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Stratified Graphical Models: Context-Specific Independence in Graphical Models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0003-1489-8512
2014 (English)In: BAYESIAN ANAL, ISSN 1931-6690, Vol. 9, no 4, 883-908 p.Article in journal (Refereed) Published
Abstract [en]

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-specific dependence structures. Here we consider an additional class of such models, termed stratified 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 specific subclass of decomposable stratified 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.

Place, publisher, year, edition, pages
2014. Vol. 9, no 4, 883-908 p.
Keyword [en]
Graphical Model, Context-Specific Interaction Model, Markov Chain Monte Carlo, Bayesian Model Learning, Multivariate Discrete Distribution
National Category
URN: urn:nbn:se:kth:diva-159988DOI: 10.1214/14-BA882ISI: 000347547500008ScopusID: 2-s2.0-84920285419OAI: diva2:790767

QC 20150225

Available from: 2015-02-25 Created: 2015-02-12 Last updated: 2015-02-25Bibliographically approved

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Koski, Timo
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Mathematical Statistics

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