# Reliable Neural Networks for Regression Uncertainty Estimation

arXiv: https://arxiv.org/abs/2109.08213 · HTML: https://mlsanity.com/paper/2109.08213/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 46 references that are in the map.
- First posted on arXiv 16 Sep 2021.

## Builds on (most cited first, 17 of 17)

- [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)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (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)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [Deep Speech: Scaling up end-to-end speech recognition](https://mlsanity.com/paper/1412.5567/) (2014)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Bayesian Deep Ensembles via the Neural Tangent Kernel](https://mlsanity.com/paper/2007.05864/) (2020)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Recalibration of Aleatoric and Epistemic Regression Uncertainty in Medical Imaging](https://mlsanity.com/paper/2104.12376/) (2021)
- [Expectation Propagation for Neural Networks with Sparsity-promoting Priors](https://mlsanity.com/paper/1303.6938/) (2013)
- [A General Model Validation and Testing Tool](https://mlsanity.com/paper/1908.11251/) (2019)

## Built on by (most cited first, 6 of 6)

- [Calibration in Machine Learning Uncertainty Quantification: beyond consistency to target adaptivity](https://mlsanity.com/paper/2309.06240/) (2023)
- [MESSY Estimation: Maximum-Entropy based Stochastic and Symbolic densitY Estimation](https://mlsanity.com/paper/2306.04120/) (2023)
- [Enhanced Human-Robot Collaboration using Constrained Probabilistic Human-Motion Prediction](https://mlsanity.com/paper/2310.03314/) (2023)
- [B-BACN: Bayesian Boundary-Aware Convolutional Network for Crack Characterization](https://mlsanity.com/paper/2302.06827/) (2023)
- [ISR: Invertible Symbolic Regression](https://mlsanity.com/paper/2405.06848/) (2024)
- [Generalization is not a universal guarantee: Estimating similarity to training data with an ensemble out-of-distribution metric](https://mlsanity.com/paper/2502.16329/) (2025)

## Abstract (arXiv)

While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function for regression uncertainty estimation based on the Bayesian Validation Metric (BVM) framework while using ensemble learning. The proposed loss reproduces maximum likelihood estimation in the limiting case. A series of experiments on in-distribution data show that the proposed method is competitive with existing state-of-the-art methods. Experiments on out-of-distribution data show that the proposed method is robust to statistical change and exhibits superior predictive capability.