smoothedLasso (version 1.6)

graphicalLasso: Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the graphical Lasso.

Description

Auxiliary function which returns the objective, penalty, and dependence structure among regression coefficients of the graphical Lasso.

Usage

graphicalLasso(S, lambda)

Arguments

S

The sample covariance matrix.

lambda

The regularization parameter of the graphical Lasso.

Value

A list with three functions, precisely the objective \(u\), penalty \(v\), and dependence structure \(w\). Not all derivatives are available in closed form, and thus computing the numerical derivative of the entire objective function is recommended.

References

Friedman, J., Hastie, T., and Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3):432-441.

Friedman, J., Hastie, T., and Tibshirani, R. (2019). glasso: Graphical Lasso: Estimation of Gaussian Graphical Models. R package version 1.11.

Hahn, G., Lutz, S., Laha, N., and Lange, C. (2020). A framework to efficiently smooth L1 penalties for linear regression. bioRxiv:2020.09.17.301788.

Examples

# NOT RUN {
library(smoothedLasso)
p <- 30
S <- matrix(rWishart(1,p,diag(p)),p)
lambda <- 1
temp <- graphicalLasso(S,lambda)

# }