scipy 未优化并返回“由于精度损失而不一定实现所需的错误"； [英] scipy is not optimizing and returns "Desired error not necessarily achieved due to precision loss"

问题描述

我有以下代码试图最小化对数似然函数.

I have the following code which attempts to minimize a log likelihood function.

#!/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])

请注意，它根本没有设法优化参数，并且最小化值 32 大于 28，这是您在 a= 0.01, alpha = 0.5, beta = 0.6 时得到的结果.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，我如何自动执行此操作?

Notice that it hasn't managed to optimize the parameters at all and the minimized value 32 is bigger than 28 which is what you get with a= 0.01, alpha = 0.5, beta = 0.6 . It's possible this problem could be avoided by choosing better initial guesses but if so, how can I do this automatically?

推荐答案

我复制了您的示例并尝试了一些.看起来如果您坚持使用 BFGS 求解器，经过几次迭代后 mu+ alpha * r 将有一些负数，这就是您获得 RuntimeWarning 的方式.

I copied your example and tried a little bit. Looks like if you stick with BFGS solver, after a few iteration the mu+ alpha * r will have some negative numbers, and that's how you get the RuntimeWarning.

我能想到的最简单的解决方法是切换到 Nelder Mead 求解器.

The easiest fix I can think of is to switch to 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

这篇关于scipy 未优化并返回“由于精度损失而不一定实现所需的错误"；的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！