Gaussian negative log-likelihood — negloglik

Computes -log|Theta| + tr(S * Theta) which is proportional to the negative log-likelihood of a multivariate Gaussian with precision Theta and sample covariance S. Used for cross-validation scoring.

Usage

negloglik_Gaussian(S, Theta)

Arguments

S: Sample covariance matrix (p x p).
Theta: Precision matrix (p x p).

Value

Scalar negative log-likelihood. Returns Inf if Theta is not positive definite.

Examples

S <- matrix(c(1, 0.5, 0.5, 1), 2, 2)
Theta <- solve(S)
negloglik_Gaussian(S, Theta)  # should equal p = 2 (up to constant)
#> [1] 1.712318