问题描述
如何使用 scipy.optimize.minimize
进行最大似然回归?我特别想在这里使用 minimize
函数,因为我有一个复杂的模型,需要添加一些约束.我目前正在尝试使用以下内容的简单示例:
How can I do a maximum likelihood regression using scipy.optimize.minimize
? I specifically want to use the minimize
function here, because I have a complex model and need to add some constraints. I am currently trying a simple example using the following:
from scipy.optimize import minimize
def lik(parameters):
m = parameters[0]
b = parameters[1]
sigma = parameters[2]
for i in np.arange(0, len(x)):
y_exp = m * x + b
L = sum(np.log(sigma) + 0.5 * np.log(2 * np.pi) + (y - y_exp) ** 2 / (2 * sigma ** 2))
return L
x = [1,2,3,4,5]
y = [2,3,4,5,6]
lik_model = minimize(lik, np.array([1,1,1]), method='L-BFGS-B', options={'disp': True})
当我运行它时,收敛失败.有谁知道我的代码有什么问题?
When I run this, convergence fails. Does anyone know what is wrong with my code?
我运行此程序时收到的消息是ABNORMAL_TERMINATION_IN_LNSRCH".我使用的算法与我在 R 中使用 optim
的算法相同.
The message I get running this is 'ABNORMAL_TERMINATION_IN_LNSRCH'. I am using the same algorithm that I have working using optim
in R.
推荐答案
谢谢 Aleksander.你是正确的,我的似然函数是错误的,而不是代码.使用我在维基百科上找到的公式,我将代码调整为:
Thank you Aleksander. You were correct that my likelihood function was wrong, not the code. Using a formula I found on wikipedia I adjusted the code to:
import numpy as np
from scipy.optimize import minimize
def lik(parameters):
m = parameters[0]
b = parameters[1]
sigma = parameters[2]
for i in np.arange(0, len(x)):
y_exp = m * x + b
L = (len(x)/2 * np.log(2 * np.pi) + len(x)/2 * np.log(sigma ** 2) + 1 /
(2 * sigma ** 2) * sum((y - y_exp) ** 2))
return L
x = np.array([1,2,3,4,5])
y = np.array([2,5,8,11,14])
lik_model = minimize(lik, np.array([1,1,1]), method='L-BFGS-B')
plt.scatter(x,y)
plt.plot(x, lik_model['x'][0] * x + lik_model['x'][1])
plt.show()
现在它似乎可以工作了.
Now it seems to be working.
感谢您的帮助!
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