Explainable artificial intelligence (XAI) post-hoc explainability methods: risks and limitations in non-discrimination law

Organizations are increasingly employing complex black-box machine learning models in high-stakes decision-making. A popular approach to addressing the problem of opacity of black-box machine learning models is the use of post-hoc explainability methods. These methods approximate the logic of underlying machine learning models with the aim of explaining their internal workings, so that human examiners can understand them. In turn, it has been alluded that the insights from post-hoc explainability methods can be used to help regulate black-box machine learning. This article examines the validity of these claims. By examining whether the insights derived from post-hoc explainability methods in post-model deployment can prima facie meet legal definitions in European (read European Union) non-discrimination law, we argue that machine learning post-hoc explanation methods cannot guarantee the insights they generate.