  Dirichlet Process(DP) is a Bayesian non-parametric prior for infinite mixture
modeling, where the number of mixture components grows with the number of data
items. The Hierarchical Dirichlet Process (HDP), is an extension of DP for
grouped data, often used for non-parametric topic modeling, where each group is
a mixture over shared mixture densities. The Nested Dirichlet Process (nDP), on
the other hand, is an extension of the DP for learning group level
distributions from data, simultaneously clustering the groups. It allows group
level distributions to be shared across groups in a non-parametric setting,
leading to a non-parametric mixture of mixtures. The nCRF extends the nDP for
multilevel non-parametric mixture modeling, enabling modeling topic
hierarchies. However, the nDP and nCRF do not allow sharing of distributions as
required in many applications, motivating the need for multi-level
non-parametric admixture modeling. We address this gap by proposing multi-level
nested HDPs (nHDP) where the base distribution of the HDP is itself a HDP at
each level thereby leading to admixtures of admixtures at each level. Because
of couplings between various HDP levels, scaling up is naturally a challenge
during inference. We propose a multi-level nested Chinese Restaurant Franchise
(nCRF) representation for the nested HDP, with which we outline an inference
algorithm based on Gibbs Sampling. We evaluate our model with the two level
nHDP for non-parametric entity topic modeling where an inner HDP creates a
countably infinite set of topic mixtures and associates them with author
entities, while an outer HDP associates documents with these author entities.
In our experiments on two real world research corpora, the nHDP is able to
generalize significantly better than existing models and detect missing author
entities with a reasonable level of accuracy.
