# Exploring Uncertainty in Deep Learning for Construction of Prediction Intervals

arXiv: https://arxiv.org/abs/2104.12953 · HTML: https://mlsanity.com/paper/2104.12953/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 60 references that are in the map.
- First posted on arXiv 27 Apr 2021.

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

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [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)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [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)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [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)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [Doubly Stochastic Variational Inference for Deep Gaussian Processes](https://mlsanity.com/paper/1705.08933/) (2017)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Structured and Efficient Variational Deep Learning with Matrix Gaussian Posteriors](https://mlsanity.com/paper/1603.04733/) (2016)
- [Bayesian Uncertainty Estimation for Batch Normalized Deep Networks](https://mlsanity.com/paper/1802.06455/) (2018)
- [Reliable training and estimation of variance networks](https://mlsanity.com/paper/1906.03260/) (2019)
- [The MBPEP: a deep ensemble pruning algorithm providing high quality uncertainty prediction](https://mlsanity.com/paper/1902.09238/) (2019)
- [Discriminative Learning of Prediction Intervals](https://mlsanity.com/paper/1710.05888/) (2017)
- [Calibrated Prediction Intervals for Neural Network Regressors](https://mlsanity.com/paper/1803.09546/) (2018)

## Built on by (most cited first, 3 of 3)

- [Quantile Extreme Gradient Boosting for Uncertainty Quantification](https://mlsanity.com/paper/2304.11732/) (2023)
- [Look Before You Leap! Designing a Human-Centered AI System for Change Risk Assessment](https://mlsanity.com/paper/2108.07951/) (2021)
- [Uncertainty Quantification in Neural-Network Based Pain Intensity Estimation](https://mlsanity.com/paper/2311.08569/) (2023)

## Abstract (arXiv)

Deep learning has achieved impressive performance on many tasks in recent years. However, it has been found that it is still not enough for deep neural networks to provide only point estimates. For high-risk tasks, we need to assess the reliability of the model predictions. This requires us to quantify the uncertainty of model prediction and construct prediction intervals. In this paper, We explore the uncertainty in deep learning to construct the prediction intervals. In general, We comprehensively consider two categories of uncertainties: aleatory uncertainty and epistemic uncertainty. We design a special loss function, which enables us to learn uncertainty without uncertainty label. We only need to supervise the learning of regression task. We learn the aleatory uncertainty implicitly from the loss function. And that epistemic uncertainty is accounted for in ensembled form. Our method correlates the construction of prediction intervals with the uncertainty estimation. Impressive results on some publicly available datasets show that the performance of our method is competitive with other state-of-the-art methods.