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，它为利用（单一）训练集（假设来自未知概率分布）所习得模型的风险提供了理论界限。然而在实际部署中，数据分布可能（且常常会）发生变化，导致领域自适应/泛化问题。本文为"可信"学习理论奠定了基础，利用凸概率集（credal集）对数据生成分布的可变性进行建模。我们认为，这种可信集可以从有限训练样本集合中推断得出。本文推导了有限假设空间（分别假设可实现与不可实现情形）以及无限模型空间下的界，这些结果直接推广了经典结论。