Abstract

Approximating intractable integrals is a common task in both statistical and scientific computation. When evaluating the function under the integral is computationally expensive—-such as when the function is the output of a fine-grained simulation—-standard Monte Carlo integration can become impractical. This creates a need for for methods that approximate integrals well with as few samples as possible. Bayesian quadrature is a probabilistic integration method in which a Gaussian process prior is placed on the integrand, allowing information about properties of the integrand—-such as smoothness—-to be used for improved sample efficiency. In this talk, I will cover two projects that used Bayesian quadrature to create better estimators: (1) an improved estimator for maximum mean discrepancy when the measure is a pushforward, and (2) estimators for conditional and nested expectations.