# Verified Training for Counterfactual Explanation Robustness under Data Shift

arXiv: https://arxiv.org/abs/2403.03773 · HTML: https://mlsanity.com/paper/2403.03773/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 38 references that are in the map.
- First posted on arXiv 6 Mar 2024.

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

- [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)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Fooling LIME and SHAP: Adversarial Attacks on Post hoc Explanation Methods](https://mlsanity.com/paper/1911.02508/) (2019)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (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)
- [Towards Stable and Efficient Training of Verifiably Robust Neural Networks](https://mlsanity.com/paper/1906.06316/) (2019)
- [Model-Agnostic Counterfactual Explanations for Consequential Decisions](https://mlsanity.com/paper/1905.11190/) (2019)
- [Predictive Multiplicity in Classification](https://mlsanity.com/paper/1909.06677/) (2019)
- [Fooling Neural Network Interpretations via Adversarial Model Manipulation](https://mlsanity.com/paper/1902.02041/) (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)
- [Fairwashing Explanations with Off-Manifold Detergent](https://mlsanity.com/paper/2007.09969/) (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)
- [Towards Robust Explanations for Deep Neural Networks](https://mlsanity.com/paper/2012.10425/) (2020)
- [Consistent Counterfactuals for Deep Models](https://mlsanity.com/paper/2110.03109/) (2021)
- [Formalising the Robustness of Counterfactual Explanations for Neural Networks](https://mlsanity.com/paper/2208.14878/) (2022)
- [Counterfactual Plans under Distributional Ambiguity](https://mlsanity.com/paper/2201.12487/) (2022)
- [Efficiently Training Low-Curvature Neural Networks](https://mlsanity.com/paper/2206.07144/) (2022)
- [Certified Robustness to Programmable Transformations in LSTMs](https://mlsanity.com/paper/2102.07818/) (2021)
- [CounterNet: End-to-End Training of Prediction Aware Counterfactual Explanations](https://mlsanity.com/paper/2109.07557/) (2021)
- [Distributionally Robust Recourse Action](https://mlsanity.com/paper/2302.11211/) (2023)
- [On Minimizing the Impact of Dataset Shifts on Actionable Explanations](https://mlsanity.com/paper/2306.06716/) (2023)

## Built on by (most cited first, 2 of 2)

- [Counterfactual Explanations for Model Ensembles Using Entropic Risk Measures](https://mlsanity.com/paper/2503.07934/) (2025)
- [The Impact of Machine Learning Uncertainty on the Robustness of Counterfactual Explanations](https://mlsanity.com/paper/2602.00063/) (2026)

## Abstract (arXiv)

Counterfactual explanations (CEs) enhance the interpretability of machine learning models by describing what changes to an input are necessary to change its prediction to a desired class. These explanations are commonly used to guide users' actions, e.g., by describing how a user whose loan application was denied can be approved for a loan in the future. Existing approaches generate CEs by focusing on a single, fixed model, and do not provide any formal guarantees on the CEs' future validity. When models are updated periodically to account for data shift, if the generated CEs are not robust to the shifts, users' actions may no longer have the desired impacts on their predictions. This paper introduces VeriTraCER, an approach that jointly trains a classifier and an explainer to explicitly consider the robustness of the generated CEs to small model shifts. VeriTraCER optimizes over a carefully designed loss function that ensures the verifiable robustness of CEs to local model updates, thus providing deterministic guarantees to CE validity. Our empirical evaluation demonstrates that VeriTraCER generates CEs that (1) are verifiably robust to small model updates and (2) display competitive robustness to state-of-the-art approaches in handling empirical model updates including random initialization, leave-one-out, and distribution shifts.