Credal Learning Theory

Michele Caprio, Maryam Sultana, Eleni Elia, Fabio Cuzzolin

Keywords: Statistical learning, imprecise probabilities, credal sets, epistemic and aleatory uncertainties

TL;DR: We develop Credal Learning Theory, which allows to derive tighter bounds wrt SLT by leveraging a finite sample of training sets

Abstract:

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment, however, the data distribution may (and often does) vary, causing domain adaptation/generalization issues. In this paper we lay the foundations for a `credal' theory of learning, using convex sets of probabilities (credal sets) to model the variability in the data-generating distribution. Such credal sets, we argue, may be inferred from a finite sample of training sets. Bounds are derived for the case of finite hypotheses spaces (both assuming realizability or not), as well as infinite model spaces, which directly generalize classical results.

Primary Area: Learning theory

Submission Number: 12019