flare (version 1.8)

sugm.select: 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)

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.

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.

Author

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

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: $$ likelihood: Tr(\Sigma \Omega) - \log|\Omega| $$ $$ tracel2: Tr(diag(\Sigma \Omega - I)^2). $$

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)