# Credal and Interval Deep Evidential Classifications

arXiv: https://arxiv.org/abs/2512.05526 · HTML: https://mlsanity.com/paper/2512.05526/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 78 references that are in the map.
- First posted on arXiv 5 Dec 2025.

## Builds on (most cited first, 25 of 25)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Puzzle Mix: Exploiting Saliency and Local Statistics for Optimal Mixup](https://mlsanity.com/paper/2009.06962/) (2020)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [On the Safety of Machine Learning: Cyber-Physical Systems, Decision Sciences, and Data Products](https://mlsanity.com/paper/1610.01256/) (2016)
- [Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?](https://mlsanity.com/paper/2306.09586/) (2023)
- [Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?](https://mlsanity.com/paper/2402.09056/) (2024)
- [AutoDEUQ: Automated Deep Ensemble with Uncertainty Quantification](https://mlsanity.com/paper/2110.13511/) (2021)
- [Learn to Accumulate Evidence from All Training Samples: Theory and Practice](https://mlsanity.com/paper/2306.11113/) (2023)
- [Engineering Safety in Machine Learning](https://mlsanity.com/paper/1601.04126/) (2016)
- [Credal Two-Sample Tests of Epistemic Uncertainty](https://mlsanity.com/paper/2410.12921/) (2024)
- [A Novel Bayes' Theorem for Upper Probabilities](https://mlsanity.com/paper/2307.06831/) (2023)
- [Integral Imprecise Probability Metrics](https://mlsanity.com/paper/2505.16156/) (2025)
- [Kronecker-factored Quasi-Newton Methods for Deep Learning](https://mlsanity.com/paper/2102.06737/) (2021)
- [An Evidential Neural Network Model for Regression Based on Random Fuzzy Numbers](https://mlsanity.com/paper/2208.00647/) (2022)
- [Using Semantic Information for Defining and Detecting OOD Inputs](https://mlsanity.com/paper/2302.11019/) (2023)
- [Generalized mixtures of finite mixtures and telescoping sampling](https://mlsanity.com/paper/2005.09918/) (2020)

## Built on by (most cited first, 8 of 8)

- [Random-Set Graph Neural Networks](https://mlsanity.com/paper/2605.11987/) (2026)
- [Statistical inference with belief functions: A survey](https://mlsanity.com/paper/2605.07908/) (2026)
- [Credal Large Language Models for Semantic Commitment under Uncertainty](https://mlsanity.com/paper/2608.23244/) (2026)
- [Structured Credal Learning](https://mlsanity.com/paper/2603.14070/) (2026)
- [What Intermediate Layers Know: Detecting Jailbreaks from Entropy Dynamics](https://mlsanity.com/paper/2606.25182/) (2026)
- [Upper Entropy for 2-Monotone Lower Probabilities](https://mlsanity.com/paper/2603.23558/) (2026)
- [Ensemble-Based Dirichlet Modeling for Predictive Uncertainty and Selective Classification](https://mlsanity.com/paper/2604.06032/) (2026)
- [XU-RS: Explaining Credal Width in Random-Set Language Models](https://mlsanity.com/paper/2609.37594/) (2026)

## Abstract (arXiv)

Uncertainty Quantification (UQ) presents a pivotal challenge in the field of Artificial Intelligence (AI), profoundly impacting decision-making, risk assessment and model reliability. In this paper, we introduce Credal and Interval Deep Evidential Classifications (CDEC and IDEC, respectively) as novel approaches to address UQ in classification tasks. CDEC and IDEC leverage a credal set (closed and convex set of probabilities) and an interval of evidential predictive distributions, respectively, allowing us to avoid overfitting to the training data and to systematically assess both epistemic (reducible) and aleatoric (irreducible) uncertainties. When those surpass acceptable thresholds, CDEC and IDEC have the capability to abstain from classification and flag an excess of epistemic or aleatoric uncertainty, as relevant. Conversely, within acceptable uncertainty bounds, CDEC and IDEC provide a collection of labels with robust probabilistic guarantees. CDEC and IDEC are trained using standard backpropagation and a loss function that draws from the theory of evidence. They overcome the shortcomings of previous efforts, and extend the current evidential deep learning literature. Through extensive experiments on MNIST, CIFAR-10 and CIFAR-100, together with their natural OoD shifts (F-MNIST/K-MNIST, SVHN/Intel, TinyImageNet), we show that CDEC and IDEC achieve competitive predictive accuracy, state-of-the-art OoD detection under epistemic and total uncertainty, and tight, well-calibrated prediction regions that expand reliably under distribution shift. An ablation over ensemble size further demonstrates that CDEC attains stable uncertainty estimates with only a small ensemble.