webinar register page

Webinar banner
Rémi Bardenet - Monte Carlo integration with repulsive point processes
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 two approaches to faster Monte Carlo rates using interacting particle systems. First, I will show how results from random matrix theory lead to a stochastic version of Gaussian quadrature in any dimension d, with mean square error decreasing as 1/N^{1+1/d}. This quadrature is based on determinantal point processes, which can be argued to be the kernel machine of point processes. Second, I will show how to further take this error rate down assuming the integrand is smooth. In particular, I will give a tight error bound when the integrand belongs to any arbitrary reproducing kernel Hilbert space, using a mixture of determinantal point processes tailored to that space. This mixture is reminiscent of volume sampling, a randomized experimental design used in linear regression.

joint work with Ayoub Belhadji, Pierre Chainais, and Adrien Hardy

Apr 7, 2021 05:00 PM in Paris

Webinar logo
Webinar is over, you cannot register now. If you have any questions, please contact Webinar host: David Rohde.