Ordered Counterfactual Explanation by Mixed-Integer Linear Optimization

Counterfactual Explanation (CE) is one of the post-hoc explanation methods that provides a perturbation vector so as to alter the prediction result obtained from a classifier. Users can directly interpret the perturbation as an "action" for obtaining their desired decision results. However, an action extracted by existing methods often becomes unrealistic for users because they do not adequately care about the characteristics corresponding to the empirical data distribution such as feature-correlations and outlier risk. To suggest an executable action for users, we propose a new framework of CE for extracting an action by evaluating its reality on the empirical data distribution. The key idea of our proposed method 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 our cost function. By experiments on real datasets, we confirm the effectiveness of our method in comparison with existing methods for CE.