Florian Maire(Universit茅 de Montr茅al)
Title: Variance reduction by occluding a Markov chain.
Abstract:
Stochastic algorithms which simulate random variables/processes on a computer to estimate intractable quantities are ubiquitous in Statistics and elsewhere. One such method is Markov chain Monte Carlo which, under mild conditions, offer asymptotical (in time) guarantees. In this talk, we define infinitely many stopping times at which an ergodic Markov chain is occluded by a (conditionally) independent process. The resulting process, called the occluded process, is not Markov, but provided that the stopping times/independent process are cleverly defined, we show that it is ergodic. One particularly powerful way to define the stopping times/independent process leverages the recent advances in ML regarding approximations of probability distributions (divergence minimization, normalizing flows, etc.). We discuss the variance reduction effect of the occluded process through some illustrations and (weak) theoretical results in some limiting regime.
Speaker
Florian Maire is an Associate Professor at Universit茅 de Montr茅al, which he joined in 2018 after a PhD from Paris 6 and Telecom SudParis and a Postdoc at University College Dublin. His research interests are mostly in computational statistics and stochastic optimization.