# Uncertainty Regularized Evidential Regression

arXiv: https://arxiv.org/abs/2401.01484 · HTML: https://mlsanity.com/paper/2401.01484/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 34 references that are in the map.
- First posted on arXiv 3 Jan 2024.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Unsupervised Monocular Depth Estimation with Left-Right Consistency](https://mlsanity.com/paper/1609.03677/) (2016)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Ensemble Distribution Distillation](https://mlsanity.com/paper/1905.00076/) (2019)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)
- [Uncertainty in Neural Networks: Approximately Bayesian Ensembling](https://mlsanity.com/paper/1810.05546/) (2018)
- [Regression Prior Networks](https://mlsanity.com/paper/2006.11590/) (2020)
- [Uncertainty on Asynchronous Time Event Prediction](https://mlsanity.com/paper/1911.05503/) (2019)
- [Multivariate Deep Evidential Regression](https://mlsanity.com/paper/2104.06135/) (2021)
- [Uncertainty-aware Traffic Prediction under Missing Data](https://mlsanity.com/paper/2309.06800/) (2023)

## Built on by (most cited first, 13 of 13)

- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Revisiting Essential and Nonessential Settings of Evidential Deep Learning](https://mlsanity.com/paper/2410.00393/) (2024)
- [Beyond Uncertainty: Evidential Deep Learning for Robust Video Temporal Grounding](https://mlsanity.com/paper/2408.16272/) (2024)
- [Metacognitive AI: Framework and the Case for a Neurosymbolic Approach](https://mlsanity.com/paper/2406.12147/) (2024)
- [Neural Network Prediction of Strong Lensing Systems with Domain Adaptation and Uncertainty Quantification](https://mlsanity.com/paper/2411.03334/) (2024)
- [PRESCRIBE: Predicting Single-Cell Responses with Bayesian Estimation](https://mlsanity.com/paper/2510.07964/) (2025)
- [DRE: An Effective Dual-Refined Method for Integrating Small and Large Language Models in Open-Domain Dialogue Evaluation](https://mlsanity.com/paper/2506.04516/) (2025)
- [Analyzing Uncertainty Quantification in Statistical and Deep Learning Models for Probabilistic Electricity Price Forecasting](https://mlsanity.com/paper/2509.19417/) (2025)
- [BD-Merging: Bias-Aware Dynamic Model Merging with Evidence-Guided Contrastive Learning](https://mlsanity.com/paper/2603.03920/) (2026)
- [CUPID: A Plug-in Framework for Joint Aleatoric and Epistemic Uncertainty Estimation with a Single Model](https://mlsanity.com/paper/2603.10745/) (2026)
- [A Visualization for Comparative Analysis of Regression Models](https://mlsanity.com/paper/2603.19291/) (2026)
- [Segment Anything with Robust Uncertainty-Accuracy Correlation](https://mlsanity.com/paper/2605.10603/) (2026)
- [Robust Evidential Learning Through Latent Consistency](https://mlsanity.com/paper/2610.01384/) (2026)

## Abstract (arXiv)

The Evidential Regression Network (ERN) represents a novel approach that integrates deep learning with Dempster-Shafer's theory to predict a target and quantify the associated uncertainty. Guided by the underlying theory, specific activation functions must be employed to enforce non-negative values, which is a constraint that compromises model performance by limiting its ability to learn from all samples. This paper provides a theoretical analysis of this limitation and introduces an improvement to overcome it. Initially, we define the region where the models can't effectively learn from the samples. Following this, we thoroughly analyze the ERN and investigate this constraint. Leveraging the insights from our analysis, we address the limitation by introducing a novel regularization term that empowers the ERN to learn from the whole training set. Our extensive experiments substantiate our theoretical findings and demonstrate the effectiveness of the proposed solution.