One-for-many Counterfactual Explanations by Column Generation
Andrea Lodi, Jasone Ramírez-Ayerbe
TL;DR
The paper tackles global counterfactual explanations under a one-for-many allocation, aiming to cover a group of negative-classified instances with as few explanations as possible while enforcing sparsity. It introduces a column generation framework that builds a restricted master problem and a pricing subproblem to iteratively generate effective counterfactual explanations for any black-box classifier, including neural networks. Compared to a direct MIP baseline, the column generation approach delivers smaller explanation sets, better scalability, and higher solution quality across multiple datasets. The methodology provides full coverage and precise decision flips, enhancing interpretability and practical applicability in high-stakes settings.
Abstract
In this paper, we consider the problem of generating a set of counterfactual explanations for a group of instances, with the one-for-many allocation rule, where one explanation is allocated to a subgroup of the instances. For the first time, we solve the problem of minimizing the number of explanations needed to explain all the instances, while considering sparsity by limiting the number of features allowed to be changed collectively in each explanation. A novel column generation framework is developed to efficiently search for the explanations. Our framework can be applied to any black-box classifier, like neural networks. Compared with a simple adaptation of a mixed-integer programming formulation from the literature, the column generation framework dominates in terms of scalability, computational performance and quality of the solutions.