# Regression Prior Networks

arXiv: https://arxiv.org/abs/2006.11590 · HTML: https://mlsanity.com/paper/2006.11590/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2020.

## Built on by (most cited first, 28 of 28)

- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [Shifts: A Dataset of Real Distributional Shift Across Multiple Large-Scale Tasks](https://mlsanity.com/paper/2107.07455/) (2021)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [On Second-Order Scoring Rules for Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2301.12736/) (2023)
- [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)
- [Disentangling Epistemic and Aleatoric Uncertainty in Reinforcement Learning](https://mlsanity.com/paper/2206.01558/) (2022)
- [Interpretable Self-Aware Neural Networks for Robust Trajectory Prediction](https://mlsanity.com/paper/2211.08701/) (2022)
- [Scaling Ensemble Distribution Distillation to Many Classes with Proxy Targets](https://mlsanity.com/paper/2105.06987/) (2021)
- [Are Uncertainty Quantification Capabilities of Evidential Deep Learning a Mirage?](https://mlsanity.com/paper/2402.06160/) (2024)
- [Word-Sequence Entropy: Towards Uncertainty Estimation in Free-Form Medical Question Answering Applications and Beyond](https://mlsanity.com/paper/2402.14259/) (2024)
- [NOMU: Neural Optimization-based Model Uncertainty](https://mlsanity.com/paper/2102.13640/) (2021)
- [ZigZag: Universal Sampling-free Uncertainty Estimation Through Two-Step Inference](https://mlsanity.com/paper/2211.11435/) (2022)
- [Natural Posterior Network: Deep Bayesian Uncertainty for Exponential Family Distributions](https://mlsanity.com/paper/2105.04471/) (2021)
- [Improving evidential deep learning via multi-task learning](https://mlsanity.com/paper/2112.09368/) (2021)
- [Uncertainty Regularized Evidential Regression](https://mlsanity.com/paper/2401.01484/) (2024)
- [Disentangling Uncertainty in Machine Translation Evaluation](https://mlsanity.com/paper/2204.06546/) (2022)
- [An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression](https://mlsanity.com/paper/2504.18433/) (2025)
- [Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression](https://mlsanity.com/paper/2308.09065/) (2023)
- [RuleFuser: An Evidential Bayes Approach for Rule Injection in Imitation Learned Planners and Predictors for Robustness under Distribution Shifts](https://mlsanity.com/paper/2405.11139/) (2024)
- [Enhancing Uncertainty Estimation and Interpretability via Bayesian Non-negative Decision Layer](https://mlsanity.com/paper/2505.22199/) (2025)
- [Uncertainty Quantification for Regression: A Unified Framework based on kernel scores](https://mlsanity.com/paper/2510.25599/) (2025)
- [Distil the informative essence of loop detector data set: Is network-level traffic forecasting hungry for more data?](https://mlsanity.com/paper/2310.20366/) (2023)
- [Spatial Bayesian Neural Networks](https://mlsanity.com/paper/2311.09491/) (2023)
- [Continuous Time Evidential Distributions for Irregular Time Series](https://mlsanity.com/paper/2307.13503/) (2023)
- [Plug-in Losses for Evidential Deep Learning: A Simplified Framework for Uncertainty Estimation that Includes the Softmax Classifier](https://mlsanity.com/paper/2605.22746/) (2026)

## Abstract (arXiv)

Prior Networks are a recently developed class of models which yield interpretable measures of uncertainty and have been shown to outperform state-of-the-art ensemble approaches on a range of tasks. They can also be used to distill an ensemble of models via Ensemble Distribution Distillation (EnD2), such that its accuracy, calibration and uncertainty estimates are retained within a single model. However, Prior Networks have so far been developed only for classification tasks. This work extends Prior Networks and EnD2 to regression tasks by considering the Normal-Wishart distribution. The properties of Regression Prior Networks are demonstrated on synthetic data, selected UCI datasets and a monocular depth estimation task, where they yield performance competitive with ensemble approaches.