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2015 High-dimensional Ising model selection with Bayesian information criteria
Rina Foygel Barber, Mathias Drton
Electron. J. Statist. 9(1): 567-607 (2015). DOI: 10.1214/15-EJS1012

Abstract

We consider the use of Bayesian information criteria for selection of the graph underlying an Ising model. In an Ising model, the full conditional distributions of each variable form logistic regression models, and variable selection techniques for regression allow one to identify the neighborhood of each node and, thus, the entire graph. We prove high-dimensional consistency results for this pseudo-likelihood approach to graph selection when using Bayesian information criteria for the variable selection problems in the logistic regressions. The results pertain to scenarios of sparsity, and following related prior work the information criteria we consider incorporate an explicit prior that encourages sparsity.

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Rina Foygel Barber. Mathias Drton. "High-dimensional Ising model selection with Bayesian information criteria." Electron. J. Statist. 9 (1) 567 - 607, 2015. https://doi.org/10.1214/15-EJS1012

Information

Published: 2015
First available in Project Euclid: 24 March 2015

zbMATH: 1309.62050
MathSciNet: MR3326135
Digital Object Identifier: 10.1214/15-EJS1012

Subjects:
Primary: 62F12 , 62J12

Keywords: Bayesian Information Criterion , Graphical model , logistic regression , Log-linear model , neighborhood selection , Variable selection

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.9 • No. 1 • 2015
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