# Evaluating Robustness of Counterfactual Explanations

arXiv: https://arxiv.org/abs/2103.02354 · HTML: https://mlsanity.com/paper/2103.02354/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 41 references that are in the map.
- First posted on arXiv 3 Mar 2021.

## Builds on (most cited first, 27 of 27)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Explaining Explanations: An Overview of Interpretability of Machine Learning](https://mlsanity.com/paper/1806.00069/) (2018)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [Fairness in Machine Learning: A Survey](https://mlsanity.com/paper/2010.04053/) (2020)
- [On the Robustness of Interpretability Methods](https://mlsanity.com/paper/1806.08049/) (2018)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Model-Agnostic Interpretability of Machine Learning](https://mlsanity.com/paper/1606.05386/) (2016)
- [Explainable Artificial Intelligence: Understanding, Visualizing and Interpreting Deep Learning Models](https://mlsanity.com/paper/1708.08296/) (2017)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [On the Apparent Conflict Between Individual and Group Fairness](https://mlsanity.com/paper/1912.06883/) (2019)
- [Fooling Neural Network Interpretations via Adversarial Model Manipulation](https://mlsanity.com/paper/1902.02041/) (2019)
- [Fairwashing Explanations with Off-Manifold Detergent](https://mlsanity.com/paper/2007.09969/) (2020)
- [On the Fairness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2010.06529/) (2020)
- [Fairness Through Robustness: Investigating Robustness Disparity in Deep Learning](https://mlsanity.com/paper/2006.12621/) (2020)
- [Equalizing Recourse across Groups](https://mlsanity.com/paper/1909.03166/) (2019)
- [A Simple and Effective Model-Based Variable Importance Measure](https://mlsanity.com/paper/1805.04755/) (2018)
- [On Adversarial Bias and the Robustness of Fair Machine Learning](https://mlsanity.com/paper/2006.08669/) (2020)
- [Defining Locality for Surrogates in Post-hoc Interpretablity](https://mlsanity.com/paper/1806.07498/) (2018)
- [On the computation of counterfactual explanations -- A survey](https://mlsanity.com/paper/1911.07749/) (2019)
- [Convex Density Constraints for Computing Plausible Counterfactual Explanations](https://mlsanity.com/paper/2002.04862/) (2020)
- [Issues with post-hoc counterfactual explanations: a discussion](https://mlsanity.com/paper/1906.04774/) (2019)

