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使用SciPy进行逻辑回归

发布于2019-10-14 20:54 阅读(447) 评论(0) 点赞(14) 收藏(5)

我正在尝试使用SciPy fmin_bfgs函数在Python中编写逻辑回归，但遇到了一些问题。我编写了用于逻辑（S型）转换函数和成本函数的函数，这些函数都很好用（我使用了通过固定软件找到的参数向量的优化值来测试这些函数，并且这些函数匹配了）。我不确定我是否实现了渐变函数，但看起来很合理。

这是代码：

# purpose: logistic regression 
import numpy as np
import scipy.optimize

# prepare the data
data = np.loadtxt('data.csv', delimiter=',', skiprows=1)
vY = data[:, 0]
mX = data[:, 1:]
intercept = np.ones(mX.shape[0]).reshape(mX.shape[0], 1)
mX = np.concatenate((intercept, mX), axis = 1)
iK = mX.shape[1]
iN = mX.shape[0]

# logistic transformation
def logit(mX, vBeta):
    return((1/(1.0 + np.exp(-np.dot(mX, vBeta)))))

# test function call
vBeta0 = np.array([-.10296645, -.0332327, -.01209484, .44626211, .92554137, .53973828, 
    1.7993371, .7148045  ])
logit(mX, vBeta0)

# cost function
def logLikelihoodLogit(vBeta, mX, vY):
    return(-(np.sum(vY*np.log(logit(mX, vBeta)) + (1-vY)*(np.log(1-logit(mX, vBeta))))))
logLikelihoodLogit(vBeta0, mX, vY) # test function call

# gradient function
def likelihoodScore(vBeta, mX, vY):
    return(np.dot(mX.T, 
                  ((np.dot(mX, vBeta) - vY)/
                   np.dot(mX, vBeta)).reshape(iN, 1)).reshape(iK, 1))

likelihoodScore(vBeta0, mX, vY).shape # test function call

# optimize the function (without gradient)
optimLogit = scipy.optimize.fmin_bfgs(logLikelihoodLogit, 
                                  x0 = np.array([-.1, -.03, -.01, .44, .92, .53,
                                            1.8, .71]), 
                                  args = (mX, vY), gtol = 1e-3)

# optimize the function (with gradient)
optimLogit = scipy.optimize.fmin_bfgs(logLikelihoodLogit, 
                                  x0 = np.array([-.1, -.03, -.01, .44, .92, .53,
                                            1.8, .71]), fprime = likelihoodScore, 
                                  args = (mX, vY), gtol = 1e-3)

