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CATEGORIES:Machine Learning @ CUED
SUMMARY:A new MCMC hybrid scheme for Poisson-Kingman Bayes
ian Nonparametric mixture models - Maria Lomeli-Ga
rcia\, UCL
DTSTART;TZID=Europe/London:20150716T110000
DTEND;TZID=Europe/London:20150716T120000
UID:TALK60146AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60146
DESCRIPTION:According to "Ghahramani":http://www.nature.com/na
ture/journal/v521/n7553/full/nature14541.html\, mo
dels that have a nonparametric component give us m
ore flexibility that could lead to better predicti
ve performance. This is because their capacity to
learn does not saturate hence their predictions sh
ould continue to improve as we get more and more d
ata. Furthermore\, we are able to fully consider o
ur uncertainty about predictions thanks to the Bay
esian paradigm. However\, a major impediment to th
e widespread use of Bayesian nonparametric models
is the problem of inference. Over the years\, many
Markov chain Monte Carlo methods have been propos
ed to perform inference which usually rely on a ta
ilored representation of the underlying process. T
his is an active research area since dealing with
this infinite dimensional component forbids the di
rect use of standard simulation-based methods for
posterior inference. Existing methods usually requ
ire a finite-dimensional representation and there
are two main sampling approaches to facilitate sim
ulation in the case of Bayesian nonparametric mixt
ure models: random truncation and marginalization.
These two schemes are known in the literature as
conditional and marginal samplers. \n\nIn this tal
k\, I will review existing schemes and introduce a
novel MCMC scheme for posterior sampling in Bayes
ian nonparametric mixture models with priors that
belong to the general Poisson-Kingman class. This
general scheme relies on a new compact way of repr
esenting the infinite dimensional component of the
model such that while explicitly representing thi
s infinite component it has less memory and storag
e requirements than previous MCMC schemes. Further
more\, in the flavour of probabilistic programming
\, we view our contribution as a step towards wide
r usage of flexible Bayesian nonparametric models\
, as it allows automated inference in probabilisti
c programs built out of a wide variety of Bayesian
nonparametric building blocks. I will present som
e comparative simulation results demonstrating the
efficacy of the proposed MCMC algorithm against e
xisting "marginal":http://arxiv.org/abs/1407.4211
and "conditional":http://www.tandfonline.com/doi/f
ull/10.1080/10618600.2012.681211 MCMC samplers for
the σ-Stable Poisson-Kingman subclass.\n\nJoint w
ork with Yee Whye Teh and Stefano Favaro.
LOCATION:Engineering Department\, CBL Room BE-438
CONTACT:
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