# Generating Interpretable Counterfactual Explanations By Implicit Minimisation of Epistemic and Aleatoric Uncertainties

arXiv: https://arxiv.org/abs/2103.08951 · HTML: https://mlsanity.com/paper/2103.08951/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 33 references that are in the map.
- First posted on arXiv 16 Mar 2021.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [The Limitations of Deep Learning in Adversarial Settings](https://mlsanity.com/paper/1511.07528/) (2015)
- [The Mythos of Model Interpretability](https://mlsanity.com/paper/1606.03490/) (2016)
- [Adversarial Patch](https://mlsanity.com/paper/1712.09665/) (2017)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Explanations based on the Missing: Towards Contrastive Explanations with Pertinent Negatives](https://mlsanity.com/paper/1802.07623/) (2018)
- [Interpretable Counterfactual Explanations Guided by Prototypes](https://mlsanity.com/paper/1907.02584/) (2019)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Towards Realistic Individual Recourse and Actionable Explanations in Black-Box Decision Making Systems](https://mlsanity.com/paper/1907.09615/) (2019)
- [The Dangers of Post-hoc Interpretability: Unjustified Counterfactual Explanations](https://mlsanity.com/paper/1907.09294/) (2019)
- [Uncertainty Estimation Using a Single Deep Deterministic Neural Network](https://mlsanity.com/paper/2003.02037/) (2020)
- [What is Interpretable? Using Machine Learning to Design Interpretable Decision-Support Systems](https://mlsanity.com/paper/1811.10799/) (2018)
- [Sufficient Conditions for Idealised Models to Have No Adversarial Examples: a Theoretical and Empirical Study with Bayesian Neural Networks](https://mlsanity.com/paper/1806.00667/) (2018)

## Built on by (most cited first, 30 of 41)

- [Diffusion Visual Counterfactual Explanations](https://mlsanity.com/paper/2210.11841/) (2022)
- [Diffusion Causal Models for Counterfactual Estimation](https://mlsanity.com/paper/2202.10166/) (2022)
- [CARLA: A Python Library to Benchmark Algorithmic Recourse and Counterfactual Explanation Algorithms](https://mlsanity.com/paper/2108.00783/) (2021)
- [Diffusion Models for Counterfactual Explanations](https://mlsanity.com/paper/2203.15636/) (2022)
- [High Fidelity Image Counterfactuals with Probabilistic Causal Models](https://mlsanity.com/paper/2306.15764/) (2023)
- [Adversarial Counterfactual Visual Explanations](https://mlsanity.com/paper/2303.09962/) (2023)
- [Sparse Visual Counterfactual Explanations in Image Space](https://mlsanity.com/paper/2205.07972/) (2022)
- [Diffeomorphic Counterfactuals with Generative Models](https://mlsanity.com/paper/2206.05075/) (2022)
- [Scientific Inference With Interpretable Machine Learning: Analyzing Models to Learn About Real-World Phenomena](https://mlsanity.com/paper/2206.05487/) (2022)
- [CounterNet: End-to-End Training of Prediction Aware Counterfactual Explanations](https://mlsanity.com/paper/2109.07557/) (2021)
- [Uncertainty Estimation and Out-of-Distribution Detection for Counterfactual Explanations: Pitfalls and Solutions](https://mlsanity.com/paper/2107.09734/) (2021)
- [Global Counterfactual Directions](https://mlsanity.com/paper/2404.12488/) (2024)
- [Rethinking Visual Counterfactual Explanations Through Region Constraint](https://mlsanity.com/paper/2410.12591/) (2024)
- [Counterfactual Explanations for Misclassified Images: How Human and Machine Explanations Differ](https://mlsanity.com/paper/2212.08733/) (2022)
- [Diffusion Counterfactual Generation with Semantic Abduction](https://mlsanity.com/paper/2506.07883/) (2025)
- [Endogenous Macrodynamics in Algorithmic Recourse](https://mlsanity.com/paper/2308.08187/) (2023)
- [Attribution of Predictive Uncertainties in Classification Models](https://mlsanity.com/paper/2107.08756/) (2021)
- [On Quantitative Evaluations of Counterfactuals](https://mlsanity.com/paper/2111.00177/) (2021)
- [DeDUCE: Generating Counterfactual Explanations Efficiently](https://mlsanity.com/paper/2111.15639/) (2021)
- [What is Flagged in Uncertainty Quantification? Latent Density Models for Uncertainty Categorization](https://mlsanity.com/paper/2207.05161/) (2022)
- [Designing User-Centric Behavioral Interventions to Prevent Dysglycemia with Novel Counterfactual Explanations](https://mlsanity.com/paper/2310.01684/) (2023)
- [Faithful Model Explanations through Energy-Constrained Conformal Counterfactuals](https://mlsanity.com/paper/2312.10648/) (2023)
- [GlyTwin: Digital Twin for Glucose Control in Type 1 Diabetes Through Optimal Behavioral Modifications Using Patient-Centric Counterfactuals](https://mlsanity.com/paper/2504.09846/) (2025)
- [From Search To Sampling: Generative Models For Robust Algorithmic Recourse](https://mlsanity.com/paper/2505.07351/) (2025)
- [Explaining Black-Box Models through Counterfactuals](https://mlsanity.com/paper/2308.07198/) (2023)
- [Causal Generative Explainers using Counterfactual Inference: A Case Study on the Morpho-MNIST Dataset](https://mlsanity.com/paper/2401.11394/) (2024)
- [Generating Feasible and Plausible Counterfactual Explanations for Outcome Prediction of Business Processes](https://mlsanity.com/paper/2403.09232/) (2024)
- [Uncertainty Quantification as a Principled Foundation for Explainable Artificial Intelligence: A Case Study of Counterfactual Explanations](https://mlsanity.com/paper/2502.17007/) (2025)
- [Concerning Uncertainty -- A Systematic Survey of Uncertainty-Aware XAI](https://mlsanity.com/paper/2603.26838/) (2026)
- [Improving Counterfactual Truthfulness for Molecular Property Prediction through Uncertainty Quantification](https://mlsanity.com/paper/2504.02606/) (2025)

## Abstract (arXiv)

Counterfactual explanations (CEs) are a practical tool for demonstrating why machine learning classifiers make particular decisions. For CEs to be useful, it is important that they are easy for users to interpret. Existing methods for generating interpretable CEs rely on auxiliary generative models, which may not be suitable for complex datasets, and incur engineering overhead. We introduce a simple and fast method for generating interpretable CEs in a white-box setting without an auxiliary model, by using the predictive uncertainty of the classifier. Our experiments show that our proposed algorithm generates more interpretable CEs, according to IM1 scores, than existing methods. Additionally, our approach allows us to estimate the uncertainty of a CE, which may be important in safety-critical applications, such as those in the medical domain.