Counterfactual Explanation (CE) is a post-hoc explanation method that provides a perturbation for altering the prediction result of a classifier. Users can interpret the perturbation as an "action" to obtain their desired decision results. Existing CE methods require complete information on the features of an input instance. However, we often encounter missing values in a given instance, and the previous methods do not work in such a practical situation. In this paper, we first empirically and theoretically show the risk that missing value imputation methods affect the validity of an action, as well as the features that the action suggests changing. Then, we propose a new framework of CE, named Counterfactual Explanation by Pairs of Imputation and Action (CEPIA), that enables users to obtain valid actions even with missing values and clarifies how actions are affected by imputation of the missing values. Specifically, our CEPIA provides a representative set of pairs of an imputation candidate for a given incomplete instance and its optimal action. We formulate the problem of finding such a set as a submodular maximization problem, which can be solved by a simple greedy algorithm with an approximation guarantee. Experimental results demonstrated the efficacy of our CEPIA in comparison with the baselines in the presence of missing values.

翻译：反事实解释是一种事后解释方法，通过提供扰动项来改变分类器的预测结果。用户可将该扰动项解读为获取期望决策结果的"行动"。现有反事实解释方法要求输入实例的特征信息完整，但在实际应用中，我们常遇到包含缺失值的实例，而现有方法在此类场景下失效。本文首先通过理论分析与实证研究，揭示了缺失值填补方法会影响行动的可行性和建议修改的特征。继而提出新型反事实解释框架——"成对填补与行动的反事实解释"（CEPIA），该框架不仅能在存在缺失值时获取有效行动，还能阐明填补缺失值如何影响行动建议。具体而言，CEPIA针对给定的不完整实例，提供了一组具有代表性的填补候选方案及其最优行动配对。我们将寻找该最优配对集的问题建模为子模最大化问题，并采用具有近似保证的简单贪心算法进行求解。实验结果表明，在存在缺失值的情况下，本文提出的CEPIA框架相较于基线方法具有显著优势。