Nested Hierarchical Dirichlet Processes

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.Comment: To appear in IEEE Transactions on Pattern Analysis and Machine Intelligence, Special Issue on Bayesian Nonparametric

The semi-hierarchical Dirichlet Process and its application to clustering homogeneous distributions

Assessing homogeneity of distributions is an old problem that has received considerable attention, especially in the nonparametric Bayesian literature. To this effect, we propose the semi-hierarchical Dirichlet process, a novel hierarchical prior that extends the hierarchical Dirichlet process of Teh et al. (2006) and that avoids the degeneracy issues of nested processes recently described by Camerlenghi et al. (2019a). We go beyond the simple yes/no answer to the homogeneity question and embed the proposed prior in a random partition model; this procedure allows us to give a more comprehensive response to the above question and in fact find groups of populations that are internally homogeneous when I greater or equal than 2 such populations are considered. We study theoretical properties of the semi-hierarchical Dirichlet process and of the Bayes factor for the homogeneity test when I = 2. Extensive simulation studies and applications to educational data are also discussed