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（单一）训练集习得的模型风险提供理论界限，该训练集假定来自未知概率分布。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，采用凸概率集（置信集）对数据生成分布的变异性进行建模。我们认为，这类置信集可从有限训练集样本中推断得出。本文推导了有限假设空间（考虑可实现性与不可实现性两种情况）以及无限模型空间下的界限，这些结果直接推广了经典结论。