2024/02/01 by Michele Caprio, M. Sultana, Caprio, Michele +5 · 3 citations
Social Sciences · #Artificial Intelligence (cs.AI) #Education and Critical Thinking Development #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML)
paper · pdf · doi:10.48550/arxiv.2402.00957
openalex publication_date 2024/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.