Towards Logical Specification of Statistical Machine Learning
This work addresses the need for rigorous specification of machine learning properties, such as performance, robustness, and fairness, for researchers and practitioners, but it is incremental as it builds on existing logical frameworks.
The paper tackles the problem of formalizing statistical properties of machine learning by introducing a logical approach based on Kripke models and epistemic logic, resulting in the first work to express these properties with logical formulas and provide new views on robustness and fairness.
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.