A Mixed-Integer Linear Programming Approach to Realistic Counterfactual Explanations

Abstract

The counterfactual explanation (CE) is one of the post-hoc explanation methods for complex machine learning models. It provides perturbed features so as to alter the prediction result obtained from a classifier. Users can directly interpret the perturbation as an "\textit{improvement action}" for obtaining their desired prediction results. However, an action extracted by existing methods often becomes unrealistic for users from the perspectives of the characteristics corresponding to the underlying data distribution, such as feature-correlations and outlier risks, because they do not adequately care about them. In this paper, we propose a new framework of CE for extracting an action by evaluating its reality on the empirical data distribution. We introduce a new cost function based on the Mahalanobis' distance and the local outlier factor, and then, we propose a mixed-integer linear programming approach to extracting an optimal action by minimizing our cost function. We conduct experiments on real datasets to evaluate the effectiveness of our method in comparison with existing methods for CE.