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2010

Extended Bayesian Information Criteria for Gaussian Graphical Models

Foygel, Rina, Drton, Mathias

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Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications.

For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique.
In this paper we establish the consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the sample size n grow.
Compared to earlier work on the regression case, our treatment allows for growth in the number of non-zero parameters in the true model, which is necessary in order to cover connected graphs.

Extended Bayesian Information Criteria for Gaussian Graphical Models · Around

Built on

Estimating the dimension of a model
Gideon Schwarz · 1978
Earlier work this paper cites.
Stochastic inequalities relating a class of log-likelihood ratio statistics to their asymptotic χ 2 \chi^{2} distribution
B. T. Porteous · 1989
Earlier work this paper cites.
Linear model selection by cross-validation
Jun Shao · 1993
Earlier work this paper cites.
Graphical models
Steffen L. Lauritzen · 1996
Earlier work this paper cites.

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Then

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