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CATEGORIES:Statistics
SUMMARY:On Independent Samples along the Langevin Dynamics
and Algorithm - Andre Wibisono\, Yale University
DTSTART;TZID=Europe/London:20240524T140000
DTEND;TZID=Europe/London:20240524T150000
UID:TALK213469AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/213469
DESCRIPTION:Sampling from a probability distribution is a fund
amental algorithmic task\, and one way to do that
is via running a Markov chain. The mixing time of
a Markov chain characterizes how long we should ru
n the Markov chain until the random variable conve
rges to the stationary distribution. In this talk\
, we discuss the “independence time”\, which is ho
w long we should run a Markov chain until the init
ial and final random variables are approximately i
ndependent\, in the sense that they have small mut
ual information. We study this question for two na
tural Markov chains: the Langevin dynamics in cont
inuous time\, and the Unadjusted Langevin Algorith
m in discrete time. When the target distribution i
s strongly log-concave\, we prove that the mutual
information between the initial and final random v
ariables decreases exponentially fast along both M
arkov chains. These convergence rates are tight\,
and lead to an estimate of the independence time w
hich is similar to the mixing time guarantees of t
hese Markov chains. We illustrate our proofs using
the strong data processing inequality and the reg
ularity properties of Langevin dynamics. Based on
joint work with Jiaming Liang and Siddharth Mitra\
, https://arxiv.org/abs/2402.17067.\n
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Dr Sergio Bacallado
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