Presented by:
Chris Sherlock
Date:
Thursday 6th July 2017 - 16:15 to 17:00
Venue:
INI Seminar Room 1
Abstract:
The Bouncy Particle Sampler (BPS) is a continuous-time, non-reversible
MCMC algorithm that shows great promise in efficiently sampling from
certain high-dimensional distributions; a particle moves with a fixed
velocity except that occasionally it "bounces" off the hyperplane
perpendicular to the gradient of the target density. One practical
difficulty is that for each specific target distribution, a
locally-valid upper bound on the component of the gradient in the
direction of movement must be found so as to allow for simulation of the
bounce times via Poisson thinning; for efficient implementation this
bound should also be tight. In dimension $d=1$, the discrete-time
version of the Bouncy Particle Sampler (and, equivalently, of the
Zig-Zag sampler, another continuous-time, non-reversible algorithm) is
known to consist of fixing a time step, $\Delta t$, and proposing a
shift of $v \Delta t$ which is accepted with a probability dependent on
the ratio of target evaluated at the proposed and current positions; on
rejection the velocity is reversed. We present a discrete-time version
of the BPS that is valid in any dimension $d\ge 1$ and the limit of
which (as $\Delta t\downarrow 0$) is the BPS, which is rejection free.
The Discrete BPS has the advantages of non-reversible algorithms in
terms of mixing, but does not require an upper bound on a Poisson
intensity and so is straightforward to apply to complex targets, such as
those which can be evaluated pointwise but for which general
properties, such as local or global Lipshitz bounds on derivatives,
cannot be obtained. [Joint work with Dr. Alex Thiery].
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