The Beta Process, Exchangeable Feature Models, and the Feature Paintbox

• Activity Number: 436
• Type: Invited
• Date/Time: Wednesday, August 1, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Tamara Broderick*+ and Michael I Jordan and Jim Pitman
• Companies: University of California at Berkeley and University of California at Berkeley and University of California at Berkeley
• Keywords: Bayesian nonparametrics ; beta process ; exchangeability ; feature models

Abstract

While the beta process has opened up a realm of practical Bayesian nonparametric feature modeling much as the Dirichlet process did for Bayesian nonparametric clustering modeling, we have yet to see a treatment of the full class of exchangeable feature models. To that end, we examine models such as the beta-Bernoulli process as examples of this larger class. Just as the exchangeable partition probability function (EPPF) can be used to describe the distribution of cluster membership under an exchangeable clustering model, we examine an analogous "exchangeable feature probability function' for certain types of feature models. Moreover, recalling Kingman's paintbox theorem as a characterization of the class of exchangeable clustering models, we study a similar construction in the feature modeling case.