scipy.optimize.fmin_bfgs优化提供了与简单函数调用不同的结果 [英] scipy.optimize.fmin_bfgs optimization gives different result from simple function call

问题描述

我正在探索一些numpy/scipy函数，并且我注意到scipy.optimize.fmin_bfgs需要对函数进行更改，以提供与直接函数调用相比正确的结果.我对fnRSS函数的第一个定义在调用该函数时返回了正确的值，但拒绝进行优化.我的第二个定义在调用函数时给出了错误的结果，但在运行优化时给出了正确的结果.有人可以告诉我，对于优化转置vY参数有什么至关重要的吗?它应该已经是164x1.

I am exploring some of the numpy/scipy functions and I noticed that scipy.optimize.fmin_bfgs requires a change in the function being called to give correct results compared to a straight function call. My first definition of the fnRSS function returns a correct value when calling the function but refuses to work in the optimization; my second definition gives the wrong result when calling the function but the right one when running the optimization. Can someone tell me what is so crucial about transposing the vY parameter for the optimization ? It should already be 164x1.

import numpy as np
import scipy as sp
import pandas as pd
from scipy import optimize

if __name__ == "__main__":
    urlSheatherData = "http://www.stat.tamu.edu/~sheather/book/docs/datasets/MichelinNY.csv"
    data = pd.read_csv(urlSheatherData)
    Xs = np.vstack(data[['Service','Decor', 'Food', 'Price']].values)
    Xs = np.concatenate((np.vstack(np.ones(Xs.shape[0])),Xs), axis=1)
    Ys = np.vstack(data[['InMichelin']].values)
    # optimal solution (given)
    vBeta = np.array([-1.49209249,  -0.01117662,  0.044193, 0.05773374, 0.00179794]).reshape(5,1)

    print Ys.shape, Xs.shape, vBeta.shape 
    # first definition of function
    def fnRSS(vBeta, vY, mX):
      return np.sum((vY - np.dot(mX, vBeta))**2) 
    print fnRSS(vBeta, Ys, Xs) # correct value
    print np.linalg.lstsq(Xs, Ys)[1] # confirm correct value
    print sp.optimize.fmin_bfgs(fnRSS, x0=vBeta, args=(Ys,Xs)) # wrong value
    # second definition
    def fnRSS(vBeta, vY, mX):
      return np.sum((vY.T - np.dot(mX, vBeta))**2) 
    print fnRSS(vBeta, Ys, Xs) # incorrect value
    print sp.optimize.fmin_bfgs(fnRSS, x0=vBeta, args=(Ys,Xs)) # correct convergence but simple call gives different value

我的输出:

(164, 1) (164, 5) (5, 1)
26.3239061505
[ 26.32390615]
Warning: Desired error not necessarily achieved due to precision loss.
         Current function value: 6660.000000
         Iterations: 39
         Function evaluations: 3558
         Gradient evaluations: 480
[  4.51220111e-01   1.32711255e-07   8.09143368e-08  -1.06633003e-07
  -5.18448332e-08]
9002.87916028
Warning: Desired error not necessarily achieved due to precision loss.
         Current function value: 26.323906
         Iterations: 29
         Function evaluations: 1954
         Gradient evaluations: 260
[-1.49209095 -0.0111764   0.04419313  0.05773347  0.00179789]

推荐答案

与vY.T无关，而是与vBeta无关，即x作为2d向量而不是2d向量被fmin_bfgs传递给fnRSS.一维数组.因此，尽管您明确尝试将x0=vBeta指定为形状(5,1)的数组，但仍会在内部将其转换为形状(5，)的1d数组，最后按原样返回.

It's not about vY.T, but vBeta, i.e. x being passed by fmin_bfgs to fnRSS as not a 2d vector but a 1d array. So despite the fact you explicetely try to specify x0=vBeta to be an array of shape (5,1), it is converted internally to 1d array of shape (5, ), and in the end is returned as such.

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