# Counterfactual Explanations with Probabilistic Guarantees on their Robustness to Model Change

arXiv: https://arxiv.org/abs/2408.04842 · HTML: https://mlsanity.com/paper/2408.04842/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 41 references that are in the map.
- First posted on arXiv 9 Aug 2024.

## Builds on (most cited first, 25 of 25)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Explaining Machine Learning Classifiers through Diverse Counterfactual Explanations](https://mlsanity.com/paper/1905.07697/) (2019)
- [Making AI Forget You: Data Deletion in Machine Learning](https://mlsanity.com/paper/1907.05012/) (2019)
- [FACE: Feasible and Actionable Counterfactual Explanations](https://mlsanity.com/paper/1909.09369/) (2019)
- [Counterfactual Explanations and Algorithmic Recourses for Machine Learning: A Review](https://mlsanity.com/paper/2010.10596/) (2020)
- [Towards Robust and Reliable Algorithmic Recourse](https://mlsanity.com/paper/2102.13620/) (2021)
- [If Only We Had Better Counterfactual Explanations: Five Key Deficits to Rectify in the Evaluation of Counterfactual XAI Techniques](https://mlsanity.com/paper/2103.01035/) (2021)
- [GANterfactual - Counterfactual Explanations for Medical Non-Experts using Generative Adversarial Learning](https://mlsanity.com/paper/2012.11905/) (2020)
- [Robust Counterfactual Explanations for Tree-Based Ensembles](https://mlsanity.com/paper/2207.02739/) (2022)
- [Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees](https://mlsanity.com/paper/2305.11997/) (2023)
- [Evaluating Robustness of Counterfactual Explanations](https://mlsanity.com/paper/2103.02354/) (2021)
- [Probabilistically Robust Recourse: Navigating the Trade-offs between Costs and Robustness in Algorithmic Recourse](https://mlsanity.com/paper/2203.06768/) (2022)
- [A Survey on the Robustness of Feature Importance and Counterfactual Explanations](https://mlsanity.com/paper/2111.00358/) (2021)
- [On the Robustness of Sparse Counterfactual Explanations to Adverse Perturbations](https://mlsanity.com/paper/2201.09051/) (2022)
- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Formalising the Robustness of Counterfactual Explanations for Neural Networks](https://mlsanity.com/paper/2208.14878/) (2022)
- [Finding Regions of Counterfactual Explanations via Robust Optimization](https://mlsanity.com/paper/2301.11113/) (2023)
- [Robust Bayesian Recourse](https://mlsanity.com/paper/2206.10833/) (2022)
- [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)
- ["Explain it in the Same Way!" -- Model-Agnostic Group Fairness of Counterfactual Explanations](https://mlsanity.com/paper/2211.14858/) (2022)
- [A multi-criteria approach for selecting an explanation from the set of counterfactuals produced by an ensemble of explainers](https://mlsanity.com/paper/2403.13940/) (2024)
- [Rigorous Probabilistic Guarantees for Robust Counterfactual Explanations](https://mlsanity.com/paper/2407.07482/) (2024)
- [Generally-Occurring Model Change for Robust Counterfactual Explanations](https://mlsanity.com/paper/2407.11426/) (2024)

## Built on by (most cited first, 10 of 10)

- [Counterfactual Explanations for Model Ensembles Using Entropic Risk Measures](https://mlsanity.com/paper/2503.07934/) (2025)
- [Reinforcement Learning for Durable Algorithmic Recourse](https://mlsanity.com/paper/2509.22102/) (2025)
- [Explaining Concept Drift through the Evolution of Group Counterfactuals](https://mlsanity.com/paper/2509.09616/) (2025)
- [PAR: Plausibility-aware Amortized Recourse Generation](https://mlsanity.com/paper/2601.17309/) (2026)
- [Provably Robust Bayesian Counterfactual Explanations under Model Changes](https://mlsanity.com/paper/2601.16659/) (2026)
- [The Impact of Machine Learning Uncertainty on the Robustness of Counterfactual Explanations](https://mlsanity.com/paper/2602.00063/) (2026)
- [A Probabilistic Consensus-Driven Approach for Robust Counterfactual Explanations](https://mlsanity.com/paper/2604.17494/) (2026)
- [Counterfactual Explanations Under Concept Drift](https://mlsanity.com/paper/2605.17651/) (2026)
- [Density-Guided Robust Counterfactual Explanations on Tabular Data under Model Multiplicity](https://mlsanity.com/paper/2605.30901/) (2026)
- [Robust to Which Model Change? A Unified Evaluation of Robust Counterfactual Explanations](https://mlsanity.com/paper/2609.30918/) (2026)

## Abstract (arXiv)

Counterfactual explanations (CFEs) guide users on how to adjust inputs to machine learning models to achieve desired outputs. While existing research primarily addresses static scenarios, real-world applications often involve data or model changes, potentially invalidating previously generated CFEs and rendering user-induced input changes ineffective. Current methods addressing this issue often support only specific models or change types, require extensive hyperparameter tuning, or fail to provide probabilistic guarantees on CFE robustness to model changes. This paper proposes a novel approach for generating CFEs that provides probabilistic guarantees for any model and change type, while offering interpretable and easy-to-select hyperparameters. We establish a theoretical framework for probabilistically defining robustness to model change and demonstrate how our BetaRCE method directly stems from it. BetaRCE is a post-hoc method applied alongside a chosen base CFE generation method to enhance the quality of the explanation beyond robustness. It facilitates a transition from the base explanation to a more robust one with user-adjusted probability bounds. Through experimental comparisons with baselines, we show that BetaRCE yields robust, most plausible, and closest to baseline counterfactual explanations.