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SUMMARY:Feature allocations\, probability functions\, and paintboxes - Tam
 ara Broderick (UC Berkeley)
DTSTART:20130227T113000Z
DTEND:20130227T123000Z
UID:TALK43745@talks.cam.ac.uk
CONTACT:Zoubin Ghahramani
DESCRIPTION:The problem of inferring a clustering of a data set has been t
 he subject of much research in Bayesian analysis\, and there currently exi
 sts a solid mathematical foundation for Bayesian approaches to clustering.
  In particular\, the class of probability distributions over partitions of
  a data set has been characterized in a number of ways\, including via exc
 hangeable partition probability functions (EPPFs) and the Kingman paintbox
 . Here\, we develop a generalization of the clustering problem\, called fe
 ature allocation\, where we allow each data point to belong to an arbitrar
 y\, non-negative integer number of groups\, now called features or topics.
  We define and study an "exchangeable feature probability function" (EFPF)
 ---analogous to the EPPF in the clustering setting---for certain types of 
 feature models. Moreover\, we introduce a "feature paintbox" characterizat
 ion---analogous to the Kingman paintbox for clustering---of the class of e
 xchangeable feature models. We use this feature paintbox construction to p
 rovide a further characterization of the subclass of feature allocations t
 hat have EFPF representations.
LOCATION:Engineering Department\, CBL Room BE-438
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