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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The zig-zag and super-efficient sampling for Bayes
ian analysis of big data - Gareth Roberts (Univers
ity of Warwick\; University of Warwick)
DTSTART;TZID=Europe/London:20180115T161000
DTEND;TZID=Europe/London:20180115T165500
UID:TALK97579AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/97579
DESCRIPTION:Standard MCMC methods can scale poorly to big data
settings due to the need to evaluate the likeliho
od at each iteration. There have been a number of
approximate MCMC algorithms that use sub-sampling
ideas to reduce this computational burden\, but wi
th the drawback that these algorithms no longer ta
rget the true posterior distribution. The talk wil
l discuss a new family of Monte Carlo methods base
d upon a multi-dimensional version of the Zig-Zag
process of (Bierkens\, Roberts\, 2016)\, a continu
ous time piecewise deterministic Markov process. W
hile traditional MCMC methods are reversible by co
nstruction the Zig-Zag process offers a flexible n
on-reversible alternative. The dynamics of the Zig
-Zag process correspond to a constant velocity mod
el\, with the velocity of the process switching at
events from a point process. The rate of this poi
nt process can be related to the invariant distrib
ution of the process. If we wish to target a given
posterior distribution\, then rates need to be se
t equal to the gradient of the log of the posterio
r. Unlike traditional MCMC\, Zig-Zag process can
be simulated without discretisation error\, and gi
ve conditions for the process to be ergodic. Most
importantly\, I will discuss two generalisations w
hich have good scaling properties for big data: fi
rstly a sub-sampling version of the Zig-Zag proces
s that is an example of an exact approximate schem
e\; and secondly a control-variate variant of the
sub-sampling idea to reduce the variance of our un
biased estimator. Very recent ergodic theory will
also be described.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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