Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learnt 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.

翻译：统计学习理论是机器学习的基础，为从（单个）训练集（假定来自未知概率分布）学习到的模型风险提供了理论界限。然而在实际部署中，数据分布可能（且经常）发生变化，导致领域自适应/泛化问题。本文为"置信"学习理论奠定基础，使用凸概率集合（置信集）对数据生成分布的变异性进行建模。我们论证此类置信集可从有限样本的训练集集合中推断得出。针对有限假设空间（分别假设可实现与否）和无限模型空间，推导出了直接推广经典结果的界限。