Robust Counterfactual Explanations in Machine Learning: A Survey

Counterfactual explanations (CEs) are advocated as being ideally suited to providing algorithmic recourse for subjects affected by the predictions of machine learning models. While CEs can be beneficial to affected individuals, recent work has exposed severe issues related to the robustness of state-of-the-art methods for obtaining CEs. Since a lack of robustness may compromise the validity of CEs, techniques to mitigate this risk are in order. In this survey, we review works in the rapidly growing area of robust CEs and perform an in-depth analysis of the forms of robustness they consider. We also discuss existing solutions and their limitations, providing a solid foundation for future developments.

Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)

Model Multiplicity (MM) arises when multiple, equally performing machine learning models can be trained to solve the same prediction task. Recent studies show that models obtained under MM may produce inconsistent predictions for the same input. When this occurs, it becomes challenging to provide counterfactual explanations (CEs), a common means for offering recourse recommendations to individuals negatively affected by models' predictions. In this paper, we formalise this problem, which we name recourse-aware ensembling, and identify several desirable properties which methods for solving it should satisfy. We show that existing ensembling methods, naturally extended in different ways to provide CEs, fail to satisfy these properties. We then introduce argumentative ensembling, deploying computational argumentation to guarantee robustness of CEs to MM, while also accommodating customisable user preferences. We show theoretically and experimentally that argumentative ensembling satisfies properties which the existing methods lack, and that the trade-offs are minimal wrt accuracy.

Recourse under Model Multiplicity via Argumentative Ensembling

Model Multiplicity (MM) arises when multiple, equally performing machine learning models can be trained to solve the same prediction task. Recent studies show that models obtained under MM may produce inconsistent predictions for the same input. When this occurs, it becomes challenging to provide counterfactual explanations (CEs), a common means for offering recourse recommendations to individuals negatively affected by models' predictions. In this paper, we formalise this problem, which we name recourse-aware ensembling, and identify several desirable properties which methods for solving it should satisfy. We show that existing ensembling methods, naturally extended in different ways to provide CEs, fail to satisfy these properties. We then introduce argumentative ensembling, deploying computational argumentation to guarantee robustness of CEs to MM, while also accommodating customisable user preferences. We show theoretically and experimentally that argumentative ensembling satisfies properties which the existing methods lack, and that the trade-offs are minimal wrt accuracy.

Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisation

Counterfactual Explanations (CEs) have received increasing interest as a major methodology for explaining neural network classifiers. Usually, CEs for an input-output pair are defined as data points with minimum distance to the input that are classified with a different label than the output. To tackle the established problem that CEs are easily invalidated when model parameters are updated (e.g. retrained), studies have proposed ways to certify the robustness of CEs under model parameter changes bounded by a norm ball. However, existing methods targeting this form of robustness are not sound or complete, and they may generate implausible CEs, i.e., outliers wrt the training dataset. In fact, no existing method simultaneously optimises for proximity and plausibility while preserving robustness guarantees. In this work, we propose Provably RObust and PLAusible Counterfactual Explanations (PROPLACE), a method leveraging on robust optimisation techniques to address the aforementioned limitations in the literature. We formulate an iterative algorithm to compute provably robust CEs and prove its convergence, soundness and completeness. Through a comparative experiment involving six baselines, five of which target robustness, we show that PROPLACE achieves state-of-the-art performances against metrics on three evaluation aspects.

Formalising the Robustness of Counterfactual Explanations for Neural Networks

The use of counterfactual explanations (CFXs) is an increasingly popular explanation strategy for machine learning models. However, recent studies have shown that these explanations may not be robust to changes in the underlying model (e.g., following retraining), which raises questions about their reliability in real-world applications. Existing attempts towards solving this problem are heuristic, and the robustness to model changes of the resulting CFXs is evaluated with only a small number of retrained models, failing to provide exhaustive guarantees. To remedy this, we propose the first notion to formally and deterministically assess the robustness (to model changes) of CFXs for neural networks, that we call {\Delta}-robustness. We introduce an abstraction framework based on interval neural networks to verify the {\Delta}-robustness of CFXs against a possibly infinite set of changes to the model parameters, i.e., weights and biases. We then demonstrate the utility of this approach in two distinct ways. First, we analyse the {\Delta}-robustness of a number of CFX generation methods from the literature and show that they unanimously host significant deficiencies in this regard. Second, we demonstrate how embedding {\Delta}-robustness within existing methods can provide CFXs which are provably robust.