## Built on by (most cited first, 30 of 41)

- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [Leveraging Explanations in Interactive Machine Learning: An Overview](https://mlsanity.com/paper/2207.14526/) (2022)
- [Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse](https://mlsanity.com/paper/2203.06768/) (2022)
- [On the Robustness of Sparse Counterfactual Explanations to Adverse Perturbations](https://mlsanity.com/paper/2201.09051/) (2022)
- [On the Trade-Off between Actionable Explanations and the Right to be Forgotten](https://mlsanity.com/paper/2208.14137/) (2022)
- [The privacy issue of counterfactual explanations: explanation linkage attacks](https://mlsanity.com/paper/2210.12051/) (2022)
- [Finding Regions of Counterfactual Explanations via Robust Optimization](https://mlsanity.com/paper/2301.11113/) (2023)
- [Generating robust counterfactual explanations](https://mlsanity.com/paper/2304.12943/) (2023)
- [Robustness Implies Fairness in Causal Algorithmic Recourse](https://mlsanity.com/paper/2302.03465/) (2023)
- [Keep Your Friends Close and Your Counterfactuals Closer: Improved Learning From Closest Rather Than Plausible Counterfactual Explanations in an Abstract Setting](https://mlsanity.com/paper/2205.05515/) (2022)
- [Counterfactual Explanations with Probabilistic Guarantees on their Robustness to Model Change](https://mlsanity.com/paper/2408.04842/) (2024)
- [Let's Go to the Alien Zoo: Introducing an Experimental Framework to Study Usability of Counterfactual Explanations for Machine Learning](https://mlsanity.com/paper/2205.03398/) (2022)
- ["Explain it in the Same Way!" -- Model-Agnostic Group Fairness of Counterfactual Explanations](https://mlsanity.com/paper/2211.14858/) (2022)
- [The Risks of Recourse in Binary Classification](https://mlsanity.com/paper/2306.00497/) (2023)
- [Time Can Invalidate Algorithmic Recourse](https://mlsanity.com/paper/2410.08007/) (2024)
- [Flexible and Robust Counterfactual Explanations with Minimal Satisfiable Perturbations](https://mlsanity.com/paper/2309.04676/) (2023)
- [Generating Likely Counterfactuals Using Sum-Product Networks](https://mlsanity.com/paper/2401.14086/) (2024)
- [On the Robustness of Explanations of Deep Neural Network Models: A Survey](https://mlsanity.com/paper/2211.04780/) (2022)
- [Faithful Model Explanations through Energy-Constrained Conformal Counterfactuals](https://mlsanity.com/paper/2312.10648/) (2023)
- [A Two-Stage Algorithm for Cost-Efficient Multi-instance Counterfactual Explanations](https://mlsanity.com/paper/2403.01221/) (2024)
- [For Better or Worse: The Impact of Counterfactual Explanations' Directionality on User Behavior in xAI](https://mlsanity.com/paper/2306.07637/) (2023)
- [The Effect of Data Poisoning on Counterfactual Explanations](https://mlsanity.com/paper/2402.08290/) (2024)
- [CE-QArg: Counterfactual Explanations for Quantitative Bipolar Argumentation Frameworks (Technical Report)](https://mlsanity.com/paper/2407.08497/) (2024)
- [A comprehensive interpretable machine learning framework for Mild Cognitive Impairment and Alzheimer's disease diagnosis](https://mlsanity.com/paper/2412.09376/) (2024)
- [Generally-Occurring Model Change for Robust Counterfactual Explanations](https://mlsanity.com/paper/2407.11426/) (2024)
- [Counterfactual Explanations for Time Series Should be Human-Centered and Temporally Coherent in Interventions](https://mlsanity.com/paper/2512.14559/) (2025)
- [Fair Recourse for All: Ensuring Individual and Group Fairness in Counterfactual Explanations](https://mlsanity.com/paper/2601.20449/) (2026)
- ["How to make them stay?" -- Diverse Counterfactual Explanations of Employee Attrition](https://mlsanity.com/paper/2303.04579/) (2023)
- [T-COL: Generating Counterfactual Explanations for General User Preferences on Variable Machine Learning Systems](https://mlsanity.com/paper/2309.16146/) (2023)
- [Collective Counterfactual Explanations: Balancing Individual Goals and Collective Dynamics](https://mlsanity.com/paper/2402.04579/) (2024)

## Abstract (arXiv)

Transparency is a fundamental requirement for decision making systems when these should be deployed in the real world. It is usually achieved by providing explanations of the system's behavior. A prominent and intuitive type of explanations are counterfactual explanations. Counterfactual explanations explain a behavior to the user by proposing actions -- as changes to the input -- that would cause a different (specified) behavior of the system. However, such explanation methods can be unstable with respect to small changes to the input -- i.e. even a small change in the input can lead to huge or arbitrary changes in the output and of the explanation. This could be problematic for counterfactual explanations, as two similar individuals might get very different explanations. Even worse, if the recommended actions differ considerably in their complexity, one would consider such unstable (counterfactual) explanations as individually unfair. In this work, we formally and empirically study the robustness of counterfactual explanations in general, as well as under different models and different kinds of perturbations. Furthermore, we propose that plausible counterfactual explanations can be used instead of closest counterfactual explanations to improve the robustness and consequently the individual fairness of counterfactual explanations.