Extended Bayesian Information Criteria for Gaussian Graphical Models

By Rina Foygel, Mathias Drton. Neural Information Processing Systems, 2010

1,121 citations recorded by the source corpus.

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. We demonstrate the performance of this criterion on simulated data when used in conjunction with the graphical lasso, and verify that the criterion indeed performs better than either cross-validation or the ordinary Bayesian information criterion when p and the number of non-zero parameters q both scale with n.

Subfields: Analytical Chemistry, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6b22036526adbfa8f93ff1a4749414d475950146

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Citations in the corpus

Network analysis: a brief overview and tutorial (2018, methodology): “The tuning parameter λ therefore needs to be carefully selected to create a network structure that minimises the number of spurious edges while maximising the number of true edges (Foygel & Drton, 2010).”
mgm: Estimating Time-Varying Mixed Graphical Models in High-Dimensional Data (2015, methodology): “Foygel and Drton (2010) used values γ ∈ { 0 , .”
Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research (2016, methodology): “For GGM estimation, minimizing the extended Bayesian information criterion [11] has been shown to work well in retrieving the true network structure [15].”
A Tutorial on Regularized Partial Correlation Networks (2016, methodology): “We estimate regularized partial correlation networks via the EBIC graphical LASSO (Foygel and Drton, 2010), using polychoric correlations as input when data are ordinal.”
A Bayesian information criterion for singular models (2013, methodology): “…problems with a large number of models it can be beneficial to adopt non-uniform prior model probabilities; compare for example the work on regression models by Chen and Chen (2008) and Scott and Berger (2010), and the work on graphical models by Foygel and Drton (2010) and Gao et al. (2012).”
Estimating psychological networks and their accuracy: A tutorial paper (2016, methodology): “We estimated Gaussian graphical models, using the graphical LASSO in combination with EBIC model selection (Epskamp and Fried, 2016; Foygel and Drton, 2010), using polychoric correlation matrices as input.”
Network Analysis of Depression and Anxiety Symptom Relations in a Psychiatric Sample (2016, methodology): “We set the starting value of γ to 0.5 as recommended by Foygel & Drton (2010).”
Generalized Network Psychometrics: Combining Network and Latent Variable Models (2016, methodology): “…as the Akaike information criterion (AIC), Bayesian information criterion (BIC) or the extended Bayesian information criterion (EBIC; Chen and Chen 2008) which is now often used in network estimation (van Psychometrika Submission October 6, 2016 22 Borkulo et al., 2014; Foygel and Drton, 2010).”
PC algorithm for nonparanormal graphical models (2013, background): “(Extensions in the spirit of Chen and Chen, 2008 and Foygel and Drton, 2010 could be attractive for this tuning problem but have yet to be adapted and studied for directed graphs.)”
The huge Package for High-dimensional Undirected Graph Estimation in R (2012, positive): “, 2010]; a modified rotation information criterion (RIC) [Lysen, 2009]; and the extended Bayesian information criterion [Foygel and Drton, 2010].”
Regularized Gaussian Psychological Networks: Brief Report on the Performance of Extended BIC Model Selection (2016, methodology): “…Bayesian Information Criterion (EBIC; Chen and Chen 2008; Foygel and Drton 2010) adds an extra penalty for model complexity to the typical BIC and has been shown to work well in high-dimensional network model selection (Foygel and Drton, 2010; Barber et al., 2015; van Borkulo et al., 2014).”
Bayesian model choice and information criteria in sparse generalized linear models (2011, methodology): “of all multivariate normal distributions with jk= 0 when jand kare two distinct non-adjacent nodes in G. Prior work proposes the use of the extended BIC for sparse Gaussian graphical model selection (Foygel and Drton, 2010; Gao et al., 2011). Accounting for a matrix parameter, the EBIC is dened as B”
High-dimensional consistency in score-based and hybrid structure learning (2015, methodology): “1), which is known to be weak for sparse high-dimensional settings [see, for example, Foygel and Drton (2010)], does not satisfy Knqn log(pn) nλn → 0, except for some very restricted choices of {pn}, {qn} and {Kn}. Further, we note that van de Geer and Bühlmann (2013) proved their high-dimensional c”
Structure Learning in Graphical Modeling (2016, background): “Foygel & Drton (2010), Gao et al. (2012) and Barber & Drton (2015) address this issue by adapting ideas from sparse high-dimensional regression.”
The Gaussian Graphical Model in Cross-Sectional and Time-Series Data (2016, methodology): “Estimating a GGM with the GLASSO algorithm in combination with EBIC model selection has been shown to work well in retrieving the true network structure (Epskamp, 2016; Foygel & Drton, 2010).”