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A Bayesian Nonparametric Stochastic Block Model for Directed Acyclic Graphs

by   Clement Lee, et al.

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.


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