python - scipy没有优化并返回“由于精度损失而无法实现所需的错误”

我有以下代码试图最小化一个对数似然函数。

#!/usr/bin/python
import math
import random
import numpy as np
from scipy.optimize import minimize

def loglikelihood(params, data):
    (mu, alpha, beta) = params
    tlist = np.array(data)
    r = np.zeros(len(tlist))
    for i in xrange(1,len(tlist)):
        r[i] = math.exp(-beta*(tlist[i]-tlist[i-1]))*(1+r[i-1])
    loglik  = -tlist[-1]*mu
    loglik = loglik+alpha/beta*sum(np.exp(-beta*(tlist[-1]-tlist))-1)
    loglik = loglik+np.sum(np.log(mu+alpha*r))
    return -loglik

atimes = [ 148.98894201,  149.70253172,  151.13717804,  160.35968355,
        160.98322609,  161.21331798,  163.60755544,  163.68994973,
        164.26131871,  228.79436067]
a= 0.01
alpha = 0.5
beta = 0.6
print loglikelihood((a, alpha, beta), atimes)

res = minimize(loglikelihood, (0.01, 0.1,0.1), method = 'BFGS',args = (atimes,))
print res

它给了我

28.3136498357
./test.py:17: RuntimeWarning: invalid value encountered in log
  loglik = loglik+np.sum(np.log(mu+alpha*r))
   status: 2
  success: False
     njev: 14
     nfev: 72
 hess_inv: array([[1, 0, 0],
       [0, 1, 0],
       [0, 0, 1]])
      fun: 32.131359359964378
        x: array([ 0.01,  0.1 ,  0.1 ])
  message: 'Desired error not necessarily achieved due to precision loss.'
      jac: array([ -2.8051672 ,  13.06962156, -48.97879982])

注意，它根本没有优化参数，最小化值32大于28，这就是a=0.01，alpha=0.5，beta=0.6得到的结果。有可能通过选择更好的初始猜测来避免这个问题，但如果是这样，我怎么能自动做到这一点呢？

最佳答案

我模仿了你的例子，试了一下。如果你坚持使用bfgs解算器，经过几次迭代，mu+ alpha * r会有一些负数，这就是你得到runtimewarning的方式。
我能想到的最简单的解决方法是切换到Nelder Mead Solver。

res = minimize(loglikelihood, (0.01, 0.1,0.1), method = 'Nelder-Mead',args = (atimes,))

它会给你这个结果：

28.3136498357
  status: 0
    nfev: 159
 success: True
     fun: 27.982451280648817
       x: array([ 0.01410906,  0.68346023,  0.90837568])
 message: 'Optimization terminated successfully.'
     nit: 92