We propose an epistemic approach to formalizing statistical properties of machine learning. Specifically, we introduce a formal model for supervised learning based on a Kripke model where each possible world corresponds to a possible dataset and modal operators are interpreted as transformation and testing on datasets. Then, we formalize various notions of the classification performance, robustness, and fairness of statistical classifiers by using our extension of statistical epistemic logic. In this formalization, we show relationships among properties of classifiers, and relevance between classification performance and robustness. As far as we know, this is the first work that uses epistemic models and logical formulas to express statistical properties of machine learning, and would be a starting point to develop theories of formal specification of machine learning.

我们提出了一种认知方法来规范机器学习的统计属性。具体来说，我们基于Kripke模型引入了正式的监督学习模型，其中每个可能的世界都对应一个可能的数据集，而模态运算符则被解释为对数据集的转换和测试。然后，我们通过使用统计认知逻辑的扩展形式化统计分类器的分类性能，鲁棒性和公平性的各种概念。在此形式化中，我们显示了分类器属性之间的关系，以及分类性能和鲁棒性之间的相关性。据我们所知，这是第一项使用认知模型和逻辑公式来表达机器学习统计特性的工作，