Gibbs Sampling for (Coupled) Infinite Mixture Models in the Stick Breaking Representation
Ian Porteous, Alexander Ihler, Padhraic Smyth, Max Welling
Nonparametric Bayesian approaches to clustering, information retrieval, language modeling and object recognition have recently shown great promise as a new paradigm for unsupervised data analysis. Most contributions have focused on the Dirichlet process mixture models or extensions thereof for which efficient Gibbs samplers exist. In this paper we explore Gibbs samplers for infinite complexity mixture models in the stick breaking representation. The advantage of this representation is improved modeling flexibility. For instance, one can design the prior distribution over cluster sizes or couple multiple infinite mixture models (e.g. over time) at the level of their parameters (i.e. the dependent Dirichlet process model). However, Gibbs samplers for infinite mixture models (as recently introduced in the statistics literature) seem to mix poorly over cluster labels. Among others issues, this can have the adverse effect that labels for the same cluster in coupled mixture models are mixed up. We introduce additional moves in these samplers to improve mixing over cluster labels and to bring clusters into correspondence. An application to modeling of storm trajectories is used to illustrate these ideas.
PDF Link: /papers/06/p385-porteous.pdf
AUTHOR = "Ian Porteous
and Alexander Ihler and Padhraic Smyth and Max Welling",
TITLE = "Gibbs Sampling for (Coupled) Infinite Mixture Models in the Stick Breaking Representation",
BOOKTITLE = "Proceedings of the Twenty-Second Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-06)",
PUBLISHER = "AUAI Press",
ADDRESS = "Arlington, Virginia",
YEAR = "2006",
PAGES = "385--392"