Gaussian processes scale prohibitively with the size of the dataset. In response, many
approximation methods have been developed, which inevitably introduce approximation …

Likelihood-free inference methods typically make use of a distance between simulated and
real data. A common example is the maximum mean discrepancy (MMD), which has …

Probabilistic numerical computation formalises the connection between machine learning
and applied mathematics. Numerical algorithms approximate intractable quantities from …

Mechanistic models with differential equations are a key component of scientific applications
of machine learning. Inference in such models is usually computationally demanding …

Bayesian probabilistic numerical methods for numerical integration offer significant
advantages over their non-Bayesian counterparts: they can encode prior information about …

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 …

Emukit is a highly flexible Python toolkit for enriching decision making under uncertainty with
statistical emulation. It is particularly pertinent to complex processes and simulations where …

Abstract Multilevel Monte Carlo is a key tool for approximating integrals involving expensive
scientific models. The idea is to use approximations of the integrand to construct an …

To enable closed form conditioning, a common assumption in Gaussian process (GP)
regression is independent and identically distributed Gaussian observation noise. This …

Sequential numerical methods for integrating initial value problems (IVPs) can be
prohibitively expensive when high numerical accuracy is required over the entire interval of …