Kullback-Leibler Divergence — kl

Compute KL divergence for a multivariate normal distribution.

kl_mvn(true, estimate, stein = FALSE)

Arguments

true	Matrix. The true precision matrix (inverse of the covariance matrix)
estimate	Matrix. The estimated precision matrix (inverse of the covariance matrix)
stein	Logical. Should Stein's loss be computed (defaults to `TRUE`)? Note KL divergence is half of Stein's loss.

Value

Numeric corresponding to KL divergence.

Note

A lower value is better, with a score of zero indicating that the estimated precision matrix is identical to the true precision matrix.

Examples

# \donttest{

# nodes
p <- 20

main <- gen_net(p = p, edge_prob = 0.15)

y <- MASS::mvrnorm(250, rep(0, p), main$cors)

fit_l1 <- ggmncv(R = cor(y),
              n = nrow(y),
              penalty = "lasso",
              progress = FALSE)

# lasso
kl_mvn(fit_l1$Theta, solve(main$cors))
#> [1] 0.3371542

fit_atan <- ggmncv(R = cor(y),
              n = nrow(y),
              penalty = "atan",
              progress = FALSE)

kl_mvn(fit_atan$Theta, solve(main$cors))
#> [1] 0.1466836

# }