  We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical
topic modeling. The nHDP is a generalization of the nested Chinese restaurant
process (nCRP) that allows each word to follow its own path to a topic node
according to a document-specific distribution on a shared tree. This alleviates
the rigid, single-path formulation of the nCRP, allowing a document to more
easily express thematic borrowings as a random effect. We derive a stochastic
variational inference algorithm for the model, in addition to a greedy subtree
selection method for each document, which allows for efficient inference using
massive collections of text documents. We demonstrate our algorithm on 1.8
million documents from The New York Times and 3.3 million documents from
Wikipedia.