第一个优化（无梯度）以零除以很多东西结束。
第二个优化（带有梯度）以矩阵未对齐的错误结束，这可能意味着我已经知道将梯度返回错误的方式。

任何帮助，不胜感激。如果有人想尝试此操作，数据将包含在下面。

low,age,lwt,race,smoke,ptl,ht,ui
0,19,182,2,0,0,0,1
0,33,155,3,0,0,0,0
0,20,105,1,1,0,0,0
0,21,108,1,1,0,0,1
0,18,107,1,1,0,0,1
0,21,124,3,0,0,0,0
0,22,118,1,0,0,0,0
0,17,103,3,0,0,0,0
0,29,123,1,1,0,0,0
0,26,113,1,1,0,0,0
0,19,95,3,0,0,0,0
0,19,150,3,0,0,0,0
0,22,95,3,0,0,1,0
0,30,107,3,0,1,0,1
0,18,100,1,1,0,0,0
0,18,100,1,1,0,0,0
0,15,98,2,0,0,0,0
0,25,118,1,1,0,0,0
0,20,120,3,0,0,0,1
0,28,120,1,1,0,0,0
0,32,121,3,0,0,0,0
0,31,100,1,0,0,0,1
0,36,202,1,0,0,0,0
0,28,120,3,0,0,0,0
0,25,120,3,0,0,0,1
0,28,167,1,0,0,0,0
0,17,122,1,1,0,0,0
0,29,150,1,0,0,0,0
0,26,168,2,1,0,0,0
0,17,113,2,0,0,0,0
0,17,113,2,0,0,0,0
0,24,90,1,1,1,0,0
0,35,121,2,1,1,0,0
0,25,155,1,0,0,0,0
0,25,125,2,0,0,0,0
0,29,140,1,1,0,0,0
0,19,138,1,1,0,0,0
0,27,124,1,1,0,0,0
0,31,215,1,1,0,0,0
0,33,109,1,1,0,0,0
0,21,185,2,1,0,0,0
0,19,189,1,0,0,0,0
0,23,130,2,0,0,0,0
0,21,160,1,0,0,0,0
0,18,90,1,1,0,0,1
0,18,90,1,1,0,0,1
0,32,132,1,0,0,0,0
0,19,132,3,0,0,0,0
0,24,115,1,0,0,0,0
0,22,85,3,1,0,0,0
0,22,120,1,0,0,1,0
0,23,128,3,0,0,0,0
0,22,130,1,1,0,0,0
0,30,95,1,1,0,0,0
0,19,115,3,0,0,0,0
0,16,110,3,0,0,0,0
0,21,110,3,1,0,0,1
0,30,153,3,0,0,0,0
0,20,103,3,0,0,0,0
0,17,119,3,0,0,0,0
0,17,119,3,0,0,0,0
0,23,119,3,0,0,0,0
0,24,110,3,0,0,0,0
0,28,140,1,0,0,0,0
0,26,133,3,1,2,0,0
0,20,169,3,0,1,0,1
0,24,115,3,0,0,0,0
0,28,250,3,1,0,0,0
0,20,141,1,0,2,0,1
0,22,158,2,0,1,0,0
0,22,112,1,1,2,0,0
0,31,150,3,1,0,0,0
0,23,115,3,1,0,0,0
0,16,112,2,0,0,0,0
0,16,135,1,1,0,0,0
0,18,229,2,0,0,0,0
0,25,140,1,0,0,0,0
0,32,134,1,1,1,0,0
0,20,121,2,1,0,0,0
0,23,190,1,0,0,0,0
0,22,131,1,0,0,0,0
0,32,170,1,0,0,0,0
0,30,110,3,0,0,0,0
0,20,127,3,0,0,0,0
0,23,123,3,0,0,0,0
0,17,120,3,1,0,0,0
0,19,105,3,0,0,0,0
0,23,130,1,0,0,0,0
0,36,175,1,0,0,0,0
0,22,125,1,0,0,0,0
0,24,133,1,0,0,0,0
0,21,134,3,0,0,0,0
0,19,235,1,1,0,1,0
0,25,95,1,1,3,0,1
0,16,135,1,1,0,0,0
0,29,135,1,0,0,0,0
0,29,154,1,0,0,0,0
0,19,147,1,1,0,0,0
0,19,147,1,1,0,0,0
0,30,137,1,0,0,0,0
0,24,110,1,0,0,0,0
0,19,184,1,1,0,1,0
0,24,110,3,0,1,0,0
0,23,110,1,0,0,0,0
0,20,120,3,0,0,0,0
0,25,241,2,0,0,1,0
0,30,112,1,0,0,0,0
0,22,169,1,0,0,0,0
0,18,120,1,1,0,0,0
0,16,170,2,0,0,0,0
0,32,186,1,0,0,0,0
0,18,120,3,0,0,0,0
0,29,130,1,1,0,0,0
0,33,117,1,0,0,0,1
0,20,170,1,1,0,0,0
0,28,134,3,0,0,0,0
0,14,135,1,0,0,0,0
0,28,130,3,0,0,0,0
0,25,120,1,0,0,0,0
0,16,95,3,0,0,0,0
0,20,158,1,0,0,0,0
0,26,160,3,0,0,0,0
0,21,115,1,0,0,0,0
0,22,129,1,0,0,0,0
0,25,130,1,0,0,0,0
0,31,120,1,0,0,0,0
0,35,170,1,0,1,0,0
0,19,120,1,1,0,0,0
0,24,116,1,0,0,0,0
0,45,123,1,0,0,0,0
1,28,120,3,1,1,0,1
1,29,130,1,0,0,0,1
1,34,187,2,1,0,1,0
1,25,105,3,0,1,1,0
1,25,85,3,0,0,0,1
1,27,150,3,0,0,0,0
1,23,97,3,0,0,0,1
1,24,128,2,0,1,0,0
1,24,132,3,0,0,1,0
1,21,165,1,1,0,1,0
1,32,105,1,1,0,0,0
1,19,91,1,1,2,0,1
1,25,115,3,0,0,0,0
1,16,130,3,0,0,0,0
1,25,92,1,1,0,0,0
1,20,150,1,1,0,0,0
1,21,200,2,0,0,0,1
1,24,155,1,1,1,0,0
1,21,103,3,0,0,0,0
1,20,125,3,0,0,0,1
1,25,89,3,0,2,0,0
1,19,102,1,0,0,0,0
1,19,112,1,1,0,0,1
1,26,117,1,1,1,0,0
1,24,138,1,0,0,0,0
1,17,130,3,1,1,0,1
1,20,120,2,1,0,0,0
1,22,130,1,1,1,0,1
1,27,130,2,0,0,0,1
1,20,80,3,1,0,0,1
1,17,110,1,1,0,0,0
1,25,105,3,0,1,0,0
1,20,109,3,0,0,0,0
1,18,148,3,0,0,0,0
1,18,110,2,1,1,0,0
1,20,121,1,1,1,0,1
1,21,100,3,0,1,0,0
1,26,96,3,0,0,0,0
1,31,102,1,1,1,0,0
1,15,110,1,0,0,0,0
1,23,187,2,1,0,0,0
1,20,122,2,1,0,0,0
1,24,105,2,1,0,0,0
1,15,115,3,0,0,0,1
1,23,120,3,0,0,0,0
1,30,142,1,1,1,0,0
1,22,130,1,1,0,0,0
1,17,120,1,1,0,0,0
1,23,110,1,1,1,0,0
1,17,120,2,0,0,0,0
1,26,154,3,0,1,1,0
1,20,106,3,0,0,0,0
1,26,190,1,1,0,0,0
1,14,101,3,1,1,0,0
1,28,95,1,1,0,0,0
1,14,100,3,0,0,0,0
1,23,94,3,1,0,0,0
1,17,142,2,0,0,1,0
1,21,130,1,1,0,1,0

