# Multivariate Deep Evidential Regression

arXiv: https://arxiv.org/abs/2104.06135 · HTML: https://mlsanity.com/paper/2104.06135/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 13 Apr 2021.

## Builds on (most cited first, 22 of 22)

- [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)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (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)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [A Simple Baseline for Bayesian Uncertainty in Deep Learning](https://mlsanity.com/paper/1902.02476/) (2019)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [Subspace Inference for Bayesian Deep Learning](https://mlsanity.com/paper/1907.07504/) (2019)
- [Avoiding pathologies in very deep networks](https://mlsanity.com/paper/1402.5836/) (2014)
- [Towards calibrated and scalable uncertainty representations for neural networks](https://mlsanity.com/paper/1911.00104/) (2019)
- [Gradient conjugate priors and multi-layer neural networks](https://mlsanity.com/paper/1802.02643/) (2018)
- [A Parsimonious Tour of Bayesian Model Uncertainty](https://mlsanity.com/paper/1902.05539/) (2019)
- [Neuro-symbolic Neurodegenerative Disease Modeling as Probabilistic Programmed Deep Kernels](https://mlsanity.com/paper/2009.07738/) (2020)
- [Sampling-based Bayesian Inference with gradient uncertainty](https://mlsanity.com/paper/1812.03285/) (2018)

## Built on by (most cited first, 23 of 23)

- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [The Unreasonable Effectiveness of Deep Evidential Regression](https://mlsanity.com/paper/2205.10060/) (2022)
- [Second-Order Uncertainty Quantification: A Distance-Based Approach](https://mlsanity.com/paper/2312.00995/) (2023)
- [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)
- [Revisiting Essential and Nonessential Settings of Evidential Deep Learning](https://mlsanity.com/paper/2410.00393/) (2024)
- [Uncertainty Regularized Evidential Regression](https://mlsanity.com/paper/2401.01484/) (2024)
- [Evidential Deep Learning: Enhancing Predictive Uncertainty Estimation for Earth System Science Applications](https://mlsanity.com/paper/2309.13207/) (2023)
- [Scaling laws for amplitude surrogates](https://mlsanity.com/paper/2601.13308/) (2026)
- [Deep Evidential Learning for Bayesian Quantile Regression](https://mlsanity.com/paper/2308.10650/) (2023)
- [Uncertainty Quantification in Neural Differential Equations](https://mlsanity.com/paper/2111.04207/) (2021)
- [Uncertainty in Physics and AI: Taxonomy, Quantification, and Validation](https://mlsanity.com/paper/2605.10378/) (2026)
- [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)
- [Uncertainty Quantification for Regression: A Unified Framework based on kernel scores](https://mlsanity.com/paper/2510.25599/) (2025)
- [Trust It or Not: Evidential Uncertainty for Feed-Forward 3D Reconstruction with Trust3R](https://mlsanity.com/paper/2605.19539/) (2026)
- [Uncertainty-Aware DNN for Multi-Modal Camera Localization](https://mlsanity.com/paper/2211.01234/) (2022)
- [CARE: Confidence-Aware Regression Estimation of building density fine-tuning EO Foundation Models](https://mlsanity.com/paper/2502.13734/) (2025)
- [Continuous Time Evidential Distributions for Irregular Time Series](https://mlsanity.com/paper/2307.13503/) (2023)
- [Robust Calibration For Improved Weather Prediction Under Distributional Shift](https://mlsanity.com/paper/2401.04144/) (2024)
- [Multivariate Bayesian Last Layer for Regression with Uncertainty Quantification and Decomposition](https://mlsanity.com/paper/2405.01761/) (2024)
- [Equivariant Evidential Deep Learning for Interatomic Potentials](https://mlsanity.com/paper/2602.10419/) (2026)
- [On the QUEST for Uncertainty Quantification via Highest Density Regions](https://mlsanity.com/paper/2606.19569/) (2026)

## Abstract (arXiv)

There is significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware neural networks (NNs), based on learning evidential distributions for aleatoric and epistemic uncertainties, shows promise over traditional deterministic methods and typical Bayesian NNs, yet several important gaps in the theory and implementation of these networks remain. We discuss three issues with a proposed solution to extract aleatoric and epistemic uncertainties from regression-based neural networks. The approach derives a technique by placing evidential priors over the original Gaussian likelihood function and training the NN to infer the hyperparameters of the evidential distribution. Doing so allows for the simultaneous extraction of both uncertainties without sampling or utilization of out-of-distribution data for univariate regression tasks. We describe the outstanding issues in detail, provide a possible solution, and generalize the deep evidential regression technique for multivariate cases.