Implements the regularization parameter selection for high dimensional undirected graph estimation. The optional approaches are rotation information criterion (ric), stability approach to regularization selection (stars) and extended Bayesian information criterion (ebic).
huge.select(est, criterion = NULL, ebic.gamma = 0.5, stars.thresh = 0.1,
stars.subsample.ratio = NULL, rep.num = 20, verbose = TRUE)An object with S3 class "huge"
Model selection criterion. "ric" and "stars" are available for all 3 graph estimation methods. ebic is only applicable when est$method = "glasso" in huge(). The default value is "ric".
The tuning parameter for ebic. The default value is 0.5. Only applicable when est$method = "glasso" and criterion = "ebic".
The variability threshold in stars. The default value is 0.1. An alternative value is 0.05. Only applicable when criterion = "stars".
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. Only applicable when criterion = "stars".
The number of subsamplings when criterion = "stars" or rotations when criterion = "ric". The default value is 20. NOT applicable when criterion = "ebic"
If verbose = FALSE, tracing information printing is disabled. The default value is TRUE.
An object with S3 class "select" is returned:
The optimal graph selected from the graph path
The optimal precision matrix from the path only applicable when method = "glasso"
The optimal covariance matrix from the path only applicable when method = "glasso" and est$cov is avaiable.
The graph path estimated by merging the subsampling paths. Only applicable when the input criterion = "stars".
The variability along the subsampling paths. Only applicable when the input criterion = "stars".
Extended BIC scores for regularization parameter selection. Only applicable when criterion = "ebic".
The index of the selected regularization parameter. NOT applicable when the input criterion = "ric"
The selected regularization/thresholding parameter.
The sparsity level of "refit".
and anything else inluded in the input est
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 overselect 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 subsampling procedure in stars may NOT be very efficient, we also provide the recent developed highly efficient, rotation information criterion approach (ric). Instead of tuning over a grid by cross-validation or subsampling, we directly estimate the optimal regularization paramter based on random Rotations. However, ric 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. Extended Bayesian information criterion (ebic) is another competive approach, but the ebic.gamma can only be tuned by experience.
1. T. Zhao and H. Liu. The huge Package for High-dimensional Undirected Graph Estimation in R. Journal of Machine Learning Research, 2012 2. H. Liu, F. Han, M. Yuan, J. Lafferty and L. Wasserman. High Dimensional Semiparametric Gaussian Copula Graphical Models. Annals of Statistics,2012 3. D. Witten and J. Friedman. New insights and faster computations for the graphical lasso. Journal of Computational and Graphical Statistics, to appear, 2011. 4. Han Liu, Kathryn Roeder and Larry Wasserman. Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models. Advances in Neural Information Processing Systems, 2010. 5. R. Foygel and M. Drton. Extended bayesian information criteria for gaussian graphical models. Advances in Neural Information Processing Systems, 2010. 6. H. Liu, J. Lafferty and L. Wasserman. The Nonparanormal: Semiparametric Estimation of High Dimensional Undirected Graphs. Journal of Machine Learning Research, 2009 7. J. Fan and J. Lv. Sure independence screening for ultra-high dimensional feature space (with discussion). Journal of Royal Statistical Society B, 2008. 8. O. Banerjee, L. E. Ghaoui, A. d'Aspremont: Model Selection Through Sparse Maximum Likelihood Estimation for Multivariate Gaussian or Binary Data. Journal of Machine Learning Research, 2008. 9. J. Friedman, T. Hastie and R. Tibshirani. Regularization Paths for Generalized Linear Models via Coordinate Descent. Journal of Statistical Software, 2008. 10. J. Friedman, T. Hastie and R. Tibshirani. Sparse inverse covariance estimation with the lasso, Biostatistics, 2007. 11. N. Meinshausen and P. Buhlmann. High-dimensional Graphs and Variable Selection with the Lasso. The Annals of Statistics, 2006.
huge and huge-package.
# NOT RUN {
#generate data
L = huge.generator(d = 20, graph="hub")
out.mb = huge(L$data)
out.ct = huge(L$data, method = "ct")
out.glasso = huge(L$data, method = "glasso")
#model selection using ric
out.select = huge.select(out.mb)
plot(out.select)
#model selection using stars
#out.select = huge.select(out.ct, criterion = "stars", stars.thresh = 0.05,rep.num=10)
#plot(out.select)
#model selection using ebic
out.select = huge.select(out.glasso,criterion = "ebic")
plot(out.select)
# }
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