# Promoting Counterfactual Robustness through Diversity

arXiv: https://arxiv.org/abs/2312.06564 · HTML: https://mlsanity.com/paper/2312.06564/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 11 Dec 2023.

## Builds on (most cited first, 13 of 13)

- [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 Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Counterfactual Explanations Can Be Manipulated](https://mlsanity.com/paper/2106.02666/) (2021)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [On Counterfactual Explanations under Predictive Multiplicity](https://mlsanity.com/paper/2006.13132/) (2020)
- [Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees](https://mlsanity.com/paper/2305.11997/) (2023)
- [Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse](https://mlsanity.com/paper/2203.06768/) (2022)
- [Formalising the Robustness of Counterfactual Explanations for Neural Networks](https://mlsanity.com/paper/2208.14878/) (2022)
- [Scaling Guarantees for Nearest Counterfactual Explanations](https://mlsanity.com/paper/2010.04965/) (2020)

## Built on by (most cited first, 17 of 17)

- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Interval Abstractions for Robust Counterfactual Explanations](https://mlsanity.com/paper/2404.13736/) (2024)
- [Rigorous Probabilistic Guarantees for Robust Counterfactual Explanations](https://mlsanity.com/paper/2407.07482/) (2024)
- [RobustX: Robust Counterfactual Explanations Made Easy](https://mlsanity.com/paper/2502.13751/) (2025)
- [A Two-Stage Algorithm for Cost-Efficient Multi-instance Counterfactual Explanations](https://mlsanity.com/paper/2403.01221/) (2024)
- [Learning-Augmented Robust Algorithmic Recourse](https://mlsanity.com/paper/2410.01580/) (2024)
- [Faster Verified Explanations for Neural Networks](https://mlsanity.com/paper/2512.00164/) (2025)
- [The Effect of Data Poisoning on Counterfactual Explanations](https://mlsanity.com/paper/2402.08290/) (2024)
- [Optimal Robust Recourse with Lp-Bounded Model Change](https://mlsanity.com/paper/2509.21293/) (2025)
- [Counterfactual Explanations for Time Series Should be Human-Centered and Temporally Coherent in Interventions](https://mlsanity.com/paper/2512.14559/) (2025)
- [Out-of-Distribution Detection using Counterfactual Distance](https://mlsanity.com/paper/2508.10148/) (2025)
- [Synthesising Counterfactual Explanations via Label-Conditional Gaussian Mixture Variational Autoencoders](https://mlsanity.com/paper/2510.04855/) (2025)
- [Axiomatic Foundations of Counterfactual Explanations](https://mlsanity.com/paper/2602.04028/) (2026)
- [Evaluating Counterfactual Explanation Methods on Incomplete Inputs](https://mlsanity.com/paper/2604.08004/) (2026)
- [RecourseBench: A Modular Framework for Reproducible Algorithmic Recourse Evaluation](https://mlsanity.com/paper/2606.16113/) (2026)
- [We Need Explanation Cards to Connect Explanation Algorithms to the Real World](https://mlsanity.com/paper/2606.16786/) (2026)
- [Algorithmic Recourse Under Competition](https://mlsanity.com/paper/2609.39877/) (2026)

## Abstract (arXiv)

Counterfactual explanations shed light on the decisions of black-box models by explaining how an input can be altered to obtain a favourable decision from the model (e.g., when a loan application has been rejected). However, as noted recently, counterfactual explainers may lack robustness in the sense that a minor change in the input can cause a major change in the explanation. This can cause confusion on the user side and open the door for adversarial attacks. In this paper, we study some sources of non-robustness. While there are fundamental reasons for why an explainer that returns a single counterfactual cannot be robust in all instances, we show that some interesting robustness guarantees can be given by reporting multiple rather than a single counterfactual. Unfortunately, the number of counterfactuals that need to be reported for the theoretical guarantees to hold can be prohibitively large. We therefore propose an approximation algorithm that uses a diversity criterion to select a feasible number of most relevant explanations and study its robustness empirically. Our experiments indicate that our method improves the state-of-the-art in generating robust explanations, while maintaining other desirable properties and providing competitive computational performance.