@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} }