scipy.stats.multivariate_normal raising `LinAlgError: singular matrix` even though my covariance matrix is invertible

Question

我在尝试使用 scipy.stats.multivariate_normal 时遇到问题，希望你们中的某个人能够提供帮助。

我有一个 2x2 矩阵，可以找到使用 numpy.linalg.inv() 的逆矩阵，但是当我尝试将它用作 multivariate_normal 中的协方差矩阵时，我收到 LinAlgError说明它是奇异矩阵：

In [89]: cov = np.array([[3.2e5**2, 3.2e5*0.103*-0.459],[3.2e5*0.103*-0.459, 0.103**2]])

In [90]: np.linalg.inv(cov)
Out[90]:
array([[  1.23722158e-11,   1.76430200e-05],
       [  1.76430200e-05,   1.19418880e+02]])

In [91]: multivariate_normal([0,0], cov)
---------------------------------------------------------------------------
LinAlgError                               Traceback (most recent call last)
<ipython-input-91-44a6625beda5> in <module>()
----> 1 multivariate_normal([0,0], cov)

/mnt/ssd/Enthought_jli199/Canopy_64bit/User/lib/python2.7/site-packages/scipy/stats/_multivariate.pyc in __call__(self, mean, cov, allow_singular, seed)
    421         return multivariate_normal_frozen(mean, cov,
    422                                           allow_singular=allow_singular,
--> 423                                           seed=seed)
    424
    425     def _logpdf(self, x, mean, prec_U, log_det_cov, rank):

/mnt/ssd/Enthought_jli199/Canopy_64bit/User/lib/python2.7/site-packages/scipy/stats/_multivariate.pyc in __init__(self, mean, cov, allow_singular, seed)
    591         """
    592         self.dim, self.mean, self.cov = _process_parameters(None, mean, cov)
--> 593         self.cov_info = _PSD(self.cov, allow_singular=allow_singular)
    594         self._dist = multivariate_normal_gen(seed)
    595

/mnt/ssd/Enthought_jli199/Canopy_64bit/User/lib/python2.7/site-packages/scipy/stats/_multivariate.pyc in __init__(self, M, cond, rcond, lower, check_finite, allow_singular)
    217         d = s[s > eps]
    218         if len(d) < len(s) and not allow_singular:
--> 219             raise np.linalg.LinAlgError('singular matrix')
    220         s_pinv = _pinv_1d(s, eps)
    221         U = np.multiply(u, np.sqrt(s_pinv))

LinAlgError: singular matrix

Answer 1

默认情况下 multivariate_normal 检查协方差矩阵的任何特征值是否小于根据其 dtype 和最大特征值的大小选择的某个容差（查看 [= 的源代码17=] 以获得完整的详细信息）。

正如@kazemakase 上面提到的，虽然根据 np.linalg.inv 使用的标准，您的协方差矩阵可能是可逆的，但它仍然是病态的，无法通过 multivariate_normal 使用的更严格的测试.

您可以将 allow_singular=True 传递给 multivariate_normal 以跳过此测试，但通常最好重新缩放数据以避免首先传递这种病态协方差矩阵。

scipy.stats.multivariate_normal raising `LinAlgError: singular matrix` even though my covariance matrix is invertible

scipy.stats.multivariate_normal raising `LinAlgError: singular matrix` even though my covariance matrix is invertible

python

statistics

numpy

linear-algebra

scipy