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...
Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 37(2015), 2 vom: 01. Feb., Seite 290-306 |
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1. Verfasser: | |
Weitere Verfasser: | , , |
Format: | Online-Aufsatz |
Sprache: | English |
Veröffentlicht: |
2015
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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. |
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 |
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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 |