Counterfactual Explanations (CE) is the de facto method for providing insight and interpretability in black-box decision-making models by identifying alternative input instances that lead to different outcomes. This paper extends the concept of CEs to a distributional context, broadening the scope from individual data points to entire input and output distributions, named Distributional Counterfactual Explanation (DCE). In DCE, our focus shifts to analyzing the distributional properties of the factual and counterfactual, drawing parallels to the classical approach of assessing individual instances and their resulting decisions. We leverage Optimal Transport (OT) to frame a chance-constrained optimization problem, aiming to derive a counterfactual distribution that closely aligns with its factual counterpart, substantiated by statistical confidence. Our proposed optimization method, DISCOUNT, strategically balances this confidence across both input and output distributions. This algorithm is accompanied by an analysis of its convergence rate. The efficacy of our proposed method is substantiated through a series of illustrative case studies, highlighting its potential in providing deep insights into decision-making models.

翻译：反事实解释（CE）是黑箱决策模型中提供洞察和可解释性的标准方法，通过识别导致不同结果的替代输入实例实现。本文将反事实解释的概念扩展到分布场景，将范围从单个数据点拓宽至整个输入和输出分布，命名为分布反事实解释（DCE）。在DCE中，我们聚焦于分析事实分布与反事实分布的分布性质，这与评估单个实例及其决策结果的经典方法形成类比。我们利用最优输运（OT）构建一个机会约束优化问题，旨在推导出与其事实分布紧密对齐的反事实分布，并以统计置信度为支撑。我们提出的优化方法DISCOUNT战略性地平衡了输入和输出分布两端的置信度，该算法附有收敛性分析。通过一系列说明性案例研究验证了所提方法的有效性，突出了其在为决策模型提供深度洞察方面的潜力。