camel (version 0.2.0)

camel.tiger.select: Model selection for high-dimensional undirected graph estimation

Description

Implements the regularization parameter selection for high dimensional undirected graph estimation. The optional approaches are stability approach to regularization selection (stars) and cross validation selection (cv).

Usage

camel.tiger.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 "camel.tiger"

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< code="">, where n is the sample size. Only applicable when criterion = "stars".

stars.thresh

The variability threshold in stars. The default value is 0.1. Only applicable when criterion = "stars".

rep.num

The number of subsamplings. The default value is 20.

fold

The number of folds used in cross validation. The default value is 5. Only applicable when criterion = "cv".

loss

Loss to be used in cross validation. Two losses are available: "likelihood" and "tracel2". Default "likelihood". Only applicable when criterion = "cv".

verbose

If verbose = FALSE, tracing information printing is disabled. The default value is 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".
• and anything else inluded in the input est

Details

Stability approach to regularization selection (stars) is a natural way to select optimal regularization parameter for all three estimation methods. It selects the optimal graph by variability of subsamplings and tends to over-select edges in Gaussian graphical models. Besides selecting the regularization parameters, stars can also provide an additional estimated graph by merging the corresponding subsampled graphs using the frequency counts. The K-fold cross validation is also provided for selecting the parameter lambda, and two loss functions are adopted as follow $$likelihood: Tr(\Sigma \Omega) - \log|\Omega|$$ $$tracel2: Tr(diag(\Sigma \Omega - I)^2).$$

References

1. H. Liu and L. Wang. TIGER: A tuning-insensitive approach for optimally estimating large undirected graphs. Technical Report, 2012. 2. 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.

See Also

camel.tiger and camel-package.

Examples

#generate data
L = camel.tiger.generator(d = 20, graph="hub")
out1 = camel.tiger(L$data)

#model selection using stars
out1.select2 = camel.tiger.select(out1, criterion = "stars", stars.thresh = 0.05)
plot(out1.select2)

#model selection using cross validation
out1.select3 = camel.tiger.select(out1, criterion = "cv")
plot(out1.select3)