Bayesian Estimation of Integrals: A Multi-task Approach

Abstract

The estimation of intractable integrals is one of the main computational challenges in machine learning. For example, Bayesian machine learning often requires the computation of posterior moments, of the model evidence, or of marginal likelihoods. This is a particular challenge when working with large-scale or computationally expensive models, in which case the cost of integrand evaluations makes most standard Monte Carlo methods prohibitively expensive. In this talk, we will review recent advances in probabilistic numerics, where the problem of numerical integration is itself seen as a Bayesian inference task, which opens up opportunities for uncertainty quantification and active learning. We will focus in particular on approaches based on multi-output Gaussian processes and Stein's method, which allow us to leverage information from related integration tasks.

Bio

Dr Francois-Xavier Briol is a lecturer (equivalent to assistant professor) in the Department of Statistical Science at University College London, and a group leader at The Alan Turing Institute in the Data-Centric Engineering programme. His research focuses on the intersection of computational statistics, machine learning and applied mathematics. He works on statistical computation and inference for large scale and computationally expensive probabilistic models, and is interested in applications in the physical and engineering sciences. Personal website: https://fxbriol.github.io/.