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Labeled Directed Acyclic Graphs: A Generalization of Context-Specific Independence in Directed Graphical Models

Johan Pensar, Henrik Nyman, Timo Koski, Jukka Corander, Labeled Directed Acyclic Graphs: A Generalization of Context-Specific Independence in Directed Graphical Models. Data mining and knowledge discovery 29(2), 503–533, 2014.

http://dx.doi.org/10.1007/s10618-014-0355-0

Abstract:

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.

BibTeX entry:

@ARTICLE{aconv23597,
  title = {Labeled Directed Acyclic Graphs: A Generalization of Context-Specific Independence in Directed Graphical Models},
  author = {Pensar, Johan and Nyman, Henrik and Koski, Timo and Corander, Jukka},
  journal = {Data mining and knowledge discovery},
  volume = {29},
  number = {2},
  pages = {503–533},
  year = {2014},
  keywords = {Directed acyclic graph, Graphical model, Context-specific independence, Bayesian model learning, Markov chain Monte Carlo },
}

Belongs to TUCS Research Unit(s): Institute for Advanced Management Systems Research (IAMSR)

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