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SUMMARY:A new MCMC hybrid scheme for Poisson-Kingman Bayesian Nonparametri
 c mixture models - Maria Lomeli-Garcia\, UCL
DTSTART:20150716T100000Z
DTEND:20150716T110000Z
UID:TALK60146@talks.cam.ac.uk
CONTACT:12852
DESCRIPTION:According to "Ghahramani":http://www.nature.com/nature/journal
 /v521/n7553/full/nature14541.html\, models that have a nonparametric compo
 nent give us more flexibility that could lead to better predictive perform
 ance. This is because their capacity to learn does not saturate hence thei
 r predictions should continue to improve as we get more and more data. Fur
 thermore\, we are able to fully consider our uncertainty about predictions
  thanks to the Bayesian paradigm. However\, a major impediment to the wide
 spread use of Bayesian nonparametric models is the problem of inference. O
 ver the years\, many Markov chain Monte Carlo methods have been proposed t
 o perform inference which usually rely on a tailored representation of the
  underlying process. This is an active research area since dealing with th
 is infinite dimensional component forbids the direct use of standard simul
 ation-based methods for posterior inference. Existing methods usually requ
 ire a finite-dimensional representation and there are two main sampling ap
 proaches to facilitate simulation in the case of Bayesian nonparametric mi
 xture models: random truncation and marginalization. These two schemes are
  known in the literature as conditional and marginal samplers. \n\nIn this
  talk\, I will review existing schemes and introduce a novel MCMC scheme f
 or posterior sampling in Bayesian nonparametric mixture models with priors
  that belong to the general Poisson-Kingman class. This general scheme rel
 ies on a new compact way of representing the infinite dimensional componen
 t of the model such that while explicitly representing this infinite compo
 nent it has less memory and storage requirements than previous MCMC scheme
 s. Furthermore\, in the flavour of probabilistic programming\, we view our
  contribution as a step towards wider usage of flexible Bayesian nonparame
 tric models\, as it allows automated inference in probabilistic programs b
 uilt out of a wide variety of Bayesian nonparametric building blocks. I wi
 ll present some comparative simulation results demonstrating the efficacy 
 of the proposed MCMC algorithm against existing "marginal":http://arxiv.or
 g/abs/1407.4211 and "conditional":http://www.tandfonline.com/doi/full/10.1
 080/10618600.2012.681211 MCMC samplers for the σ-Stable Poisson-Kingman s
 ubclass.\n\nJoint work with Yee Whye Teh and Stefano Favaro.
LOCATION:Engineering Department\, CBL Room BE-438
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