Labeled Directed Acyclic Graphs: a generalization of context-specific independence in directed graphical models
This work addresses the need for more flexible and interpretable probabilistic models in machine learning and statistics, particularly for domains with discrete data, by extending graphical models to allow local independence structures, though it is incremental as it builds on existing DAG frameworks.
The paper tackles the problem of modeling local structures in conditional probability distributions for discrete variables by introducing labeled directed acyclic graphs (LDAGs), which generalize context-specific independence in directed graphical models, and it develops efficient Bayesian learning methods with analytical marginal likelihood calculations and a novel prior for structure learning, demonstrating properties on real and synthetic data.
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.