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December 2018 Learning Markov Equivalence Classes of Directed Acyclic Graphs: An Objective Bayes Approach
Federico Castelletti, Guido Consonni, Marco L. Della Vedova, Stefano Peluso
Bayesian Anal. 13(4): 1235-1260 (December 2018). DOI: 10.1214/18-BA1101

Abstract

A Markov equivalence class contains all the Directed Acyclic Graphs (DAGs) encoding the same conditional independencies, and is represented by a Completed Partially Directed Acyclic Graph (CPDAG), also named Essential Graph (EG). We approach the problem of model selection among noncausal sparse Gaussian DAGs by directly scoring EGs, using an objective Bayes method. Specifically, we construct objective priors for model selection based on the Fractional Bayes Factor, leading to a closed form expression for the marginal likelihood of an EG. Next we propose a Markov Chain Monte Carlo (MCMC) strategy to explore the space of EGs using sparsity constraints, and illustrate the performance of our method on simulation studies, as well as on a real dataset. Our method provides a coherent quantification of inferential uncertainty, requires minimal prior specification, and shows to be competitive in learning the structure of the data-generating EG when compared to alternative state-of-the-art algorithms.

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Federico Castelletti. Guido Consonni. Marco L. Della Vedova. Stefano Peluso. "Learning Markov Equivalence Classes of Directed Acyclic Graphs: An Objective Bayes Approach." Bayesian Anal. 13 (4) 1235 - 1260, December 2018. https://doi.org/10.1214/18-BA1101

Information

Published: December 2018
First available in Project Euclid: 15 March 2018

zbMATH: 06989983
MathSciNet: MR3855370
Digital Object Identifier: 10.1214/18-BA1101

Keywords: Bayesian model selection , CPDAG , essential graph , fractional Bayes factor , Graphical model

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Vol.13 • No. 4 • December 2018
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