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SUMMARY:The combinatorial structure underlying a beta processes is that of
  a continuum of Blackwell-MacQueen urn schemes - Dr Daniel Roy (University
  of Cambridge)
DTSTART:20121120T130000Z
DTEND:20121120T143000Z
UID:TALK41632@talks.cam.ac.uk
CONTACT:Konstantina Palla
DESCRIPTION:We uncover a novel urn scheme underlying conditionally indepen
 dent sequences of Bernoulli processes that share a common beta process haz
 ard measure.  As shown by Thibaux and Jordan (2007)\, in the special case 
 when the underlying beta process has a constant concentration function and
  a finite and non-atomic base measure\, the combinatorial structure is tha
 t of the Indian buffet process (IBP) introduced by Griffiths and Ghahraman
 i (2005).  By reinterpreting the beta process introduced by Hjort (1990) a
 s a continuum of Dirichlet processes\, we obtain a simple predictive rule 
 for the general case\, and then show that a continuum of Pitman-Yor proces
 ses recovers a three-parameter variant of the IBP introduced by Teh and Go
 rur (2009) that exhibits power-law behavior\, as further studied by Broder
 ick\, Pitman and Jordan (2012).  The idea extends to arbitrary exchangeabl
 e partition probability functions.  In the same way that hierarchies of Di
 richlet processes can be given Chinese restaurant franchise representation
 s as shown by Teh\, Jordan\, Beal and Blei (2006)\, one can construct repr
 esentations of hierarchies of beta processes using the stochastic process 
 we uncover.  This new perspective has obvious implications for inference a
 lgorithms.
LOCATION:Engineering Department\, CBL Room BE-438
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