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Jon Cockayne

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5 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

SMRS: advocating a unified reporting standard for surrogate models in the artificial intelligence era.

Elizaveta Semenova
Siobhan Mackenzie Hall
Timothy James Hitge
Alisa Sheinkman
Jon Cockayne

Surrogate models are widely used to approximate complex systems across science and engineering to reduce computational costs. Despite their widespread adoption, the field lacks standardisation across key stages of the modelling pipeline, including data sampling, model selection, evaluation, and downstream analysis. This fragmentation limits reproducibility and cross-domain utility – a challengefurther exacerbated by the rapid proliferation of AI-driven surrogate models. We argue for the urgent need to establish a structured reporting standard, the Surrogate Model Reporting Standard (SMRS), that systematically captures essential design and evaluation choices while remaining agnostic to implementation specifics. By promoting a standardised yet flexible framework, we aim to improve the reliabilityof surrogate modelling, foster interdisciplinary knowledge transfer, and, as a result, accelerate scientific progress in the AI era.

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TMLR Journal 2023 Journal Article

A probabilistic Taylor expansion with Gaussian processes

Toni Karvonen
Jon Cockayne
Filip Tronarp
Simo Särkkä

We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior covariance kernel belongs to the class of Taylor kernels, which can be written in a certain power series form. We discuss and prove some results on maximum likelihood estimation of parameters of Taylor kernels. The proposed framework is a special case of Gaussian process regression based on data that is orthogonal in the reproducing kernel Hilbert space of the covariance kernel.

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JMLR Journal 2022 Journal Article

Testing Whether a Learning Procedure is Calibrated

Jon Cockayne
Matthew M. Graham
Chris J. Oates
T. J. Sullivan
Onur Teymur

A learning procedure takes as input a dataset and performs inference for the parameters $\theta$ of a model that is assumed to have given rise to the dataset. Here we consider learning procedures whose output is a probability distribution, representing uncertainty about $\theta$ after seeing the dataset. Bayesian inference is a prime example of such a procedure, but one can also construct other learning procedures that return distributional output. This paper studies conditions for a learning procedure to be considered calibrated, in the sense that the true data-generating parameters are plausible as samples from its distributional output. A learning procedure whose inferences and predictions are systematically over- or under-confident will fail to be calibrated. On the other hand, a learning procedure that is calibrated need not be statistically efficient. A hypothesis-testing framework is developed in order to assess, using simulation, whether a learning procedure is calibrated. Several vignettes are presented to illustrate different aspects of the framework. [abs] [ pdf ][ bib ] &copy JMLR 2022. ( edit, beta )

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JMLR Journal 2021 Journal Article

Probabilistic Iterative Methods for Linear Systems

Jon Cockayne
Ilse C.F. Ipsen
Chris J. Oates
Tim W. Reid

This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x} \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x} = \mathbf{b}$. Classically, an iterative method produces a sequence $\mathbf{x}_m$ of approximations that converge to $\mathbf{x}$ in $\mathbb{R}^d$. Our approach, instead, lifts a standard iterative method to act on the set of probability distributions, $\mathcal{P}(\mathbb{R}^d)$, outputting a sequence of probability distributions $\mu_m \in \mathcal{P}(\mathbb{R}^d)$. The output of a probabilistic iterative method can provide both a "best guess" for $\mathbf{x}$, for example by taking the mean of $\mu_m$, and also probabilistic uncertainty quantification for the value of $\mathbf{x}$ when it has not been exactly determined. A comprehensive theoretical treatment is presented in the case of a stationary linear iterative method, where we characterise both the rate of contraction of $\mu_m$ to an atomic measure on $\mathbf{x}$ and the nature of the uncertainty quantification being provided. We conclude with an empirical illustration that highlights the potential for probabilistic iterative methods to provide insight into solution uncertainty. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2021. ( edit, beta )

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ICML Conference 2017 Conference Paper

On the Sampling Problem for Kernel Quadrature

François-Xavier Briol
Chris J. Oates
Jon Cockayne
Wilson Ye Chen
Mark A. Girolami

The standard Kernel Quadrature method for numerical integration with random point sets (also called Bayesian Monte Carlo) is known to converge in root mean square error at a rate determined by the ratio s/d, where s and d encode the smoothness and dimension of the integrand. However, an empirical investigation reveals that the rate constant C is highly sensitive to the distribution of the random points. In contrast to standard Monte Carlo integration, for which optimal importance sampling is well-understood, the sampling distribution that minimises C for Kernel Quadrature does not admit a closed form. This paper argues that the practical choice of sampling distribution is an important open problem. One solution is considered; a novel automatic approach based on adaptive tempering and sequential Monte Carlo. Empirical results demonstrate a dramatic reduction in integration error of up to 4 orders of magnitude can be achieved with the proposed method.

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