Numpy：多元正态分布的对数似然性

Question

我想计算多元正态分布的对数似然性。

数据：

data = np.random.multivariate_normal(mean=[2,5], cov=[[1, 0], [0, 10]], size=1000) 

似然（我也跟着Wikipedia）：

def likelihood(mean, cov): 
    # mean = np.array([y1, y2]), cov = np.array([[c1, 0], [0, c2]]) 

    loglikelihood = -0.5*( np.log(np.linalg.det(cov)) + (data - mean).transpose() * np.linalg.inv(cov) * (data - mean) + 2 * np.log(2 * np.pi) ) 

    loglikelihoodsum = loglikelihood.sum() 

    return loglikelihoodsum 

返回以下错误：

> likelihood(mean, cov) 
--------------------------------------------------------------------------- 
ValueError       Traceback (most recent call last) 
<ipython-input-54-3b20c2eefea4> in <module>() 
----> 1 likelihood(mean, cov) 

<ipython-input-53-8a2a7219131c> in likelihood(mean, cov) 
     2  # param = mean[y1, y2], cov = [[c1, 0], [0, c2]] 
     3 
----> 4  loglikelihood = -0.5*( np.log(np.linalg.det(cov)) + (data - mean).transpose() * np.linalg.inv(cov) * (data - mean) + 2 * np.log(2 * np.pi) ) 
     5 
     6  loglikelihoodsum = loglikelihood.sum() 

ValueError: operands could not be broadcast together with shapes (2,1000) (2,2) 

我怎样才能解决呢？

Answer 1

我找到答案：

def likelihood(mean, cov): # Wikipedia 
    def calc_loglikelihood(residuals): 
     return -0.5 * (np.log(np.linalg.det(cov)) + residuals.T.dot(np.linalg.inv(cov)).dot(residuals) + 2 * np.log(2 * np.pi)) 

    # mean = np.array([y1, y2]), cov = np.array([[c1, 0], [0, c2]]) 
    residuals = (data - mean) 

    loglikelihood = np.apply_along_axis(calc_loglikelihood, 1, residuals) 
    loglikelihoodsum = loglikelihood.sum() 

    return loglikelihoodsum 

Answer 2

乘以*运营商在numpy是指元素乘法。要计算，而不是使用np.einsum内积：

mean = np.random.normal(0, 1, 2) 
cov = np.random.normal(0, 1, (2, 2)) 
data = np.random.normal(0, 1, (1000, 2)) 

residuals = data - mean 
loglikelihood = -0.5 * (
    np.log(np.linalg.det(cov)) 
    + np.einsum('...j,jk,...k', residuals, np.linalg.inv(cov), residuals) 
    + len(mean) * np.log(2 * np.pi) 
) 
np.sum(loglikelihood)