Bayesian model choice and information criteria in sparse generalized linear models
By Rina Foygel, Mathias Drton. 2011
67 citations recorded by the source corpus.
We consider Bayesian model selection in generalized linear models that are high-dimensional, with the number of covariates p being large relative to the sample size n, but sparse in that the number of active covariates is small compared to p. Treating the covariates as random and adopting an asymptotic scenario in which p increases with n, we show that Bayesian model selection using certain priors on the set of models is asymptotically equivalent to selecting a model using an extended Bayesian information criterion. Moreover, we prove that the smallest true model is selected by either of these methods with probability tending to one. Having addressed random covariates, we are also able to give a consistency result for pseudo-likelihood approaches to high-dimensional sparse graphical modeling. Experiments on real data demonstrate good performance of the extended Bayesian information criterion for regression and for graphical models.
View Paper: https://www.semanticscholar.org/paper/3a9cc64efe48c6978a4e896df314425e1e0ebf35
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- Sacha Epskamp
- Richard J. McNally
- Alexandre Heeren
- Denny Borsboom
- Lourens J. Waldorp
- Eiko I. Fried
- Claudia D van Borkulo
- Emily E. Bernstein
Citations in the corpus
- Unpacking Rumination and Executive Control: A Network Perspective (2017, methodology): “We used the R package qgraph (Epskamp et al., 2012) that automatically implements the graphical LASSO regularization in combination with extended Bayesian information criterion (EBIC) model selection (Foygel & Drton, 2011).”
- Social Anxiety Disorder as a Densely Interconnected Network of Fear and Avoidance for Social Situations (2017, methodology): “2012) that automatically implements the graphical LASSO regularization in combination with an extended Bayesian Information Criterion (EBIC) model selection (Foygel and Drton 2011).”
- State of the aRt personality research: A tutorial on network analysis of personality data in R (2015, unknown): “If the data indeed arise from a sparse network with pairwise interactions only, such a procedure will in fact converge on the generating network (Foygel & Drton, 2011).”
- A new method for constructing networks from binary data (2014, methodology): “In this procedure, a hyperparameter called c determines the strength of the extra penalty on the number of neighbours 29,33 .”