Mixed Membership Modeling: De Finetti and Nonparametrics

• Activity Number: 54
• Type: Invited
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Michael Jordan and Tamara Broderick* and Ashia Wilson
• Companies: UC Berkeley and MIT and UC Berkeley
• Keywords: Bayesian analysis ; Bayesian nonparametrics ; completely random measures

Abstract

One way to conceive of the decade-long development of mixed membership modeling is as a fleshing-out of De Finetti's theorem on exchangeability; the idea that underlying an admixture is a random measure that is being sampled from repeatedly. This perspective naturally leads one into nonparametrics, where the random measure is no longer assumed to have fixed and finite support, and thence into the realm of completely random measures (CRMs), where independence properties deriving from the Poisson process make the programme viable. I will review some of the history of mixed membership from this point of view, focusing in part on the distinction between mixture models and feature models, and discussing some recent research on CRMs, where notions of conjugacy, exponential families and size-biased sampling can be developed in a general nonparametric framework.