升算法有

进一步得到

我们可以初始化向量为0,或者随机值,然后进行迭代达到指定的精度为止。

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" alt="" width="492" height="346" />

 def sigmoid(inX):
return 1.0/(1+exp(-inX))
 def gradAscent(dataMatIn, classLabels):
dataMatrix = mat(dataMatIn) #convert to NumPy matrix
labelMat = mat(classLabels).transpose() #convert to NumPy matrix
m,n = shape(dataMatrix)
alpha = 0.001
maxCycles = 500
weights = ones((n,1))
for k in range(maxCycles): #heavy on matrix operations
h = sigmoid(dataMatrix*weights) #matrix mult
error = (labelMat - h) #vector subtraction
weights = weights + alpha * dataMatrix.transpose()* error #matrix mult
return weights

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