Combinatorial Clustering and the Beta Negative Binomial Process.
We develop a Bayesian nonparametric approach to a general family of latent class problems in which individuals can belong simultaneously to multiple classes and where each class can be exhibited multiple times by an individual. We introduce a combinatorial stochastic process known as the negative binomial process ( NBP ) as an infinite-dimensional prior appropriate for such problems. We show that the NBP is conjugate to the beta process, and we characterize the posterior distribution under the beta-negative binomial process ( BNBP) and hierarchical models based on the BNBP (the HBNBP). We study the asymptotic properties of the BNBP and develop a three-parameter extension of the BNBP that exhibits power-law behavior. We derive MCMC algorithms for posterior inference under the HBNBP , and we present experiments using these algorithms in the domains of image segmentation, object recognition, and document analysis.
Tamara
T
Broderick
Lester
L
Mackey
John
J
Paisley
Michael I
MI
Jordan
D000465:Algorithms; D001499:Bayes Theorem; D016000:Cluster Analysis; D003198:Computer Simulation; D007091:Image Processing, Computer-Assisted; D048088:Informatics / Q000379:methods*; D008962:Models, Theoretical; D018709:Statistics, Nonparametric