Counterfactual explanations provide individuals with cost-optimal actions
that can alter their labels to desired classes. However, if substantial
instances seek state modification, such individual-centric methods can lead to
new competitions and unanticipated costs. Furthermore, these recommendations,
disregarding the underlying data distribution, may suggest actions that users
perceive as outliers. To address these issues, our work proposes a collective
approach for formulating counterfactual explanations, with an emphasis on
utilizing the current density of the individuals to inform the recommended
actions. Our problem naturally casts as an optimal transport problem.
Leveraging the extensive literature on optimal transport, we illustrate how
this collective method improves upon the desiderata of classical counterfactual
explanations. We support our proposal with numerical simulations, illustrating
the effectiveness of the proposed approach and its relation to classic methods.

我们的研究提出了一种集体方法来制定反事实解释，强调利用个体的当前密度来提供推荐行动，这种方法通过解决最优输运问题，在改进经典反事实解释的同时支持其提案，通过数值模拟验证了该方法的有效性及其与经典方法的关系。