Towards Logical Specification of Statistical Machine Learning

• Published in: Software Engineering and Formal Methods Vol. 11724; pp. 293 - 311
• Main Author: Kawamoto, Yusuke
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2019; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Divergence; Epistemic logic; Fairness; Machine learning; Possible world semantics; Robustness; Statistical classification
• ISBN: 3030304450; 9783030304454
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-30446-1_16

We introduce a logical approach to formalizing statistical properties of machine learning. Specifically, we propose a formal model for statistical classification based on a Kripke model, and formalize various notions of classification performance, robustness, and fairness of classifiers by using epistemic logic. Then we show some relationships among properties of classifiers and those between classification performance and robustness, which suggests robustness-related properties that have not been formalized in the literature as far as we know. To formalize fairness properties, we define a notion of counterfactual knowledge and show techniques to formalize conditional indistinguishability by using counterfactual epistemic operators. As far as we know, this is the first work that uses logical formulas to express statistical properties of machine learning, and that provides epistemic (resp. counterfactually epistemic) views on robustness (resp. fairness) of classifiers.