使用SciPy进行逻辑回归 [英] Logistic regression using SciPy

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问题描述

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，这些函数运行良好(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，但是看起来很合理.

I am trying to code up logistic regression in Python using the SciPy fmin_bfgs function, but am running into some issues. I wrote functions for the logistic (sigmoid) transformation function, and the cost function, and those work fine (I have used the optimized values of the parameter vector found via canned software to test the functions, and those match up). I am not that sure of my implementation of the gradient function, but it looks reasonable.

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)以关于零除的很多东西结束.

The first optimization (without gradient) ends with a whole lot of stuff about division by zero.

第二个优化(带有渐变)以矩阵未对齐错误结束，这可能意味着我已经知道错误返回渐变的方式.

The second optimization (with gradient) ends with a matrices not aligned error, which probably means I have got the way the gradient is to be returned wrong.

对此有任何帮助，我们将不胜感激.如果有人想尝试此操作，数据将包含在下面.

Any help with this is appreciated. If anyone wants to try this, the data is included below.

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

推荐答案

此处为

Here is the answer I sent back to the SciPy list where this question was cross-posted. Thanks to @tiago for his answer. Basically, I reparametrized the likelihood function. Also, added a call to the check_grad function.

#=====================================================
# 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)
#=====================================================

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使用SciPy进行逻辑回归 [英] Logistic regression using SciPy

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