Credal Learning Theory

• URL: http://arxiv.org/abs/2402.00957v4
• Date: Wed, 23 Oct 2024 15:40:23 GMT
• Title: Credal Learning Theory
• Authors: Michele Caprio, Maryam Sultana, Eleni Elia, Fabio Cuzzolin,
• Abstract summary: We lay the foundations for a credal' theory of learning, using convex sets of probabilities to model the variability in the data-generating distribution. Bounds are derived for the case of finite hypotheses spaces, as well as infinite model spaces, which directly generalize classical results.
• Score: 4.64390130376307
• License:
• 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.

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