treeple.experimental.mutual_info.mi_gaussian#
- treeple.experimental.mutual_info.mi_gaussian(cov)[source]#
Compute mutual information of a multivariate Gaussian.
- Parameters:
- covarray_like of shape (d,d)
The covariance matrix of the distribution.
- Returns:
- true_mi
float The true analytical entropy of the generated multivariate Gaussian distribution.
- true_mi
Notes
Analytical solution for entropy, \(H(X)\) of a multivariate Gaussian is given by:
H(X) = \frac{d}{2} (1 + log(2\pi)) + \frac{1}{2} log(det(C))