Sharing Clusters among Related Groups: Hierarchical Dirichlet Processes

@article{citeulike:635668, 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 necessarily 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 “Chinese restaurant franchise.” 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.}, address = {Cambridge, MA}, author = {Teh, Yee W. and Jordan, Michael I. and Beal, Matthew J. and Blei, David M. }, citeulike-article-id = {635668}, journal = {Advances in Neural Information Processing Systems 17}, keywords = {bayesian, clustering, dirichlet, hierarchical, process}, pages = {1385--1392}, posted-at = {2008-03-05 14:08:52}, priority = {2}, publisher = {MIT Press}, title = {Sharing Clusters among Related Groups: Hierarchical Dirichlet Processes}, url = {http://www.cs.berkeley.edu/\~{}russell/classes/cs294/f05/papers/teh al-2005tr.pdf}, year = {2005} }

TY - JOUR ID - citeulike:635668 L3 - citeulike-article-id:635668 N2 - 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 necessarily 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 “Chinese restaurant franchise.” 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. JF - Advances in Neural Information Processing Systems 17 AD - Cambridge, MA EP - 1392 TI - Sharing Clusters among Related Groups: Hierarchical Dirichlet Processes PB - MIT Press SP - 1385 KW - bayesian KW - clustering KW - dirichlet KW - hierarchical KW - process AU - Teh, Yee AU - Jordan, Michael AU - Beal, Matthew AU - Blei, David PY - 2005/// UR - http://www.cs.berkeley.edu/~russell/classes/cs294/f05/papers/teh al-2005tr.pdf ER -