# Evidential Uncertainty Quantification: A Variance-Based Perspective

arXiv: https://arxiv.org/abs/2311.11367 · HTML: https://mlsanity.com/paper/2311.11367/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 46 references that are in the map.
- First posted on arXiv 19 Nov 2023.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Deep Batch Active Learning by Diverse, Uncertain Gradient Lower Bounds](https://mlsanity.com/paper/1906.03671/) (2019)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [VisDA: The Visual Domain Adaptation Challenge](https://mlsanity.com/paper/1710.06924/) (2017)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Understanding Measures of Uncertainty for Adversarial Example Detection](https://mlsanity.com/paper/1803.08533/) (2018)
- [Evidential Deep Learning for Open Set Action Recognition](https://mlsanity.com/paper/2107.10161/) (2021)
- [Uncertainty Aware Semi-Supervised Learning on Graph Data](https://mlsanity.com/paper/2010.12783/) (2020)
- [Deep Active Learning: Unified and Principled Method for Query and Training](https://mlsanity.com/paper/1911.09162/) (2019)
- [Active Adversarial Domain Adaptation](https://mlsanity.com/paper/1904.07848/) (2019)
- [Active Domain Adaptation via Clustering Uncertainty-weighted Embeddings](https://mlsanity.com/paper/2010.08666/) (2020)
- [Active Learning for Domain Adaptation: An Energy-Based Approach](https://mlsanity.com/paper/2112.01406/) (2021)
- [Bayesian QuickNAT: Model Uncertainty in Deep Whole-Brain Segmentation for Structure-wise Quality Control](https://mlsanity.com/paper/1811.09800/) (2018)
- [Density estimation in representation space to predict model uncertainty](https://mlsanity.com/paper/1908.07235/) (2019)
- [Disentangling Epistemic and Aleatoric Uncertainty in Reinforcement Learning](https://mlsanity.com/paper/2206.01558/) (2022)
- [Dirichlet-based Uncertainty Calibration for Active Domain Adaptation](https://mlsanity.com/paper/2302.13824/) (2023)
- [DEAL: Deep Evidential Active Learning for Image Classification](https://mlsanity.com/paper/2007.11344/) (2020)
- [Region-Based Evidential Deep Learning to Quantify Uncertainty and Improve Robustness of Brain Tumor Segmentation](https://mlsanity.com/paper/2208.06038/) (2022)
- [Learning Distinctive Margin toward Active Domain Adaptation](https://mlsanity.com/paper/2203.05738/) (2022)
- [Discrepancy-Based Active Learning for Domain Adaptation](https://mlsanity.com/paper/2103.03757/) (2021)
- [Quantifying Classification Uncertainty using Regularized Evidential Neural Networks](https://mlsanity.com/paper/1910.06864/) (2019)
- [Adversarial Examples - A Complete Characterisation of the Phenomenon](https://mlsanity.com/paper/1810.01185/) (2018)

## Built on by (most cited first, 14 of 14)

- [Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?](https://mlsanity.com/paper/2402.09056/) (2024)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Label-wise Aleatoric and Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2406.02354/) (2024)
- [Second-Order Uncertainty Quantification: Variance-Based Measures](https://mlsanity.com/paper/2401.00276/) (2023)
- [On Information-Theoretic Measures of Predictive Uncertainty](https://mlsanity.com/paper/2410.10786/) (2024)
- [Revisiting Essential and Nonessential Settings of Evidential Deep Learning](https://mlsanity.com/paper/2410.00393/) (2024)
- [Uncertainty Estimation by Flexible Evidential Deep Learning](https://mlsanity.com/paper/2510.18322/) (2025)
- [Weakly-Supervised 3D Hand Reconstruction with Knowledge Prior and Uncertainty Guidance](https://mlsanity.com/paper/2407.12307/) (2024)
- [Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisition](https://mlsanity.com/paper/2501.18268/) (2025)
- [Linear Opinion Pooling for Uncertainty Quantification on Graphs](https://mlsanity.com/paper/2406.04041/) (2024)
- [Not Just How Much, But Where: Decomposing Epistemic Uncertainty into Per-Class Contributions](https://mlsanity.com/paper/2602.21160/) (2026)
- [CUQ-GNN: Committee-based Graph Uncertainty Quantification using Posterior Networks](https://mlsanity.com/paper/2409.04159/) (2024)
- [Fairness-Aware Multi-view Evidential Learning with Adaptive Prior](https://mlsanity.com/paper/2508.12997/) (2025)
- [Enhancing the Reliability of Medical AI through Expert-guided Uncertainty Modeling](https://mlsanity.com/paper/2604.01898/) (2026)

## Abstract (arXiv)

Uncertainty quantification of deep neural networks has become an active field of research and plays a crucial role in various downstream tasks such as active learning. Recent advances in evidential deep learning shed light on the direct quantification of aleatoric and epistemic uncertainties with a single forward pass of the model. Most traditional approaches adopt an entropy-based method to derive evidential uncertainty in classification, quantifying uncertainty at the sample level. However, the variance-based method that has been widely applied in regression problems is seldom used in the classification setting. In this work, we adapt the variance-based approach from regression to classification, quantifying classification uncertainty at the class level. The variance decomposition technique in regression is extended to class covariance decomposition in classification based on the law of total covariance, and the class correlation is also derived from the covariance. Experiments on cross-domain datasets are conducted to illustrate that the variance-based approach not only results in similar accuracy as the entropy-based one in active domain adaptation but also brings information about class-wise uncertainties as well as between-class correlations. The code is available at https://github.com/KerryDRX/EvidentialADA. This alternative means of evidential uncertainty quantification will give researchers more options when class uncertainties and correlations are important in their applications.