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SUMMARY:Differential Geometric MCMC Methods - Prof. Mark Girolami (UCL)
DTSTART:20110201T110000Z
DTEND:20110201T120000Z
UID:TALK28511@talks.cam.ac.uk
CONTACT:Zoubin Ghahramani
DESCRIPTION:In recent years a reliance on MCMC methods has been developing
  as the "last resort" to perform inference over increasingly sophisticated
  statistical models used to describe complex phenomena. This presents a ma
 jor challenge as issues surrounding correct and efficient MCMC-based stati
 stical inference over such models are of growing importance. This talk wil
 l argue that differential geometry provides the tools required to develop 
 MCMC sampling methods suitable for challenging statistical models. By defi
 ning appropriate Riemannian metric tensors and corresponding Levi-Civita m
 anifold connections MCMC methods based on Langevin diffusions across the m
 odel manifold are developed. Furthermore proposal mechanisms which follow 
 geodesic flows across the manifold will be presented. The optimality of th
 ese methods in terms of mixing time shall be discussed and the strengths (
 and weaknesses) of such methods will be experimentally assessed on a range
  of statistical models such as Log-Gaussian Cox Point Process models and M
 ixture Models\, inference over Latent Dirichlet Allocation and Copula Proc
 ess style models will also be considered. This talk is based on work that 
 was presented as a Discussion Paper to the Royal Statistical Society and a
  dedicated website with Matlab codes is available at http://www.ucl.ac.uk/
 statistics/research/rmhmc
LOCATION:Engineering Department\, CBL Room 438
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