A Bayesian Nonparametric Stochastic Block Model for Directed Acyclic Graphs

Directed acyclic graphs (DAGs) are commonly used in statistics as models, such as Bayesian networks. In this article, we propose a stochastic block model for data that are DAGs. Two main features of this model are the incorporation of the topological ordering of nodes as a parameter, and the use of the Pitman-Yor process as the prior for the allocation vector. In the resultant Markov chain Monte Carlo sampler, not only are the topological ordering and the number of groups inferred, but a model selection step is also included to select between the two regimes of the Pitman-Yor process. The model and the sampler are applied to two citation networks.