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CATEGORIES:Machine Learning @ CUED
SUMMARY:Stable Poisson-Kingman species sampling priors gen
erated by general ordered size biased generalized
gamma mixing distributions - Prof. Lancelot James
(HKUST)
DTSTART;TZID=Europe/London:20140508T110000
DTEND;TZID=Europe/London:20140508T123000
UID:TALK52235AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/52235
DESCRIPTION: Discrete random distribution functions play a cen
tral role in applications in Bayesian Nonparametri
cs\, Statistical Machine Learning\, and also in th
e fields broadly defined as employing Combinatoria
l Stochastic processes. Arguably the most popular
models are the Dirichlet Process and its two Param
eter extension derived from a stable subordinator\
, the latter process\nis also known as Pitman-Yor
process. \nPerhaps the third most popular model\,
and one which is being used more frequently\, is t
he class obtained by normalizing a generalized ga
mma subordinator. The law of a generalized gamma r
andom variable is defined by exponentially tilting
a stable density. \nAs we shall describe\, all mo
dels can be considered in a unified way by using t
he Poisson-Kingman framework applied to a stable s
ubordinator. This amounts to conditioning on the t
otal mass of a normalized stable process and then
mixing over a new distribution of the total mass.
\n The focus of this talk will be based on new cl
asses of models that encompass the special cases m
entioned above. These classes are defined by mixin
g over random variables based on the expectation o
f a generalized gamma variable raised to an arbitr
ary real valued power. \n\nOur results include exp
licit stick-breaking representations derived from
a generalized residual allocation scheme for this
entire class. Representations in terms of normaliz
ed subordinators. A posterior analysis etc. What i
s quite interesting is that these results can be s
een to arise from mappings that project random var
iables in a lower ordered class to higher ones. Fu
rthermore this necessitates randomization of a gen
eralized gamma parameter. If time permits we shall
describe how our analysis leads to transparent re
sults related to recent work on species richness e
stimators.\n
LOCATION:Engineering Department\, CBL Room BE-438
CONTACT:Zoubin Ghahramani
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