Mathematical optimization modelling for group counterfactual explanations

Counterfactual Analysis has shown to be a powerful tool in the burgeoning field of Explainable Artificial Intelligence. In Supervised Classification, this means associating with each record a so-called counterfactual explanation: an instance that is close to the record and whose probability of being classified in the opposite class by a given classifier is high. While the literature focuses on the problem of finding one counterfactual for one record, in this paper we take a stakeholder perspective, and we address the more general setting in which a group of counterfactual explanations is sought for a group of instances. We introduce some mathematical optimization models as illustration of each possible allocation rule between counterfactuals and instances, and we identify a number of research challenges for the Operations Research community.