解决方案

这是我发回SciPy列表的答案，此问题在此交叉发布。感谢@tiago的回答。基本上，我重新设定了似然函数。此外，还添加了对check_grad函数的调用。

#=====================================================
# purpose: logistic regression 
import numpy as np
import scipy as sp
import scipy.optimize

import matplotlib as mpl
import os

# prepare the data
data = np.loadtxt('data.csv', delimiter=',', skiprows=1)
vY = data[:, 0]
mX = data[:, 1:]
# mX = (mX - np.mean(mX))/np.std(mX)  # standardize the data; if required

intercept = np.ones(mX.shape[0]).reshape(mX.shape[0], 1)
mX = np.concatenate((intercept, mX), axis = 1)
iK = mX.shape[1]
iN = mX.shape[0]

# logistic transformation
def logit(mX, vBeta):
    return((np.exp(np.dot(mX, vBeta))/(1.0 + np.exp(np.dot(mX, vBeta)))))

# test function call
vBeta0 = np.array([-.10296645, -.0332327, -.01209484, .44626211, .92554137, .53973828, 
    1.7993371, .7148045  ])
logit(mX, vBeta0)

# cost function
def logLikelihoodLogit(vBeta, mX, vY):
    return(-(np.sum(vY*np.log(logit(mX, vBeta)) + (1-vY)*(np.log(1-logit(mX, vBeta))))))
logLikelihoodLogit(vBeta0, mX, vY) # test function call

# different parametrization of the cost function
def logLikelihoodLogitVerbose(vBeta, mX, vY):
    return(-(np.sum(vY*(np.dot(mX, vBeta) - np.log((1.0 + np.exp(np.dot(mX, vBeta))))) +
                    (1-vY)*(-np.log((1.0 + np.exp(np.dot(mX, vBeta))))))))
logLikelihoodLogitVerbose(vBeta0, mX, vY)  # test function call

# gradient function
def likelihoodScore(vBeta, mX, vY):
    return(np.dot(mX.T, 
                  (logit(mX, vBeta) - vY)))
likelihoodScore(vBeta0, mX, vY).shape # test function call
sp.optimize.check_grad(logLikelihoodLogitVerbose, likelihoodScore, 
                       vBeta0, mX, vY)  # check that the analytical gradient is close to 
                                                # numerical gradient

# optimize the function (without gradient)
optimLogit = scipy.optimize.fmin_bfgs(logLikelihoodLogitVerbose, 
                                  x0 = np.array([-.1, -.03, -.01, .44, .92, .53,
                                            1.8, .71]), 
                                  args = (mX, vY), gtol = 1e-3)

# optimize the function (with gradient)
optimLogit = scipy.optimize.fmin_bfgs(logLikelihoodLogitVerbose, 
                                  x0 = np.array([-.1, -.03, -.01, .44, .92, .53,
                                            1.8, .71]), fprime = likelihoodScore, 
                                  args = (mX, vY), gtol = 1e-3)
#=====================================================