Seminar: The use of geometry in MCMC

SpeakerBen Calderhead and Simon Byrne
AffiliationUCL
DateFriday, 23 Nov 2012
Time12:30 - 14:00
LocationCruciform B404 - LT2
Event seriesDeepMind CSML Seminar Series
Description

In the first half of this talk, Ben Calderhead will give an introduction to Markov chain Monte Carlo methods, in which he will demonstrate the main challenges encountered when performing inference over many of the complex statistical models that are of interest in current biological scientific research. He will then introduce the connection between statistical models and Riemannian geometry, and show how this allows far more efficient MCMC algorithms to be developed. Finally he will discuss his very recent NIPS paper, which presents a sampling scheme based on a Langevin type diffusion that approximates the local Riemannian geometry. This work extends differential geometric MCMC methods to statistical models where the metric tensor (given by the Expected Fisher Information) is analytically intractable.

In the second part, Simon Byrne will talk about MCMC methods over embedded manifolds. Embedded manifolds, such as simplices and hyperspheres, arise in a variety of statistical models, but can often be difficult to work with computationally. I'll talk about the Hamiltonian Monte Carlo algorithm, and how it may be modified to operate on these complicated spaces by exploiting their unique geometric structure. Applications include dimension reduction models such as mixture models and latent factor models.

Slides for the talk: Ben Calderhead (PDF), Simon Byrne (PDF)

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