# Robust Counterfactual Explanations for Neural Networks With Probabilistic Guarantees

arXiv: https://arxiv.org/abs/2305.11997 · HTML: https://mlsanity.com/paper/2305.11997/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 46 references that are in the map.
- First posted on arXiv 19 May 2023.

## Builds on (most cited first, 26 of 26)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [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)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Learning Model-Agnostic Counterfactual Explanations for Tabular Data](https://mlsanity.com/paper/1910.09398/) (2019)
- [A survey of algorithmic recourse: definitions, formulations, solutions, and prospects](https://mlsanity.com/paper/2010.04050/) (2020)
- [The Hidden Assumptions Behind Counterfactual Explanations and Principal Reasons](https://mlsanity.com/paper/1912.04930/) (2019)
- [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)
- [On the Adversarial Robustness of Causal Algorithmic Recourse](https://mlsanity.com/paper/2112.11313/) (2021)
- [Equalizing Recourse across Groups](https://mlsanity.com/paper/1909.03166/) (2019)
- [Robust Counterfactual Explanations for Tree-Based Ensembles](https://mlsanity.com/paper/2207.02739/) (2022)
- [Rashomon Capacity: A Metric for Predictive Multiplicity in Classification](https://mlsanity.com/paper/2206.01295/) (2022)
- [Predictive Multiplicity in Probabilistic Classification](https://mlsanity.com/paper/2206.01131/) (2022)
- [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)
- [Consistent Counterfactuals for Deep Models](https://mlsanity.com/paper/2110.03109/) (2021)
- [CERTIFAI: Counterfactual Explanations for Robustness, Transparency, Interpretability, and Fairness of Artificial Intelligence models](https://mlsanity.com/paper/1905.07857/) (2019)
- [Issues with post-hoc counterfactual explanations: a discussion](https://mlsanity.com/paper/1906.04774/) (2019)
- [BRPO: Batch Residual Policy Optimization](https://mlsanity.com/paper/2002.05522/) (2020)
- [Formalising the Robustness of Counterfactual Explanations for Neural Networks](https://mlsanity.com/paper/2208.14878/) (2022)
- [Counterfactual Shapley Additive Explanations](https://mlsanity.com/paper/2110.14270/) (2021)
- [Finding Regions of Counterfactual Explanations via Robust Optimization](https://mlsanity.com/paper/2301.11113/) (2023)
- [Robustness Implies Fairness in Causal Algorithmic Recourse](https://mlsanity.com/paper/2302.03465/) (2023)
- [Global Counterfactual Explanations: Investigations, Implementations and Improvements](https://mlsanity.com/paper/2204.06917/) (2022)
- [Bayesian Hierarchical Models for Counterfactual Estimation](https://mlsanity.com/paper/2301.08833/) (2023)

## Built on by (most cited first, 30 of 45)

- [Robust Counterfactual Explanations in Machine Learning: A Survey](https://mlsanity.com/paper/2402.01928/) (2024)
- [Provably Robust and Plausible Counterfactual Explanations for Neural Networks via Robust Optimisation](https://mlsanity.com/paper/2309.12545/) (2023)
- [Promoting Counterfactual Robustness through Diversity](https://mlsanity.com/paper/2312.06564/) (2023)
- [Systemizing Multiplicity: The Curious Case of Arbitrariness in Machine Learning](https://mlsanity.com/paper/2501.14959/) (2025)
- [Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)](https://mlsanity.com/paper/2312.15097/) (2023)
- [Model Reconstruction Using Counterfactual Explanations: A Perspective From Polytope Theory](https://mlsanity.com/paper/2405.05369/) (2024)
- [T-SHIRT: Token-Selective Hierarchical Data Selection for Instruction Tuning](https://mlsanity.com/paper/2506.01317/) (2025)
- [Counterfactual Explanations with Probabilistic Guarantees on their Robustness to Model Change](https://mlsanity.com/paper/2408.04842/) (2024)
- [Time Can Invalidate Algorithmic Recourse](https://mlsanity.com/paper/2410.08007/) (2024)
- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [Interval Abstractions for Robust Counterfactual Explanations](https://mlsanity.com/paper/2404.13736/) (2024)
- [Quantifying Prediction Consistency Under Fine-Tuning Multiplicity in Tabular LLMs](https://mlsanity.com/paper/2407.04173/) (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)
- [Even-Ifs From If-Onlys: Are the Best Semi-Factual Explanations Found Using Counterfactuals As Guides?](https://mlsanity.com/paper/2403.00980/) (2024)
- [Demystifying the Accuracy-Interpretability Trade-Off: A Case Study of Inferring Ratings from Reviews](https://mlsanity.com/paper/2503.07914/) (2025)
- [Counterfactual Explanations for Model Ensembles Using Entropic Risk Measures](https://mlsanity.com/paper/2503.07934/) (2025)
- [From Search To Sampling: Generative Models For Robust Algorithmic Recourse](https://mlsanity.com/paper/2505.07351/) (2025)
- [Trust Regions for Explanations via Black-Box Probabilistic Certification](https://mlsanity.com/paper/2402.11168/) (2024)
- [Learning-Augmented Robust Algorithmic Recourse](https://mlsanity.com/paper/2410.01580/) (2024)
- [Few-Shot Knowledge Distillation of LLMs With Counterfactual Explanations](https://mlsanity.com/paper/2510.21631/) (2025)
- [Faster Verified Explanations for Neural Networks](https://mlsanity.com/paper/2512.00164/) (2025)
- [A Unified View of Group Fairness Tradeoffs Using Partial Information Decomposition](https://mlsanity.com/paper/2406.04562/) (2024)
- [VISION: Robust and Interpretable Code Vulnerability Detection Leveraging Counterfactual Augmentation](https://mlsanity.com/paper/2508.18933/) (2025)
- [Optimal Robust Recourse with Lp-Bounded Model Change](https://mlsanity.com/paper/2509.21293/) (2025)
- [Counterfactual Modeling with Fine-Tuned LLMs for Health Intervention Design and Sensor Data Augmentation](https://mlsanity.com/paper/2601.14590/) (2026)
- [Verified Training for Counterfactual Explanation Robustness under Data Shift](https://mlsanity.com/paper/2403.03773/) (2024)
- [Generally-Occurring Model Change for Robust Counterfactual Explanations](https://mlsanity.com/paper/2407.11426/) (2024)
- [Private Counterfactual Retrieval](https://mlsanity.com/paper/2410.13812/) (2024)
- [ElliCE: Efficient and Provably Robust Algorithmic Recourse via the Rashomon Sets](https://mlsanity.com/paper/2602.07674/) (2026)

## Abstract (arXiv)

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model m and the new model M are bounded in the parameter space, i.e., |Params(M)-Params(m)|<Delta. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed textitnaturally-occurring model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call textitStability -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of textitStability as defined by our measure will remain valid after potential textitnaturally-occurring model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes. This work also has interesting connections with model multiplicity, also known as, the Rashomon effect.