Generalising realisability in statistical learning theory under epistemic uncertainty
Fabio Cuzzolin
TL;DR
This paper investigates how core PAC guarantees and the realisability assumption in statistical learning theory extend when train and test distributions are drawn from a convex credal set representing epistemic uncertainty. It revisits classical bounds for finite realisable cases and extends to infinite hypothesis spaces using uniform convergence, McDiarmid's inequality, and Rademacher complexity, then provides a sketch of credal generalisation focusing on max-risk over the credal set and uniform credal realisability concepts. The authors derive a distribution-free bound in the finite realisable setting and outline two plausible credal extensions, highlighting challenges posed by distributional ambiguity and the need for new concentration tools. The discussion points to future work on random-set formalisms, concentration inequalities for credal models, and alternative learning frameworks that better capture epistemic uncertainty in data-generating processes.
Abstract
The purpose of this paper is to look into how central notions in statistical learning theory, such as realisability, generalise under the assumption that train and test distribution are issued from the same credal set, i.e., a convex set of probability distributions. This can be considered as a first step towards a more general treatment of statistical learning under epistemic uncertainty.