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CATEGORIES:Machine Learning @ CUED
SUMMARY:The combinatorial structure underlying a beta proc
esses is that of a continuum of Blackwell-MacQueen
urn schemes - Dr Daniel Roy (University of Cambri
dge)
DTSTART;TZID=Europe/London:20121120T130000
DTEND;TZID=Europe/London:20121120T143000
UID:TALK41632AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/41632
DESCRIPTION:We uncover a novel urn scheme underlying condition
ally independent sequences of Bernoulli processes
that share a common beta process hazard measure.
As shown by Thibaux and Jordan (2007)\, in the spe
cial case when the underlying beta process has a c
onstant concentration function and a finite and no
n-atomic base measure\, the combinatorial structur
e is that of the Indian buffet process (IBP) intro
duced by Griffiths and Ghahramani (2005). By rein
terpreting the beta process introduced by Hjort (1
990) as a continuum of Dirichlet processes\, we ob
tain a simple predictive rule for the general case
\, and then show that a continuum of Pitman-Yor pr
ocesses recovers a three-parameter variant of the
IBP introduced by Teh and Gorur (2009) that exhibi
ts power-law behavior\, as further studied by Brod
erick\, Pitman and Jordan (2012). The idea extend
s to arbitrary exchangeable partition probability
functions. In the same way that hierarchies of Di
richlet processes can be given Chinese restaurant
franchise representations as shown by Teh\, Jordan
\, Beal and Blei (2006)\, one can construct repres
entations of hierarchies of beta processes using t
he stochastic process we uncover. This new perspe
ctive has obvious implications for inference algor
ithms.
LOCATION:Engineering Department\, CBL Room BE-438
CONTACT:Konstantina Palla
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