# Provably Robust Bayesian Counterfactual Explanations under Model Changes

Source: [Provably Robust Bayesian Counterfactual Explanations under Model Changes](<https://www.sota2.com/research/paper/6976f4e9a2b28e761d87c0f0>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-02-13T05:00:04.183Z

Authors: Jamie Duell, Xiuyi Fan

Published: 2026-01-23T11:24:57.000Z

## Abstract

Counterfactual explanations (CEs) offer interpretable insights into machine learning predictions by answering \`\`what if?" questions. However, in real-world settings where models are frequently updated, existing counterfactual explanations can quickly become invalid or unreliable. In this paper, we introduce Probabilistically Safe CEs (PSCE), a method for generating counterfactual explanations that are $\\delta$-safe, to ensure high predictive confidence, and $\\epsilon$-robust to ensure low predictive variance. Based on Bayesian principles, PSCE provides formal probabilistic guarantees for CEs under model changes which are adhered to in what we refer to as the $\\langle \\delta, \\epsilon \\rangle$-set. Uncertainty-aware constraints are integrated into our optimization framework and we validate our method empirically across diverse datasets. We compare our approach against state-of-the-art Bayesian CE methods, where PSCE produces counterfactual explanations that are not only more plausible and discriminative, but also provably robust under model change.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Counterfactual Explanations on Breast Cancer (test)](<https://www.sota2.com/research/sota/counterfactual-explanations-on-breast-cancer-test.md>): Counterfactual Explanations; Breast Cancer (test); IM1: 1.554.

- [Counterfactual Explanation on MNIST (test)](<https://www.sota2.com/research/sota/counterfactual-explanation-on-mnist-test.md>): Counterfactual Explanation; MNIST (test); Validity Score: 98.2.

- [Counterfactual Explanations on MNIST (test)](<https://www.sota2.com/research/sota/counterfactual-explanations-on-mnist-test.md>): Counterfactual Explanations; MNIST (test); IM1 Score: 0.9768.

- [Counterfactual Explanations on Credit (test)](<https://www.sota2.com/research/sota/counterfactual-explanations-on-credit-test.md>): Counterfactual Explanations; Credit (test); IM1: 0.7383.

- [Counterfactual Explanations on Spam (test)](<https://www.sota2.com/research/sota/counterfactual-explanations-on-spam-test.md>): Counterfactual Explanations; Spam (test); IM1: 0.8967.

- [Counterfactual Explanations on PneumoniaMNIST (test)](<https://www.sota2.com/research/sota/counterfactual-explanations-on-pneumoniamnist-test.md>): Counterfactual Explanations; PneumoniaMNIST (test); IM1: 0.63.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2601.16659>)

[PDF](<https://arxiv.org/pdf/2601.16659.pdf>)