On the Robustness of Sparse Counterfactual Explanations to Adverse Perturbations

Abstract

Counterfactual explanations (CEs) are a powerful means for understanding how decisions made by algorithms can be changed.Researchers have proposed a number of desiderata that CEs should meet to be practically useful, such as requiring minimal effort to enact, or complying with causal models. We consider a further aspect to improve the usability of CEs: robustness to adverse perturbations, which may naturally happen due to unfortunate circumstances. Since CEs typically prescribe a sparse form of intervention (i.e., only a subset of the features should be changed), we provide two definitions of robustness, which concern, respectively, the features to change and to keep as they are. These definitions are workable in that they can be incorporated as penalty terms in the loss functions that are used for discovering CEs. To experiment with the proposed definitions of robustness, we create and release code where five data sets (commonly used in the field of fair and explainable machine learning) have been enriched with feature-specific annotations that can be used to sample meaningful perturbations. Our experiments show that CEs are often not robust and, if adverse perturbations take place, the intervention they prescribe may require a much larger cost than anticipated, or even become impossible. However, accounting for robustness in the search process, which can be done rather easily, allows discovering robust CEs systematically.

The Robustness of Counterfactual Explanations Over Time

“…In summary, feasible, actionable, and sparse counterfactual explanations recommend causality-consistent scenarios that can be reasonably implemented by the individuals impacted by algorithmically-generated outcomes, once they act on the values of a limited number of features. Finally, we note that authors have recently suggested additional desiderata of counterfactual explanations, such as diversity and robustness to local perturbations [10], [12], [17]. The former refers to the possibility of generating diverse counterfactuals for a given outcome to explain [10].…”

“…In fact, the goal of diversity is to provide individuals with different counterfactual scenarios to perform algorithmic recourse [10]. The latter refers to the degree to which counterfactuals are sensitive to (possibly adverse) perturbations of the data point whose machine learning outcome has to be explained, instead [12], [17]. We refer to [10], [12], [17] for all details.…”

“…The latter refers to the degree to which counterfactuals are sensitive to (possibly adverse) perturbations of the data point whose machine learning outcome has to be explained, instead [12], [17]. We refer to [10], [12], [17] for all details.…”

“…They are an example of "contrastive explanations in xAI" [5], [9]: they explain a given model outcome by sharing a "whatif" alternative scenario comprising of feature-perturbed versions of the same individual [10]- [12]. Recent literature from the xAI domain has discussed selected desiderata that may support the applicability of counterfactual explanations in real-world machine learning model pipelines [10], [12]- [17]. In particular, the desiderata of feasibility, actionability and sparsity would allow to generate and share cognitively accessible counterfactual explanations that respect causal models between features, and suggest actionable strategies whose alternative scenarios comprise the change of a limited number of features.…”