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 use `cascades' 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.