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

Johan Pensar, Henrik Nyman, Timo Koski, Jukka Corander

    Tutkimustuotos: LehtiartikkeliArtikkeliTieteellinenvertaisarvioitu

    18 Sitaatiot (Scopus)

    Abstrakti

    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. 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.
    AlkuperäiskieliEi tiedossa
    Sivut503–533
    JulkaisuData Mining and Knowledge Discovery
    Vuosikerta29
    DOI - pysyväislinkit
    TilaJulkaistu - 2014
    OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

    Keywords

    • graphical model
    • context-specific interaction model
    • Markov chain Monte Carlo
    • Directed acyclic graph

    Viittausmuodot