Abstract

Machine learning systems increasingly support high-stakes decisions in domains such as healthcare, autonomous systems, and scientific discovery, where reliable assessment of uncertainty is as important as accurate prediction. While modern probabilistic models estimate predictive distributions, they remain uncertain about the quality of these predictions due to finite data, model misspecification, and optimisation error. This talk introduces the notion of higher-order uncertainty—uncertainty about the predictive distribution itself—and surveys the principal approaches for representing it. We begin by reviewing classical probabilistic prediction and distinguish aleatoric from epistemic uncertainty. We then discuss Bayesian approaches, including Gaussian processes, Bayesian neural networks, and deep ensembles, highlighting both their conceptual foundations and computational challenges. The second part introduces credal prediction, which represents uncertainty through sets of plausible probability distributions rather than distributions over distributions, providing an alternative semantics for modelling incomplete knowledge. Finally, we discuss how higher-order uncertainty can be quantified and evaluated in downstream tasks such as selective prediction and out-of-distribution detection, and examine recent evidence comparing distribution-based and set-based representations. The talk aims to provide a unified overview of modern uncertainty-aware machine learning while highlighting open challenges in faithfully representing and reasoning about uncertainty.

About the Speaker

Siu Lun Chau is an Assistant Professor at the College of Computing and Data Science, Nanyang Technological University (NTU), Singapore. He received his DPhil in Statistics in 2023 and his MMath in Mathematics and Statistics in 2018, both from the University of Oxford. From 2023 to 2025, he was a Postdoctoral Researcher at the CISPA Helmholtz Centre for Information Security in Saarbrücken, Germany. His research focuses on the theoretical foundations and methodological development of epistemic uncertainty-aware machine learning. In particular, he leverages tools from imprecise probabilities, cooperative game theory, and kernel methods to represent, quantify, and resolve epistemic uncertainty, as well as to support learning and decision-making under uncertainty. His work has been recognised via an IJAR Young Researcher Award (First prize) along with several spotlight and oral presentations at leading machine learning conferences, including UAI, AAAI, ICML, and NeurIPS.