Johan Pensar (Åbo Akademi University): Bayesian learning of Labeled Directed Acyclic Graphs using non-reversible MCMC

An LDAG is a directed acyclic graph for which labels have been added to the edges. The labels represent certain local statements of context-specific independence. A probabilistic graphical model based on an LDAG has thereby a more refined dependence structure than a traditional Bayesian network. 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 to the marginal likelihood, we introduce a novel prior distribution that can appropriately penalize a model for its labeling complexity. To search the model space for high-posterior models, we combine a non-reversible MCMC algorithm with a greedy hill-climbing approach.

Joint work with Henrik Nyman, Timo Koski, and Jukka Corander.