Conditional Bayesian Quadrature

Zonghao Chen, Masha Naslidnyk, Arthur Gretton, Francois-Xavier Briol

Keywords: Bayesian Quadrature, Probabilistic Numerics, Gaussian Process, Conditional Expectation

TL;DR: We propose a novel approach for estimating conditional expectations through the framework of Bayesian quadrature with a fast convergence rate.

Abstract: We propose a novel approach for estimating conditional or parametric expectations in the setting where obtaining samples or evaluating integrands is costly. Through the framework of probabilistic numerical methods (such as Bayesian quadrature), our novel approach allows to incorporates prior information about the integrands especially the prior smoothness knowledge about the integrands and the conditional expectation. As a result, our approach provides a way of quantifying uncertainty and leads to a fast convergence rate, which is confirmed both theoretically and empirically on challenging tasks in Bayesian sensitivity analysis, computational finance and decision making under uncertainty.

Submission Number: 16