Credal Learning Theory
This foundational work addresses domain adaptation issues for machine learning practitioners by extending statistical learning theory to handle distribution shifts.
The paper tackles the problem of domain adaptation and generalization by developing a credal learning theory that models data distribution variability using convex sets of probabilities, deriving bounds for finite and infinite hypothesis spaces that generalize classical statistical learning results.
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.