Hierarchical Dirichlet processes

Hierarchical Dirichlet processes (2004)

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by Yee Whye Teh , Michael I. Jordan , Matthew J. Beal , David M. Blei

Venue:	Journal of the American Statistical Association
Citations:	328 - 44 self

BibTeX

@ARTICLE{Teh04hierarchicaldirichlet,
    author = {Yee Whye Teh and Michael I. Jordan and Matthew J. Beal and David M. Blei},
    title = {Hierarchical Dirichlet processes},
    journal = {Journal of the American Statistical Association},
    year = {2004},
    volume = {101}
}

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Abstract

program. The authors wish to acknowledge helpful discussions with Lancelot James and Jim Pitman and the referees for useful comments. 1 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

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