The Hierarchical Dirichlet Process (HDP) is a Bayesian non-parametric prior for grouped data, such as collections of documents, where each group is a mixture of a set of shared mixture densities, or topics, where the number of topics is not fixed, but grows with data size. The Nested Dirichlet Process (NDP) builds on the HDP to cluster the documents, but allowing them to choose only from a set of specific topic mixtures. In many applications, such a set of topic mixtures may be identified with the set of entities for the collection. However, in many applications, multiple entities are associated with documents, and often the set of entities may also not be known completely in advance. In this paper, we address this problem using a nested HDP (nHDP), where the base distribution of an outer HDP is itself an HDP. The inner HDP creates a countably infinite set of topic mixtures and associates them with entities, while the outer HDP associates documents with these entities or topic mixtures. Making use of a nested Chinese Restaurant Franchise (nCRF) representation for the nested HDP, we propose a collapsed Gibbs sampling based inference algorithm for the model. Because of couplings between two HDP levels, scaling up is naturally a challenge for the inference algorithm. We propose an inference algorithm by extending the direct sampling scheme of the HDP to two levels. In our experiments on two real world research corpora, we show that, even when large fractions of author entities are hidden, the nHDP is able to generalize significantly better than existing models. More importantly, we are able to detect missing authors at a reasonable level of accuracy.
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