DACE: Distribution-Aware Counterfactual Explanation by Mixed-Integer Linear Optimization

Abstract

<jats:p>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.</jats:p>

If Only We Had Better Counterfactual Explanations: Five Key Deficits to Rectify in the Evaluation of Counterfactual XAI Techniques

“…CFs need to focus on features. The second major insight that quickly emerged in the area, was on the need to focus on the "right" features (actionable ones) to perturb and avoid the "wrong" ones (immutable ones), by using predictive importance [Maartens and Provost, 2014;Guidotti et al, 2018;Pedreschi et al, 2019], "actionablility" [Ustun et al, 2019;Karimi et al, 2020b;Chou et al, 2021], "coherence" Gomez et al, 2020] and "causality" [Karimi et al, 2020c;Chou et al, 2021]; while also considering dependencies between features [Mothilal et al, 2020;Kanamori et al, 2020]. In our evaluation guidelines we discuss some of the issues around evaluating this insight.…”

The Intriguing Relation Between Counterfactual Explanations and Adversarial Examples

“…For both (targeted/untargeted) CEs and AEs there exist many other formulations as an optimization problem (Serban et al 2020;Verma et al 2020). For example, for CEs Poyiadzi et al (2020), Kanamori et al (2020), and Van Looveren and Klaise (2019) add additional terms to Eq. 1 encoding further desiderata (see aims and distances below), Dandl et al (2020) instead add these desiderata by formulating a multi-objective optimizations problem, and Karimi et al (2020a) formulate a search for the smallest intervention on the variables needed to attain a change in classification.…”

“…However, some distances to attain sparsity of counterfactuals have not been used to reach imperceptibility of AEs. One way by which sparsity can be guaranteed is to explicitly put a constraint on the number of features allowed to change (Kanamori et al 2020;Ustun et al 2019;Sokol and Flach 2019). Another is to constrain the number of actions that can be taken, but not the number of the corresponding feature changes (Karimi et al 2020c).…”

“…One common way to attain plausibility is to take into account the distance of the CE to the closest training-datapoint (Kanamori et al 2020;Dandl et al 2020;Sharma et al 2020) or the allowed path to the counterfactual (Poyiadzi et al 2020). Often, additional constraints are posed such that only actionable features should be changed to avoid non-helpful recommendations (Ustun et al 2019).…”

A Framework and Benchmarking Study for Counterfactual Generating Methods on Tabular Data

“…This metric is reported [40,46] as being a valuable metric since it can work with different ranges across features, as it considers the variation of each changed feature. The Mahalanobis Distance (MD) [76], commonly used to find multivariate outliers, can take the correlation between features into account [62,77]. Together, these three distance metrics measure different aspects of the solutions that might be important for specific user defined requirements.…”