treeple.experimental.mutual_info.entropy_gaussian

treeple.experimental.mutual_info.entropy_gaussian(cov)

Compute entropy of a multivariate Gaussian.

Computes the analytical solution due to [1].

Parameters:

covarray_like of shape (d,d)

The covariance matrix of the distribution.

Returns:

true_mifloat

The true analytical mutual information of the generated multivariate Gaussian distribution.

Notes

The analytical solution for the true mutual information, I(X; Y) is given by:

I(X; Y) = H(X) + H(Y) - H(X, Y) = -\frac{1}{2} log(det(C))

References

[1]

Georges A. Darbellay and Igor Vajda. Estimation of the information by an adaptive partitioning of the observation space. IEEE Trans. Inf. Theory, 45:1315–1321, 1999.