Marginal Pseudo-Likelihood Learning of Discrete Markov Network Structures

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http://hdl.handle.net/10138/231261

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Pensar , J , Nyman , H , Niiranen , J & Corander , J 2017 , ' Marginal Pseudo-Likelihood Learning of Discrete Markov Network Structures ' , Bayesian analysis , vol. 12 , no. 4 , pp. 1195-1215 . https://doi.org/10.1214/16-BA1032

Title: Marginal Pseudo-Likelihood Learning of Discrete Markov Network Structures
Author: Pensar, Johan; Nyman, Henrik; Niiranen, Juha; Corander, Jukka
Other contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics

Date: 2017-12
Language: eng
Number of pages: 21
Belongs to series: Bayesian analysis
ISSN: 1931-6690
DOI: https://doi.org/10.1214/16-BA1032
URI: http://hdl.handle.net/10138/231261
Abstract: Markov networks are a popular tool for modeling multivariate distributions over a set of discrete variables. The core of the Markov network representation is an undirected graph which elegantly captures the dependence structure over the variables. Traditionally, the Bayesian approach of learning the graph structure from data has been done under the assumption of chordality since non-chordal graphs are difficult to evaluate for likelihood-based scores. Recently, there has been a surge of interest towards the use of regularized pseudo-likelihood methods as such approaches can avoid the assumption of chordality. Many of the currently available methods necessitate the use of a tuning parameter to adapt the level of regularization for a particular dataset. Here we introduce the marginal pseudo-likelihood which has a built-in regularization through marginalization over the graph-specific nuisance parameters. We prove consistency of the resulting graph estimator via comparison with the pseudo-Bayesian information criterion. To identify high-scoring graph structures in a high-dimensional setting we design a two-step algorithm that exploits the decomposable structure of the score. Using synthetic and existing benchmark networks, the marginal pseudo-likelihood method is shown to perform favorably against recent popular structure learning methods.
Subject: Markov networks
structure learning
pseudo-likelihood
non-chordal graph
Bayesian inference
regularization
CONTEXT-SPECIFIC INDEPENDENCE
ISING-MODEL SELECTION
RANDOM-FIELDS
BAYESIAN NETWORKS
GRAPHICAL MODELS
TREES
111 Mathematics
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