论文标题
统计机器学习正式规范的认识论方法
An Epistemic Approach to the Formal Specification of Statistical Machine Learning
论文作者
论文摘要
我们提出了一种认识论方法来形式化机器学习的统计特性。具体来说，我们基于Kripke模型引入了一种用于监督学习的正式模型，在该模型中，每个可能的世界都对应于一个可能的数据集，而模态运算符则将其解释为数据集中的转换和测试。然后，我们通过使用统计认知逻辑（Statel）的扩展来形式化分类性能，鲁棒性和公平性的各种概念。在这种形式上，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，这是第一部使用认知模型和逻辑公式来表达机器学习的统计特性的作品，并且将是发展机器学习正式规范理论的起点。
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 (StatEL). 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.
