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Labeled directed acyclic graphs: a generalization of context-specific independence in directed graphical models
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.ORCID iD: 0000-0003-1489-8512
2015 (English)In: Data mining and knowledge discovery, ISSN 1384-5810, E-ISSN 1573-756X, Vol. 29, no 2, 503-533 p.Article in journal (Refereed) Published
Abstract [en]

We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such that unrestricted label sets determine which edges can be deleted from the underlying directed acyclic graph (DAG) for a given context. Several properties of these models are derived, including a generalization of the concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is enabled by introducing an LDAG-based factorization of the Dirichlet prior for the model parameters, such that the marginal likelihood can be calculated analytically. In addition, we develop a novel prior distribution for the model structures that can appropriately penalize a model for its labeling complexity. A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill climbing approach is used for illustrating the useful properties of LDAG models for both real and synthetic data sets.

Place, publisher, year, edition, pages
2015. Vol. 29, no 2, 503-533 p.
Keyword [en]
Directed acyclic graph, Graphical model, Context-specific independence, Bayesian model learning, Markov chain Monte Carlo
National Category
Computer Science
Identifiers
URN: urn:nbn:se:kth:diva-161600DOI: 10.1007/s10618-014-0355-0ISI: 000349369300007Scopus ID: 2-s2.0-84923215211OAI: oai:DiVA.org:kth-161600DiVA: diva2:798005
Note

QC 20150325

Available from: 2015-03-25 Created: 2015-03-13 Last updated: 2017-12-04Bibliographically approved

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Koski, Timo

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