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

A1 Journal article (refereed)


Internal Authors/Editors


Publication Details

List of Authors: Johan Pensar, Henrik Nyman, Timo Koski, Jukka Corander
Publication year: 2014
Journal: Data Mining and Knowledge Discovery
Volume number: 29
Start page: 503
End page: 533


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.
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.


Keywords

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

Last updated on 2019-16-10 at 02:50