## Electronic Journal of Statistics

### High-dimensional Ising model selection with Bayesian information criteria

#### 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.

#### Article information

Source
Electron. J. Statist., Volume 9, Number 1 (2015), 567-607.

Dates
First available in Project Euclid: 24 March 2015

https://projecteuclid.org/euclid.ejs/1427203129

Digital Object Identifier
doi:10.1214/15-EJS1012

Mathematical Reviews number (MathSciNet)
MR3326135

Zentralblatt MATH identifier
1309.62050

#### Citation

Barber, Rina Foygel; Drton, Mathias. High-dimensional Ising model selection with Bayesian information criteria. Electron. J. Statist. 9 (2015), no. 1, 567--607. doi:10.1214/15-EJS1012. https://projecteuclid.org/euclid.ejs/1427203129

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