# Learning Credal Ensembles via Distributionally Robust Optimization

arXiv: https://arxiv.org/abs/2602.08470 · HTML: https://mlsanity.com/paper/2602.08470/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 73 references that are in the map.
- First posted on arXiv 9 Feb 2026.

## Builds on (most cited first, 30 of 45)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Natural Adversarial Examples](https://mlsanity.com/paper/1907.07174/) (2019)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)
- [Fairness without Demographics through Adversarially Reweighted Learning](https://mlsanity.com/paper/2006.13114/) (2020)
- [Deep Deterministic Uncertainty: A Simple Baseline](https://mlsanity.com/paper/2102.11582/) (2021)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Distributionally Robust Language Modeling](https://mlsanity.com/paper/1909.02060/) (2019)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)
- [DropConnect Is Effective in Modeling Uncertainty of Bayesian Deep Networks](https://mlsanity.com/paper/1906.04569/) (2019)
- [Masksembles for Uncertainty Estimation](https://mlsanity.com/paper/2012.08334/) (2020)
- [Benchmarking Uncertainty Disentanglement: Specialized Uncertainties for Specialized Tasks](https://mlsanity.com/paper/2402.19460/) (2024)
- [Bayesian Hypernetworks](https://mlsanity.com/paper/1710.04759/) (2017)
- [A Call to Reflect on Evaluation Practices for Failure Detection in Image Classification](https://mlsanity.com/paper/2211.15259/) (2022)
- [Packed-Ensembles for Efficient Uncertainty Estimation](https://mlsanity.com/paper/2210.09184/) (2022)
- [Credal Bayesian Deep Learning](https://mlsanity.com/paper/2302.09656/) (2023)
- [Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?](https://mlsanity.com/paper/2306.09586/) (2023)
- [On Second-Order Scoring Rules for Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2301.12736/) (2023)
- [Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?](https://mlsanity.com/paper/2402.09056/) (2024)
- [CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Tasks](https://mlsanity.com/paper/2401.05043/) (2024)
- [The Two Dimensions of Worst-case Training and the Integrated Effect for Out-of-domain Generalization](https://mlsanity.com/paper/2204.04384/) (2022)

## Built on by (most cited first, 7 of 7)

- [Credal Large Language Models for Semantic Commitment under Uncertainty](https://mlsanity.com/paper/2608.23244/) (2026)
- [Set-based v.s. Distribution-based Representations of Epistemic Uncertainty: A Comparative Study](https://mlsanity.com/paper/2602.22747/) (2026)
- [A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classification](https://mlsanity.com/paper/2605.16383/) (2026)
- [Unification and Optimization of Robust Supervised Learning](https://mlsanity.com/paper/2605.28165/) (2026)
- [XU-RS: Explaining Credal Width in Random-Set Language Models](https://mlsanity.com/paper/2609.37594/) (2026)
- [Compact set-valued deep ensembling in multi-class classification](https://mlsanity.com/paper/2610.05332/) (2026)
- [Credal Machine Learning for Risk-Averse Decision Making](https://mlsanity.com/paper/2610.12115/) (2026)

## Abstract (arXiv)

Credal predictors are models that are aware of epistemic uncertainty and produce a convex set of probabilistic predictions. They offer a principled way to quantify predictive epistemic uncertainty (EU) and have been shown to improve model robustness in various settings. However, most state-of-the-art methods mainly define EU as disagreement caused by random training initializations, which mostly reflects sensitivity to optimization randomness rather than uncertainty from deeper sources. To address this, we define EU as disagreement among models trained with varying relaxations of the i.i.d. assumption between training and test data. Based on this idea, we propose CreDRO, which learns an ensemble of plausible models through distributionally robust optimization. As a result, CreDRO captures EU not only from training randomness but also from meaningful disagreement due to potential distribution shifts between training and test data. Empirical results show that CreDRO consistently outperforms existing credal methods on tasks such as out-of-distribution detection across multiple benchmarks and selective classification in medical applications.