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.

翻译：反事实解释为个体提供能够将标签改变为期望类别的成本最优行动。然而，当大量实例寻求状态修改时，这种以个体为中心的方法可能导致新的竞争和不可预见的成本。此外，这些忽视底层数据分布的建议可能会推荐用户视为异常值的行动。为解决这些问题，本文提出了一种制定反事实解释的群体方法，重点在于利用个体当前密度来指导推荐行动。该问题自然归结为最优传输问题。借助最优传输领域的广泛文献，我们展示了这种群体方法如何改进经典反事实解释的理想特性。我们通过数值模拟支持所提出的方案，阐明了该方法相对于经典方法的有效性及其与经典方法的关联。