Post-hoc explanation methods for machine learning models have been widely used to support decision-making. One of the popular methods is Counterfactual Explanation (CE), also known as Actionable Recourse, which provides a user with a perturbation vector of features that alters the prediction result. Given a perturbation vector, a user can interpret it as an "action" for obtaining one's desired decision result. In practice, however, showing only a perturbation vector is often insufficient for users to execute the action. The reason is that if there is an asymmetric interaction among features, such as causality, the total cost of the action is expected to depend on the order of changing features. Therefore, practical CE methods are required to provide an appropriate order of changing features in addition to a perturbation vector. For this purpose, we propose a new framework called Ordered Counterfactual Explanation (OrdCE). We introduce a new objective function that evaluates a pair of an action and an order based on feature interaction. To extract an optimal pair, we propose a mixed-integer linear optimization approach with our objective function. Numerical experiments on real datasets demonstrated the effectiveness of our OrdCE in comparison with unordered CE methods.

翻译：机器学习模型的热后解释方法被广泛用于支持决策。一种流行的方法是反事实解释(CE),又称“可采取行动的路径”,它为用户提供了改变预测结果的特征的扰动矢量。考虑到扰动矢量,用户可以将其解释为获得预期的决定结果的“动作”。然而,在实践中,仅显示扰动矢量往往不足以让用户执行动作。原因是,如果各种特征(如因果关系)存在不对称的相互作用,预期行动的总成本取决于变化特性的顺序。因此,除了扰动矢量之外,实际的CEE方法需要提供一个改变特征的适当顺序。为此,我们提议了一个称为有秩序的反事实解释(OrdCE)的新框架。我们引入一个新的客观功能,即评估一对动作和基于特征互动的顺序。为了提取最佳配对,我们建议采用混合的线性优化方法与我们客观的功能相匹配。在真实的OrcE方法上,对实际的数值进行了对比。