Numpy：多元正态分布的对数似然

我想计算多元正态分布的对数似然

数据：

可能性（我遵循）：

它返回以下错误：

> 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) 

>可能性（平均值，cov）
---------------------------------------------------------------------------
ValueError回溯（最近一次调用上次）
在（）
---->1可能性（平均值，cov）
可能性（平均值，cov）
2#param=平均值[y1，y2]，cov=[[c1，0]，[0，c2]]
3.
---->4对数似然=-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=loglikelike.sum（）
ValueError:操作数无法与形状（21000）（2,2）一起广播

---

如何修复它？

在

numpy

中使用

*

运算符进行乘法是指元素乘法。您希望使用

np.einsum

计算内积：

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)

我找到了一个答案：

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

---

您可以使用scipy.stats.multivariable_normal.logpdf

谢谢，但我仍然得到以下错误：

shapes（21000）和（2,2）未对齐：1000（dim 1）！=2（尺寸0）

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)

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