huge (version 0.9.1)

huge.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 Permutational Information Criterion (PIC), Stability Approach to Regularization Selection (StARS) and Extended Bayesian Information Criterion(EBIC).

Usage

huge.select(est, criterion = NULL, r.num = 200, EBIC.gamma = 0.5, 
stars.thresh = 0.1, stars.subsample.ratio = NULL, stars.rep.num = 20, 
verbose = TRUE)

Arguments

est

An object with S3 class "huge" (output from huge)

criterion

Model selection criterion. For Meinshausen & Buhlmann Graph Estimation via Lasso (GEL), all 3 options are available, "PIC", "EBIC" and "stars". For Graph Approximation via Correlation Thresholding (GACT), "star

r.num

The number of random permutations in PIC selection. The default value is 200. ONLY applicable when criterion = "PIC"

EBIC.gamma

The tuning parameter for the EBIC. The default value is 0.5. Only applicable when est$method = "GEL" or est$method = "GLASSO" and criterion = "EBIC".

stars.thresh

The variability threshold in the StARS. The default value is 0.1. An alternative value is 0.05. Only applicable when criterion = "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.rep.num

The number of subsampling for the StARS. The default value is 20.Only applicable when criterion = "stars"

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 solution path
• merge
  The solution 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".
• EBIC.scores
  Extended BIC scores for regularization parameter selection. Only applicable when criterion = "EBIC".
• opt.index
  The index of the selected regularization parameter. NOT applicable when the input criterion = "PIC"
• opt.lambda
  The selected regularization/thresholding parameter.
• opt.sparsity
  The sparsity level of "refit".
• graph
  return "subgraph" when k and "fullgraph" when k==d
• and anything else inluded in the input est

Details

The 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 overselect edges in Gaussian graphical models. Besides selecting the regularization parameters, the StARS can also provide an additional estimated graph by merging the corresponding subsampled graphs using the frequency counts. The subsampling procedure in StARS may NOT be very efficient, we also proved the recent developed highly efficient PIC approach. Instead of tuning over a grid by cross-validation or subsampling, we directly estimate the optimal regularization paramter based on random permutations. However, the PIC usually has very good empirical performances but suffers from underselections sometimes. Therefore, we suggest if user are sensitive of false negative rates, they should either consider increasing r.num or applying the StARS to model selection. The extended BIC is another competive approach, but the EBIC.gamma can only be tuned by experience. The EBIC score for the GEL is based on pseudo-likelihood and the theoretical properties have NOT been justified yet.

References

1. Tuo Zhao and Han Liu. HUGE: A Package for High-dimensional Undirected Graph Estimation. Technical Report, Carnegie Mellon University, 2010 2. Han Liu, Kathryn Roeder and Larry Wasserman. Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models. Advances in Neural Information Processing Systems (NIPS), 2010. Jiahua Chen and Zehua Chen. Extended Bayesian information criterion for model selection with large model space. Biometrika, 2008.

See Also

huge and huge-package.

Examples

#generate data
L = huge.generator(d = 200, graph="hub")
out.GEL = huge(L)
out.GACT = huge(L, method = "GACT")
out.GLASSO = huge(L, method = "GLASSO")

#model selection using PIC
out.select = huge.select(out.GEL)
summary(out.select)
plot(out.select)

#model selection using stars
out.select = huge.select(out.GACT, stars.rep.num = 5)
summary(out.select)
plot(out.select)

#model selection using EBIC
out.select = huge.select(out.GLASSO)
summary(out.select)
plot(out.select)