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CATEGORIES:Statistics
SUMMARY:On the robustness of gradient-based MCMC algorithm
s - Sam Livingstone — University College London
DTSTART;TZID=Europe/London:20191011T140000
DTEND;TZID=Europe/London:20191011T150000
UID:TALK130063AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/130063
DESCRIPTION:We analyse the tension between robustness and effi
ciency for Markov chain Monte Carlo (MCMC) samplin
g algorithms. In particular\, we focus on robustne
ss of MCMC algorithms with respect to heterogeneit
y in the target and their sensitivity to tuning\,
an issue of great practical relevance but still un
derstudied theoretically. We show that the spectra
l gap of the Markov chains induced by classical gr
adient-based MCMC schemes (e.g. Langevin and Hamil
tonian Monte Carlo) decays exponentially fast in t
he degree of mismatch between the scales of the pr
oposal and target distributions\, while for the ra
ndom walk Metropolis (RWM) the decay is linear. Th
is result provides theoretical support to the noti
on that gradient-based MCMC schemes are less robus
t to heterogeneity and more sensitive to tuning. M
otivated by these considerations\, we propose a no
vel and simple to implement gradient-based MCMC al
gorithm\, inspired by the classical Barker accept-
reject rule\, with improved robustness properties.
Extensive theoretical results\, dealing with robu
stness to heterogeneity\, geometric ergodicity and
scaling with dimensionality\, show that the novel
scheme combines the robustness of RWM with the ef
ficiency of classical gradient-based schemes. We i
llustrate with simulation studies how this type of
robustness is particularly beneficial in the cont
ext of adaptive MCMC\, giving examples in which th
e new scheme gives orders of magnitude improvement
s in performance over state-of-the-art alternative
s. \n\n \nThis is joint work with Giacomo Zanella\
, see the preprint here: https://arxiv.org/abs/190
8.11812
LOCATION:MR12
CONTACT:Dr Sergio Bacallado
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