@article {citation209,
title = {Hierarchical Dirichlet processes},
journal = {Journal of the American Statistical Association},
volume = {101},
year = {2006},
month = {11/2005},
pages = {1566-1581},
abstract = {We consider problems involving groups of data, where each observation within a group is
a draw from a mixture model, and where it is desirable to share mixture components between
groups. We assume that the number of mixture components is unknown a priori and is to be
inferred from the data. In this setting it is natural to consider sets of Dirichlet processes, one
for each group, where the well-known clustering property of the Dirichlet process provides a
nonparametric prior for the number of mixture components within each group. Given our desire
to tie the mixture models in the various groups, we consider a hierarchical model, specifically
one in which the base measure for the child Dirichlet processes is itself distributed according to
a Dirichlet process. Such a base measure being discrete, the child Dirichlet processes necessar-
ily share atoms. Thus, as desired, the mixture models in the different groups necessarily share
mixture components. We discuss representations of hierarchical Dirichlet processes in terms of
a stick-breaking process, and a generalization of the Chinese restaurant process that we refer
to as the {\textquotedblleft}Chinese restaurant franchise.{\textquotedblright} We present Markov chain Monte Carlo algorithms
for posterior inference in hierarchical Dirichlet process mixtures, and describe applications to
problems in information retrieval and text modelling.
},
url = {http://www.cs.berkeley.edu/~jordan/papers/hdp.pdf},
author = {Y. W. Teh and M. I. Jordan and M. J. Beal and D. M. Blei}
}