# Ensemble-based Uncertainty Quantification: Bayesian versus Credal Inference

arXiv: https://arxiv.org/abs/2107.10384 · HTML: https://mlsanity.com/paper/2107.10384/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 21 Jul 2021.

## Builds on (most cited first, 6 of 6)

- [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)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [DropConnect Is Effective in Modeling Uncertainty of Bayesian Deep Networks](https://mlsanity.com/paper/1906.04569/) (2019)
- [Analysis of dropout learning regarded as ensemble learning](https://mlsanity.com/paper/1706.06859/) (2017)

## Built on by (most cited first, 16 of 16)

- [Benchmarking Uncertainty Disentanglement: Specialized Uncertainties for Specialized Tasks](https://mlsanity.com/paper/2402.19460/) (2024)
- [Classifier Calibration: A survey on how to assess and improve predicted class probabilities](https://mlsanity.com/paper/2112.10327/) (2021)
- [CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Tasks](https://mlsanity.com/paper/2401.05043/) (2024)
- [Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement](https://mlsanity.com/paper/2306.12803/) (2023)
- [Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification](https://mlsanity.com/paper/2405.15047/) (2024)
- [Integral Imprecise Probability Metrics](https://mlsanity.com/paper/2505.16156/) (2025)
- [Scoring Rules and Calibration for Imprecise Probabilities](https://mlsanity.com/paper/2410.23001/) (2024)
- [C-LoRA: Contextual Low-Rank Adaptation for Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2505.17773/) (2025)
- [Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'](https://mlsanity.com/paper/2505.04950/) (2025)
- [Learning Credal Ensembles via Distributionally Robust Optimization](https://mlsanity.com/paper/2602.08470/) (2026)
- [Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometry](https://mlsanity.com/paper/2602.01667/) (2026)
- [A view on model misspecification in uncertainty quantification](https://mlsanity.com/paper/2210.16938/) (2022)
- [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)
- [ElemeNet: Multiscale Molecular Machine Learning with Uncertainty Quantification Across the Periodic Table](https://mlsanity.com/paper/2606.30961/) (2026)
- [ST-LoRA: Single Trajectory LoRA Ensemble for Uncertainty Aware Agricultural Segmentation](https://mlsanity.com/paper/2608.01530/) (2026)

## Abstract (arXiv)

The idea to distinguish and quantify two important types of uncertainty, often referred to as aleatoric and epistemic, has received increasing attention in machine learning research in the last couple of years. In this paper, we consider ensemble-based approaches to uncertainty quantification. Distinguishing between different types of uncertainty-aware learning algorithms, we specifically focus on Bayesian methods and approaches based on so-called credal sets, which naturally suggest themselves from an ensemble learning point of view. For both approaches, we address the question of how to quantify aleatoric and epistemic uncertainty. The effectiveness of corresponding measures is evaluated and compared in an empirical study on classification with a reject option.