Bay Area Discrete Math Day XII: Hierarchial Dirichlet Processes
Bay Area Discrete Math Day XII
April 15, 2006
Michael Jordan (UC Berkeley)
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.