Distribution-aware counterfactual explanation by mixed-integer linear optimization

Abstract

Post-hoc explanation methods for machine learning models have been widely used to support decision-making. Counterfactual Explanation (CE), also known as Actionable Recourse, is one of the post-hoc explanation methods that provides a perturbation vector that alters the prediction result obtained from a classifier. Users can directly interpret the perturbation as an “action” to obtain their desired decision results. However, actions extracted by existing methods often become unrealistic for users because they do not adequately consider the characteristics corresponding to the data distribution, such as feature-correlations and outlier risk. To suggest an executable action for users, we propose a new framework of CE, which we refer to as Distribution-Aware Counterfactual Explanation (DACE), that extracts a realistic action by evaluating its reality on the empirical data distribution. Here, the key idea is to define a new cost function based on the Mahalanobis distance and the local outlier factor. Then, we propose a mixed-integer linear optimization approach to extracting an optimal action by minimizing the defined cost function. Experiments conducted on real datasets demonstrate the effectiveness of the proposed method compared with existing CE methods.