# An Epistemic Approach to the Formal Specification of Statistical Machine Learning

arXiv: https://arxiv.org/abs/2004.12734 · HTML: https://mlsanity.com/paper/2004.12734/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Apr 2020.

## Built on by (most cited first, 4 of 4)

- [Sound and Relatively Complete Belief Hoare Logic for Statistical Hypothesis Testing Programs](https://mlsanity.com/paper/2208.07074/) (2022)
- [Formalizing Statistical Causality via Modal Logic](https://mlsanity.com/paper/2210.16751/) (2022)
- [StatWhy: Formal Verification Tool for Statistical Hypothesis Testing Programs](https://mlsanity.com/paper/2405.17492/) (2024)
- [Why3-py: A Tool for Formal Verification of Hypothesis Testing and Meta-Analysis in Python](https://mlsanity.com/paper/2607.03951/) (2026)

## Abstract (arXiv)

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.