golazo: Performs GOLAZO algorithm by optimizing the dual problem.

In pzwiernik/golazo: Regularized likelihood for Gaussian graphical models under a general asymmetric lasso-type penalty

Description

This function implements a simple block-coordinate descent algorithm to find the maximum of the regularized Gaussiann log-likelihood with a an assymetric penalty of lasso type.

Usage

golazo(S, L, U, tol = 1e-07, verbose = TRUE)

Arguments

S	Positive semidefinite matrix. This will be typically the sample covariance matrix but it can be somethink different in the dual likelihood computation or when the data follow the non-paranormal distribution.
L	Matrix of lower penalties. It should have all entries non-positive (-Inf is a valid entry). The entries of L say how much negative entries of the inverse of Sigma are penalized. For GLASSO all entries should of L should be -rho and all entries of U should be rho (in both cases with zero diagonal). For positive GOLAZO L should be zero and U should be like for GLASSO.
U	Matrix of upper penalties. It should have all entries non-negative (Inf is a valid entry). The entries of U say how much positive entries of the inverse of Sigma are penalized.
tol	The convergence tolerance (default tol=1e-7). The algorithm termininnates when teh dual gap (guaranteed to be nonnegative) is less than tol.
verbose	if TRUE (default) the output will be printed.

Value

K the optimal value of the concentration matrix

Sig the optimal value of the covariance matrix

it the number of iterations

Examples

data(ability.cov)
S <- ability.cov$cov
R <- stats::cov2cor(S)
d <- nrow(R)
L <- matrix(0,d,d)
U <- matrix(0.2,d,d)
diag(U) <- 0
res <- golazo(R,L=L,U=U)
Khat <- res$K
print(Khat)

pzwiernik/golazo documentation built on Aug. 13, 2020, 4:15 p.m.