Batch Selection for Parallelisation of Bayesian Quadrature

Abstract: Integration over non-negative integrands is a central problem in machine learning (e.g. for model averaging, (hyper-)parameter marginalisation, and computing posterior predictive distributions). Bayesian Quadrature is a probabilistic numerical integration technique that performs promisingly when compared to traditional Markov Chain Monte Carlo methods. However, in contrast to easily-parallelised MCMC methods, Bayesian Quadrature methods have, thus far, been essentially serial in nature, selecting a single point to sample at each step of the algorithm. We deliver methods to select batches of points at each step, based upon those recently presented in the Batch Bayesian Optimisation literature. Such parallelisation significantly reduces computation time, especially when the integrand is expensive to sample.