# On the Robustness of Sparse Counterfactual Explanations to Adverse Perturbations

arXiv: https://arxiv.org/abs/2201.09051 · HTML: https://mlsanity.com/paper/2201.09051/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 71 references that are in the map.
- First posted on arXiv 22 Jan 2022.

## Builds on (most cited first, 30 of 34)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [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)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [This Looks Like That: Deep Learning for Interpretable Image Recognition](https://mlsanity.com/paper/1806.10574/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [European Union regulations on algorithmic decision-making and a "right to explanation"](https://mlsanity.com/paper/1606.08813/) (2016)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Algorithmic Recourse: from Counterfactual Explanations to Interventions](https://mlsanity.com/paper/2002.06278/) (2020)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Local Rule-Based Explanations of Black Box Decision Systems](https://mlsanity.com/paper/1805.10820/) (2018)
- [Multi-Objective Counterfactual Explanations](https://mlsanity.com/paper/2004.11165/) (2020)
- [Algorithmic recourse under imperfect causal knowledge: a probabilistic approach](https://mlsanity.com/paper/2006.06831/) (2020)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [Artificial Intelligence: the global landscape of ethics guidelines](https://mlsanity.com/paper/1906.11668/) (2019)
- [The Dangers of Post-hoc Interpretability: Unjustified Counterfactual Explanations](https://mlsanity.com/paper/1907.09294/) (2019)
- [Good Counterfactuals and Where to Find Them: A Case-Based Technique for Generating Counterfactuals for Explainable AI (XAI)](https://mlsanity.com/paper/2005.13997/) (2020)
- [On Counterfactual Explanations under Predictive Multiplicity](https://mlsanity.com/paper/2006.13132/) (2020)
- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis](https://mlsanity.com/paper/2106.09992/) (2021)
- [The Intriguing Relation Between Counterfactual Explanations and Adversarial Examples](https://mlsanity.com/paper/2009.05487/) (2020)
- [Evaluating Robustness of Counterfactual Explanations](https://mlsanity.com/paper/2103.02354/) (2021)
- [Algorithmic Recourse in the Wild: Understanding the Impact of Data and Model Shifts](https://mlsanity.com/paper/2012.11788/) (2020)
- [Imperceptible Adversarial Attacks on Tabular Data](https://mlsanity.com/paper/1911.03274/) (2019)
- [Interpreting Neural Network Judgments via Minimal, Stable, and Symbolic Corrections](https://mlsanity.com/paper/1802.07384/) (2018)

## Built on by (most cited first, 30 of 32)

- [Leveraging Explanations in Interactive Machine Learning: An Overview](https://mlsanity.com/paper/2207.14526/) (2022)
- [Adversarial attacks and defenses in explainable artificial intelligence: A survey](https://mlsanity.com/paper/2306.06123/) (2023)
- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [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)
- [Setting the Right Expectations: Algorithmic Recourse Over Time](https://mlsanity.com/paper/2309.06969/) (2023)
- [Counterfactual Explanations with Probabilistic Guarantees on their Robustness to Model Change](https://mlsanity.com/paper/2408.04842/) (2024)
- [A.I. Robustness: a Human-Centered Perspective on Technological Challenges and Opportunities](https://mlsanity.com/paper/2210.08906/) (2022)
- [The Risks of Recourse in Binary Classification](https://mlsanity.com/paper/2306.00497/) (2023)
- [The Utility of "Even if..." Semifactual Explanation to Optimise Positive Outcomes](https://mlsanity.com/paper/2310.18937/) (2023)
- [Contrastive Learning with Counterfactual Explanations for Radiology Report Generation](https://mlsanity.com/paper/2407.14474/) (2024)
- [Time Can Invalidate Algorithmic Recourse](https://mlsanity.com/paper/2410.08007/) (2024)
- [Interval Abstractions for Robust Counterfactual Explanations](https://mlsanity.com/paper/2404.13736/) (2024)
- [Flexible and Robust Counterfactual Explanations with Minimal Satisfiable Perturbations](https://mlsanity.com/paper/2309.04676/) (2023)
- [The Effect of Data Poisoning on Counterfactual Explanations](https://mlsanity.com/paper/2402.08290/) (2024)
- [TraCE: Trajectory Counterfactual Explanation Scores](https://mlsanity.com/paper/2309.15965/) (2023)
- [Perfect Counterfactuals in Imperfect Worlds: Modelling Noisy Implementation of Actions in Sequential Algorithmic Recourse](https://mlsanity.com/paper/2410.02273/) (2024)
- [Factor Graph-based Interpretable Neural Networks](https://mlsanity.com/paper/2502.14572/) (2025)
- [Iterative Partial Fulfillment of Counterfactual Explanations: Benefits and Risks](https://mlsanity.com/paper/2303.11111/) (2023)
- [T-COL: Generating Counterfactual Explanations for General User Preferences on Variable Machine Learning Systems](https://mlsanity.com/paper/2309.16146/) (2023)
- [Introducing User Feedback-based Counterfactual Explanations (UFCE)](https://mlsanity.com/paper/2403.00011/) (2024)
- [Weak Robust Compatibility Between Learning Algorithms and Counterfactual Explanation Generation Algorithms](https://mlsanity.com/paper/2405.20664/) (2024)
- [Understanding Fixed Predictions via Confined Regions](https://mlsanity.com/paper/2502.16380/) (2025)
- [A Framework for Feasible Counterfactual Exploration incorporating Causality, Sparsity and Density](https://mlsanity.com/paper/2404.13476/) (2024)
- [Improving Decision Sparsity](https://mlsanity.com/paper/2410.20483/) (2024)
- [DiCE-Extended: A Robust Approach to Counterfactual Explanations in Machine Learning](https://mlsanity.com/paper/2504.19027/) (2025)
- [RealAC: A Domain-Agnostic Framework for Realistic and Actionable Counterfactual Explanations](https://mlsanity.com/paper/2508.10455/) (2025)
- [Structure-Aware Robust Counterfactual Explanations via Conditional Gaussian Network Classifiers](https://mlsanity.com/paper/2602.08021/) (2026)
- [RecourseBench: A Modular Framework for Reproducible Algorithmic Recourse Evaluation](https://mlsanity.com/paper/2606.16113/) (2026)
- [Taking the Whys Seriously: Limitations of Counterfactual Explanations in Justification and Recourse](https://mlsanity.com/paper/2608.30956/) (2026)

## Abstract (arXiv)

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 study the effect of addressing robustness separately for the features that are recommended to be changed and those that are not. Our 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 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 (even if not worst-case), 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. Robust CEs make additional intervention to contrast perturbations much less costly than non-robust CEs. We also find that robustness is easier to achieve for the features to change, posing an important point of consideration for the choice of what counterfactual explanation is best for the user. Our code is available at: https://github.com/marcovirgolin/robust-counterfactuals.