Ordered Counterfactual Explanation by Mixed-Integer Linear Optimization

Abstract

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.

"How to make them stay?" -- Diverse Counterfactual Explanations of Employee Attrition

“…However, given that the recommended salary increase is large, companies could apply the recommendation on talented employees that can not afford to loose. Similar actions are recommended by (Kanamori et al, 2022), thus highlighting the importance of salary (monthly income) as key factors for retention, while also provides confidence in our preliminary results. In addition, as highlighted in the literature the method also identifies that job satisfaction is a key property for preventing attrition if combined with salary increase.…”

“…As already noted by (Kanamori et al, 2022), there often might not exist a single change δ cf that is applicable to all employees in D. Furthermore, there might also exist several different changes δ cf that work equally well (and maybe also work for different subgroups of employees), we therefore propose an extension to our formalization from Section 4.1 that computes not a single recommendation of changes δ cf but a set of different & diverse changes δ cf so that the decision makers are provided with a list of possible actions on how to increase retention rate. Therefore, the HR manager can choose the action that is more suitable to his/her case.…”

“…Recently, another approach (Kanamori et al, 2022) for simultaneously computing counterfactual explanations for different groups of individuals was proposed that is similar to the approach presented in this paper.…”

“…The authors of (Kanamori et al, 2022) deal with a very similar problem, which they call "group-wise counterfactual explanations". However, the authors do not try to find a single explanation applicable to as many as possible employees like we do in Section 4.1, but instead propose an algorithm/heuristic called "counterfactual explanation tree" for partitioning the employees into groups for which a single applicable explanation (i.e.…”

Getting Away with More Network Pruning: From Sparsity to Geometry and Linear Regions

“…Based on the characterization of linear regions in terms of which neurons are active and inactive, we can count the number of linear regions defined by a trained network with a Mixed-Integer Linear Programming (MILP) formulation [62]. Among other things, these formulations have also been used for network verification [9], embedding the relationship between inputs and outputs of a network into optimization problems [59,11,5], identifying stable neurons [69] to facilitate adversarial robustness verification [75] as well as network compression [60,63], and producing counterfactual explanations [37]. Moreover, several studies have analyzed and improved such formulations [15,2,8,61,1,63].…”