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SUMMARY:The zig-zag and super-efficient sampling for Bayesian analysis of 
 big data - Gareth Roberts (University of Warwick\; University of Warwick)
DTSTART:20180115T161000Z
DTEND:20180115T165500Z
UID:TALK97579@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Standard MCMC methods can scale poorly to big data settings du
 e to the need to evaluate the likelihood at each iteration. There have bee
 n a number of approximate MCMC algorithms that use sub-sampling ideas to r
 educe this computational burden\, but with the drawback that these algorit
 hms no longer target the true posterior distribution. The talk will discus
 s a new family of Monte Carlo methods based upon a multi-dimensional versi
 on of the Zig-Zag process of (Bierkens\, Roberts\, 2016)\, a continuous ti
 me piecewise deterministic Markov process. While traditional MCMC methods 
 are reversible by construction the Zig-Zag process offers a flexible non-r
 eversible alternative. The dynamics of the Zig-Zag process correspond to a
  constant velocity model\, with the velocity of the process switching at e
 vents from a point process. The rate of this point process can be related 
 to the invariant distribution of the process. If we wish to target a given
  posterior distribution\, then rates need to be set equal to the gradient 
 of the log of the posterior. Unlike traditional MCMC\,  Zig-Zag process ca
 n be simulated without discretisation error\, and give conditions for the 
 process to be ergodic. Most importantly\, I will discuss two generalisatio
 ns which have good scaling properties for big data: firstly a sub-sampling
  version of the Zig-Zag process that is an example of an exact approximate
  scheme\; and secondly a control-variate variant of the sub-sampling idea 
 to reduce the variance of our unbiased estimator. Very recent ergodic theo
 ry will also be described.
LOCATION:Seminar Room 1\, Newton Institute
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