Stratified graphical models - context-specific independence in graphical models

A1 Journal article (refereed)


Internal Authors/Editors


Publication Details

List of Authors: Henrik Nyman, Johan Pensar, Timo Koski, Jukka Corander
Publication year: 2014
Journal: Bayesian Analysis
Volume number: 9
Issue number: 4
Start page: 883
End page: 908


Abstract

Theory of graphical models has matured over more than three decades
to provide the backbone for several classes of models that are used in a myriad of
applications such as genetic mapping of diseases, credit risk evaluation, reliability
and computer security. Despite their generic applicability and wide adoption, the
constraints imposed by undirected graphical models and Bayesian networks have
also been recognized to be unnecessarily stringent under certain circumstances.
This observation has led to the proposal of several generalizations that aim at
more relaxed constraints by which the models can impose local or context-speci c
dependence structures. Here we consider an additional class of such models, termed
strati ed graphical models. We develop a method for Bayesian learning of these
models by deriving an analytical expression for the marginal likelihood of data under
a speci c subclass of decomposable strati ed models. A non-reversible Markov
chain Monte Carlo approach is further used to identify models that are highly
supported by the posterior distribution over the model space. Our method is illustrated
and compared with ordinary graphical models through application to
several real and synthetic datasets.
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and computer security. Despite their generic applicability and wide adoption, the constraints imposed by undirected graphical models and Bayesian networks have also been recognized to be unnecessarily stringent under certain circumstances. This observation has led to the proposal of several generalizations that aim at more relaxed constraints by which the models can impose local or context-speci fic dependence structures. Here we consider an additional class of such models, termed stratifi ed graphical models. We develop a method for Bayesian learning of these models by deriving an analytical expression for the marginal likelihood of data under a specifi c subclass of decomposable stratifi ed models. A non-reversible Markov chain Monte Carlo approach is further used to identify models that are highly supported by the posterior distribution over the model space. Our method is illustrated and compared with ordinary graphical models through application to several real and synthetic datasets.


Keywords

Bayesian model learning, context-specific interaction model, graphical model, Markov chain Monte Carlo, multivariate discrete distribution

Last updated on 2019-19-10 at 03:26