Hierarchical Dirichlet Processes
A Dirichlet process (DP) is a random probability measure that concentrates on discrete measures. It has interesting and well-explored connections to various topics in combinatorics and probability. It has also played an important role in nonparametric Bayesian statistics, via sampling algorithms that are based on its exchangeability properties. I define a hierarchical Dirichlet process (HDP), in which the base measure for each of a set of child DPs is itself distributed according to a DP. I discuss representations of HDPs in terms of stick-breaking processes and a generalization of the Chinese restaurant process referred to as a “Chinese restaurant franchise.” I discuss Monte Carlo and variational algorithms for posterior inference in HDP mixtures, and describe applications to problems in information retrieval and bioinformatics.
[Joint work with Yee Whye Teh, Matt Beal and David Blei.]