# Deep Evidential Learning for Bayesian Quantile Regression

arXiv: https://arxiv.org/abs/2308.10650 · HTML: https://mlsanity.com/paper/2308.10650/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 54 references that are in the map.
- First posted on arXiv 21 Aug 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Deep Bayesian Active Learning with Image Data](https://mlsanity.com/paper/1703.02910/) (2017)
- [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)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awareness](https://mlsanity.com/paper/2006.10108/) (2020)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Efficient Object Localization Using Convolutional Networks](https://mlsanity.com/paper/1411.4280/) (2014)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Uncertainty in Neural Networks: Approximately Bayesian Ensembling](https://mlsanity.com/paper/1810.05546/) (2018)
- [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)
- [Beyond expectation: Deep joint mean and quantile regression for spatio-temporal problems](https://mlsanity.com/paper/1808.08798/) (2018)
- [Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecasting](https://mlsanity.com/paper/2101.10460/) (2021)
- [Learn to Accumulate Evidence from All Training Samples: Theory and Practice](https://mlsanity.com/paper/2306.11113/) (2023)
- [Multivariate Deep Evidential Regression](https://mlsanity.com/paper/2104.06135/) (2021)
- [Bayesian Quantile and Expectile Optimisation](https://mlsanity.com/paper/2001.04833/) (2020)
- [Improving evidential deep learning via multi-task learning](https://mlsanity.com/paper/2112.09368/) (2021)
- [Evidential Conditional Neural Processes](https://mlsanity.com/paper/2212.00131/) (2022)
- [Gradient conjugate priors and multi-layer neural networks](https://mlsanity.com/paper/1802.02643/) (2018)
- [Modeling Censored Mobility Demand through Quantile Regression Neural Networks](https://mlsanity.com/paper/2104.01214/) (2021)

## Built on by (most cited first, 5 of 5)

- [Echoes of Socratic Doubt: Embracing Uncertainty in Calibrated Evidential Reinforcement Learning](https://mlsanity.com/paper/2402.07107/) (2024)
- [Certainty In, Certainty Out: REVQCs for Quantum Machine Learning](https://mlsanity.com/paper/2310.10629/) (2023)
- [Post-Hoc Split-Point Self-Consistency Verification for Efficient, Unified Quantification of Aleatoric and Epistemic Uncertainty in Deep Learning](https://mlsanity.com/paper/2509.13262/) (2025)
- [Evidential Domain Adaptation for Remaining Useful Life Prediction with Incomplete Degradation](https://mlsanity.com/paper/2603.15687/) (2026)
- [Uncertainty-Driven Replay Memory for Reinforcement Learning](https://mlsanity.com/paper/2608.29860/) (2026)

## Abstract (arXiv)

It is desirable to have accurate uncertainty estimation from a single deterministic forward-pass model, as traditional methods for uncertainty quantification are computationally expensive. However, this is difficult because single forward-pass models do not sample weights during inference and often make assumptions about the target distribution, such as assuming it is Gaussian. This can be restrictive in regression tasks, where the mean and standard deviation are inadequate to model the target distribution accurately. This paper proposes a deep Bayesian quantile regression model that can estimate the quantiles of a continuous target distribution without the Gaussian assumption. The proposed method is based on evidential learning, which allows the model to capture aleatoric and epistemic uncertainty with a single deterministic forward-pass model. This makes the method efficient and scalable to large models and datasets. We demonstrate that the proposed method achieves calibrated uncertainties on non-Gaussian distributions, disentanglement of aleatoric and epistemic uncertainty, and robustness to out-of-distribution samples.