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.

通过将 Counterfactual Explanations 方法扩展到分布情境，引入了分布式 Counterfactual Explanation（DCE）的概念，该方法通过优化问题来推导一个与事实相吻合并具有统计置信度的反事实分布。同时，通过一系列案例研究验证了该方法在深入理解决策模型方面的潜力。