sugm.select: Model selection for high-dimensional undirected graphical...

In flare: Family of Lasso Regression

Model selection for high-dimensional undirected graphical models

Description

Implements regularization parameter selection for high-dimensional undirected graphical models. Supported approaches are Stability Approach to Regularization Selection ("stars") and cross-validation ("cv").

Usage

sugm.select(est, criterion = "stars", stars.subsample.ratio = NULL,
            stars.thresh = 0.1, rep.num = 20, fold = 5,
            loss="likelihood", verbose = TRUE)

Arguments

est	An object with S3 class "sugm"
criterion	Model selection criterion. "stars" and "cv" are available for both graph estimation methods. The default value is "stars".
stars.subsample.ratio	The subsampling ratio. The default value is 10*sqrt(n)/n when n > 144 and 0.8 when n <= 144, where n is the sample size. Must be in (0,1). Only applicable when criterion = "stars".
stars.thresh	The variability threshold in STARS. Must be in [0,1]. The default value is 0.1. Only applicable when criterion = "stars".
rep.num	The number of subsamples. Must be at least 1. The default value is 20.
fold	The number of folds used in cross-validation. Must be between 2 and n. The default value is 5. Only applicable when criterion = "cv".
loss	Loss used in cross-validation. Two losses are available: "likelihood" and "tracel2". Default is "likelihood". Only applicable when criterion = "cv".
verbose	If verbose = FALSE, tracing information printing is disabled. The default value is TRUE.

Details

Stability Approach to Regularization Selection (STARS) selects an optimal regularization parameter by variability across subsamples, and tends to over-select edges in Gaussian graphical models. In addition to selecting regularization parameters, STARS can provide an additional merged graph estimate based on edge frequencies across subsamples. K-fold cross-validation is also available for selecting lambda, using the following losses:

likelihood: Tr(\Sigma \Omega) - \log|\Omega|

tracel2: Tr(diag(\Sigma \Omega - I)^2).

Value

An object with S3 class "select" is returned:

refit	The optimal graph selected from the graph path
opt.icov	The optimal precision matrix selected.
merge	The graph path estimated by merging the subsampling paths. Only applicable when the input criterion = "stars".
variability	The variability along the subsampling paths. Only applicable when the input criterion = "stars".
opt.index	The index of the selected regularization parameter.
opt.lambda	The selected regularization/thresholding parameter.
opt.sparsity	The sparsity level of "refit".
loss	Cross-validation loss used for selection. Only applicable when criterion = "cv".

and anything else included in the input est.

Note

Model selection is not available when the data input is a sample covariance matrix.

Author(s)

Xingguo Li, Tuo Zhao, Lie Wang, Xiaoming Yuan and Han Liu
Maintainer: Tuo Zhao <[e-mail]>

References

1. T. Cai, W. Liu and X. Luo. A constrained \ell_1 minimization approach to sparse precision matrix estimation. Journal of the American Statistical Association, 2011.
2. B. He and X. Yuan. On non-ergodic convergence rate of Douglas-Rachford alternating direction method of multipliers. Technical Report, 2012.

See Also

sugm and flare-package.

Examples

## load package required
library(flare)

#generate data
L = sugm.generator(d = 10, graph="hub")
out1 = sugm(L$data)

#model selection using stars
#out1.select1 = sugm.select(out1, criterion = "stars", stars.thresh = 0.1)
#plot(out1.select1)

#model selection using cross validation
out1.select2 = sugm.select(out1, criterion = "cv")
plot(out1.select2)

flare documentation built on Feb. 19, 2026, 5:06 p.m.