Infinite State Bayes-Nets for Structured Domains

A general modeling framework is proposed that unifies nonparametric-Bayesian models, topic-models and Bayesian networks. This class of infinite state Bayes nets (ISBN) can be viewed as directed networks of hierarchical Dirichlet processes' (HDPs) where the domain of the variables can be structured (e.g. words in documents or features in images). To model the structure and to share groups between them we usecascades' of Dirichlet priors. We show that collapsed Gibbs sampling can be done efficiently in these models by leveraging the structure of the Bayes net and using the forward-filtering-backward-sampling algorithm for junction trees. Existing models, such as nested-DP, Pachinko allocation, mixed membership models etc. are described as ISBNs. Two experiments have been implemented to illustrate these ideas.