This paper is an attempt to bridge the conceptual gaps between researchers working on the
two widely used approaches based on positive definite kernels: Bayesian learning or …

Information overload is a major obstacle to scientific progress. The explosive growth in
scientific literature and data has made it ever harder to discover useful insights in a large …

A non-parametric extension of control variates is presented. These leverage gradient
information on the sampling density to achieve substantial variance reduction. It is not …

A research frontier has emerged in scientific computation, wherein discretisation error is
regarded as a source of epistemic uncertainty that can be modelled. This raises several …

Bayesian optimization (BO) has emerged during the last few years as an effective approach
to optimize black-box functions where direct queries of the objective are expensive. We …

We show that repulsive random variables can yield Monte Carlo methods with faster
convergence rates than the typical N^-1/2, where N is the number of integrand evaluations …

Many probabilistic models of interest in scientific computing and machine learning have
expensive, black-box likelihoods that prevent the application of standard techniques for …

We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb {P} $
more effectively than iid sampling or standard thinning. Given a suitable reproducing kernel …

Calculation of Bayesian posteriors and model evidences typically requires numerical
integration. Bayesian quadrature (BQ), a surrogate-model-based approach to numerical …

We study kernel quadrature rules with convex weights. Our approach combines the spectral
properties of the kernel with recombination results about point measures. This results in …