Speaker: Rémi Bardenet (CNRS) is a recipient of a 2021 CNRS bronze medal and PI of the ERC Starting Grant Blackjack (https://rbardenet.github.io/).
Place: Amphi Chappe/Lamarr, 6 avenue des arts, La Doua Campus
Title: Monte Carlo integration with repulsive point processes
Abstract: Joint work with Adrien Hardy, Ayoub Belhadji, Pierre Chainais, Diala Hawat, and Raphaël Lachièze-Rey.
Monte Carlo integration is the workhorse of Bayesian inference, but the mean square error of Monte Carlo estimators decreases slowly, typically as 1/N, where N is the number of integrand evaluations. This becomes a bottleneck in Bayesian applications where evaluating the integrand can take tens of seconds, like in the life sciences, where evaluating the likelihood often requires solving a large system of differential equations. I will present recent results on variance reduction and fast Monte Carlo rates using interacting particle systems. The underlying idea is that to integrate a function with a handful of evaluations, one should evaluate the function at well-spread (random) locations, where “well-spread” means “so that one can benefit from the smoothness of the target function”.