loglik {sglasso} | R Documentation |
This function extracts the log-likelihood for the sequence of weighted l1-penalized RCON(V, E) models estimated by sglasso
function.
loglik(object, N = 2)
object |
a fitted |
N |
sample size. Default value is 2 to remove the constant term in the log-likelihood function. See below for more details. |
Denoted with ψ = (η',θ')' the parameter vector of the structured concentration matrix K(ψ), the log-likelihood function of the RCON(V, E) model is equal, up to a constant, to the following expression
l(ψ) = N/2[log det K(ψ) - tr{S K(ψ)}],
where S = N^{-1}∑_{i=1}^N X_i X_i', N is the sample size and X_i is the ith observed p-dimensional vector. Denoted with hat{ψ} = (hat{η}', hat{θ}')' the sglasso estimates, straightforward algebra shows that
l(hat{ψ}) = N/2[log det K(hat{ψ}) - p + ρ∑_{m=1}^S w_m |hat{θ_m|}],
where ρ is the tuning parameter and w_m are the weights used to define the weighted l1-norm.
loglik
returns a vector containing the log-likelihood computed for the sequence of weighted l1-penalized RCON(V, E).
Luigi Augugliaro
Maintainer: Luigi Augugliaro luigi.augugliaro@unipa.it
summary.sglasso
method and sglasso
function.
N <- 100 p <- 5 X <- matrix(rnorm(N * p), N, p) S <- crossprod(X) / N mask <- outer(1:p, 1:p, function(i, j) 0.5^abs(i-j)) out.sglasso_path <- sglasso(S, mask, nrho = 5, tol = 1.0e-13) out.sglasso_path loglik(out.sglasso_path, N = N) rho <- out.sglasso_path$rho[3] out.sglasso_single <- sglasso(S, mask, nrho = 1, min_rho = rho, tol = 1.0e-13, algorithm = "ccm") loglik(out.sglasso_single, N = N)