# Structured Credal Learning

arXiv: https://arxiv.org/abs/2603.14070 · HTML: https://mlsanity.com/paper/2603.14070/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 46 references that are in the map.
- First posted on arXiv 14 Mar 2026.

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

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [Learning Models with Uniform Performance via Distributionally Robust Optimization](https://mlsanity.com/paper/1810.08750/) (2018)
- [What Can We Learn from Collective Human Opinions on Natural Language Inference Data?](https://mlsanity.com/paper/2010.03532/) (2020)
- [Is one annotation enough? A data-centric image classification benchmark for noisy and ambiguous label estimation](https://mlsanity.com/paper/2207.06214/) (2022)
- [Diagnosing Model Performance Under Distribution Shift](https://mlsanity.com/paper/2303.02011/) (2023)
- [Credal Learning Theory](https://mlsanity.com/paper/2402.00957/) (2024)
- [Investigating Reasons for Disagreement in Natural Language Inference](https://mlsanity.com/paper/2209.03392/) (2022)
- [Conformalized Credal Set Predictors](https://mlsanity.com/paper/2402.10723/) (2024)
- [Not all distributional shifts are equal: Fine-grained robust conformal inference](https://mlsanity.com/paper/2402.13042/) (2024)
- [Robust Importance Weighting for Covariate Shift](https://mlsanity.com/paper/1910.06324/) (2019)
- [Handling Out-of-Distribution Data: A Survey](https://mlsanity.com/paper/2507.21160/) (2025)
- [Noisy Label Processing for Classification: A Survey](https://mlsanity.com/paper/2404.04159/) (2024)
- [Credal Prediction based on Relative Likelihood](https://mlsanity.com/paper/2505.22332/) (2025)
- [Credal Ensemble Distillation for Uncertainty Quantification](https://mlsanity.com/paper/2511.13766/) (2025)
- [Credal and Interval Deep Evidential Classifications](https://mlsanity.com/paper/2512.05526/) (2025)
- [Learning Fair Invariant Representations under Covariate and Correlation Shifts Simultaneously](https://mlsanity.com/paper/2408.09312/) (2024)
- [Random-Set Large Language Models](https://mlsanity.com/paper/2504.18085/) (2025)
- [Enhancing Uncertainty Quantification in Drug Discovery with Censored Regression Labels](https://mlsanity.com/paper/2409.04313/) (2024)
- [Beyond Minimax Rates in Group Distributionally Robust Optimization via a Novel Notion of Sparsity](https://mlsanity.com/paper/2410.00690/) (2024)
- [Pooling Image Datasets With Multiple Covariate Shift and Imbalance](https://mlsanity.com/paper/2403.02598/) (2024)
- [Revisiting Active Learning under (Human) Label Variation](https://mlsanity.com/paper/2507.02593/) (2025)
- [On the Ramifications of Human Label Uncertainty](https://mlsanity.com/paper/2211.05871/) (2022)
- [CASUAL: Conditional Support Alignment for Domain Adaptation with Label Shift](https://mlsanity.com/paper/2305.18458/) (2023)
- [GenKL: An Iterative Framework for Resolving Label Ambiguity and Label Non-conformity in Web Images Via a New Generalized KL Divergence](https://mlsanity.com/paper/2307.09810/) (2023)
- [Multiple Wasserstein Gradient Descent Algorithm for Multi-Objective Distributional Optimization](https://mlsanity.com/paper/2505.18765/) (2025)
- [Generalized Decision Focused Learning under Imprecise Uncertainty--Theoretical Study](https://mlsanity.com/paper/2502.17984/) (2025)
- [Leveraging Robust Optimization for LLM Alignment under Distribution Shifts](https://mlsanity.com/paper/2504.05831/) (2025)
- [Moment Alignment: Unifying Gradient and Hessian Matching for Domain Generalization](https://mlsanity.com/paper/2506.07378/) (2025)
- [Out-of-distribution Robust Optimization](https://mlsanity.com/paper/2410.14899/) (2024)

## Built on by (most cited first, 1 of 1)

- [What Intermediate Layers Know: Detecting Jailbreaks from Entropy Dynamics](https://mlsanity.com/paper/2606.25182/) (2026)

## Abstract (arXiv)

Real-world learning tasks often encounter uncertainty due to covariate shift and noisy or inconsistent labels. However, existing robust learning methods merge these effects into a single distributional uncertainty set. In this work, we introduce a novel structured credal learning framework that explicitly separates these two sources. Specifically, we derive geometric bounds on the total variation diameter of structured credal sets and demonstrate how this quantity decomposes into contributions from covariate shift and expected label disagreement. This decomposition reveals a gating effect: covariate modulates how much label disagreement contributes to the joint uncertainty, such that seemingly benign covariate shifts can substantially increase the effective uncertainty. We also establish finite-sample concentration bounds in a fixed covariate regime and demonstrate that this quantity can be efficiently estimated. Lastly, we show that robust optimization over these structured credal sets reduces to a tractable discrete min-max problem, avoiding ad-hoc robustness parameters. Overall, our approach provides a principled and practical foundation for robust learning under combined covariate and label mechanism ambiguity.