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 bi...

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Veröffentlicht in:IEEE transactions on pattern analysis and machine intelligence. - 1979. - 37(2015), 2 vom: 01. Feb., Seite 290-306
1. Verfasser: Broderick, Tamara (VerfasserIn)
Weitere Verfasser: Mackey, Lester, Paisley, John, Jordan, Michael I
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2015
Zugriff auf das übergeordnete Werk:IEEE transactions on pattern analysis and machine intelligence
Schlagworte:Journal Article Research Support, U.S. Gov't, Non-P.H.S.
Beschreibung
Zusammenfassung: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
Beschreibung:Date Completed 27.05.2016
Date Revised 10.09.2015
published: Print
Citation Status MEDLINE
ISSN:1939-3539
DOI:10.1109/TPAMI.2014.2318721