# Accurate Prediction and Uncertainty Estimation using Decoupled Prediction Interval Networks

arXiv: https://arxiv.org/abs/2202.09664 · HTML: https://mlsanity.com/paper/2202.09664/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 19 Feb 2022.

## Builds on (most cited first, 12 of 12)

- [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)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networks](https://mlsanity.com/paper/1502.05336/) (2015)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [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)
- [A Bayesian encourages dropout](https://mlsanity.com/paper/1412.7003/) (2014)
- [Probabilistic Regression of Rotations using Quaternion Averaging and a Deep Multi-Headed Network](https://mlsanity.com/paper/1904.03182/) (2019)

## Built on by (most cited first, 2 of 2)

- [Uncertainty quantification in neural network classifiers -- a local linear approach](https://mlsanity.com/paper/2303.07114/) (2023)
- [Interval and fuzzy physics-augmented neural networks (iPANN and fPANN) for uncertainty quantification and propagation in constitutive modeling](https://mlsanity.com/paper/2607.20339/) (2026)

## Abstract (arXiv)

We propose a network architecture capable of reliably estimating uncertainty of regression based predictions without sacrificing accuracy. The current state-of-the-art uncertainty algorithms either fall short of achieving prediction accuracy comparable to the mean square error optimization or underestimate the variance of network predictions. We propose a decoupled network architecture that is capable of accomplishing both at the same time. We achieve this by breaking down the learning of prediction and prediction interval (PI) estimations into a two-stage training process. We use a custom loss function for learning a PI range around optimized mean estimation with a desired coverage of a proportion of the target labels within the PI range. We compare the proposed method with current state-of-the-art uncertainty quantification algorithms on synthetic datasets and UCI benchmarks, reducing the error in the predictions by 23 to 34% while maintaining 95% Prediction Interval Coverage Probability (PICP) for 7 out of 9 UCI benchmark datasets. We also examine the quality of our predictive uncertainty by evaluating on Active Learning and demonstrating 17 to 36% error reduction on UCI benchmarks.