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.

Post-hoc explanation methods for machine learning models have been widely used to support decision-making. One of the popular methods is Counterfactual Explanation (CE), also known as Actionable Recourse, which provides a user with a perturbation vector of features that alters the prediction result. Given a perturbation vector, a user can interpret it as an "action" for obtaining one's desired decision result. In practice, however, showing only a perturbation vector is often insufficient for users to execute the action. The reason is that if there is an asymmetric interaction among features, such as causality, the total cost of the action is expected to depend on the order of changing features. Therefore, practical CE methods are required to provide an appropriate order of changing features in addition to a perturbation vector. For this purpose, we propose a new framework called Ordered Counterfactual Explanation (OrdCE). We introduce a new objective function that evaluates a pair of an action and an order based on feature interaction. To extract an optimal pair, we propose a mixed-integer linear optimization approach with our objective function. Numerical experiments on real datasets demonstrated the effectiveness of our OrdCE in comparison with unordered CE methods.

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In the application of machine learning models to decision-making tasks (e.g., loan approval), fairness of their predictions has emerged as an important topic in recent years. If decision-makers detect unfairness in their models during deployment, they must modify the models to satisfy constraints on a specific discrimination criterion. However, simply retraining a model from scratch under fairness constraints may raise serious reliability issues caused by differences in prediction and interpretation between the initial model and retrained model. In this paper, we propose a post-processing framework, named Fairness-Aware Decision tree Editing (FADE), that converts a given biased decision tree into a fair decision tree without significantly changing it in terms of its prediction and interpretation. For this purpose, we introduce two dissimilarity measures between decision trees based on the prediction discrepancy and edit distance. We propose a mixed-integer linear optimization formulation for minimizing the dissimilarity measures under fairness constraints. Numerical experiments on real datasets demonstrate the effectiveness of our method in comparison with existing methods.