Labeled directed acyclic graphs: a generalization of context-specific independence in directed graphical models

• Autores: Johan Pensar, Henrik Nyman, Timo Koski, Jukka Corander
• Localización: Data mining and knowledge discovery, ISSN 1384-5810, Vol. 29, Nº 2, 2015, págs. 503-533
• Idioma: inglés
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• Resumen

  • 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.