This paper proposes a new framework of algorithmic recourse (AR) that works even in the presence of missing values. AR aims to provide a recourse action for altering the undesired prediction result given by a classifier. Existing AR methods assume that we can access complete information on the features of an input instance. However, we often encounter missing values in a given instance (e.g., due to privacy concerns), and previous studies have not discussed such a practical situation. In this paper, we first empirically and theoretically show the risk that a naive approach with a single imputation technique fails to obtain good actions regarding their validity, cost, and features to be changed. To alleviate this risk, we formulate the task of obtaining a valid and low-cost action for a given incomplete instance by incorporating the idea of multiple imputation. Then, we provide some theoretical analyses of our task and propose a practical solution based on mixed-integer linear optimization. Experimental results demonstrated the efficacy of our method in the presence of missing values compared to the baselines.

翻译：本文提出了一种新的算法追索框架，该框架即使在存在缺失值的情况下仍能有效工作。算法追索旨在为改变分类器给出的不良预测结果提供追索行动。现有AR方法假设我们能够获取输入实例特征的完整信息。然而，我们经常遇到给定实例中存在缺失值的情况（例如出于隐私考虑），而先前研究尚未讨论这种实际场景。本文首先通过实证和理论分析表明：采用单一插补技术的朴素方法存在风险，难以在有效性、成本及待修改特征方面获得优质行动方案。为降低此风险，我们通过融合多重插补思想，构建了针对不完整实例获取有效且低成本追索行动的任务框架。随后，我们对该任务进行了理论分析，并提出基于混合整数线性优化的实用解决方案。实验结果表明，在存在缺失值的情况下，我们的方法相较于基线模型具有显著优势。