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SUMMARY:On Independent Samples along the Langevin Dynamics and Algorithm -
  Andre Wibisono\, Yale University
DTSTART:20240524T130000Z
DTEND:20240524T140000Z
UID:TALK213469@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:Sampling from a probability distribution is a fundamental algo
 rithmic task\, and one way to do that is via running a Markov chain. The m
 ixing time of a Markov chain characterizes how long we should run the Mark
 ov chain until the random variable converges to the stationary distributio
 n. In this talk\, we discuss the “independence time”\, which is how lo
 ng we should run a Markov chain until the initial and final random variabl
 es are approximately independent\, in the sense that they have small mutua
 l information. We study this question for two natural Markov chains: the L
 angevin dynamics in continuous time\, and the Unadjusted Langevin Algorith
 m in discrete time. When the target distribution is strongly log-concave\,
  we prove that the mutual information between the initial and final random
  variables decreases exponentially fast along both Markov chains. These co
 nvergence rates are tight\, and lead to an estimate of the independence ti
 me which is similar to the mixing time guarantees of these Markov chains. 
 We illustrate our proofs using the strong data processing inequality and t
 he regularity properties of Langevin dynamics. Based on joint work with Ji
 aming Liang and Siddharth Mitra\, https://arxiv.org/abs/2402.17067.\n
LOCATION:MR12\, Centre for Mathematical Sciences
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