# Tight Prediction Intervals Using Expanded Interval Minimization

arXiv: https://arxiv.org/abs/1806.11222 · HTML: https://mlsanity.com/paper/1806.11222/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jun 2018.

## Built on by (most cited first, 4 of 4)

- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [How to Evaluate Uncertainty Estimates in Machine Learning for Regression?](https://mlsanity.com/paper/2106.03395/) (2021)
- [Structure and Distribution Metric for Quantifying the Quality of Uncertainty: Assessing Gaussian Processes, Deep Neural Nets, and Deep Neural Operators for Regression](https://mlsanity.com/paper/2203.04515/) (2022)
- [Confident Neural Network Regression with Bootstrapped Deep Ensembles](https://mlsanity.com/paper/2202.10903/) (2022)

## Abstract (arXiv)

Prediction intervals are a valuable way of quantifying uncertainty in regression problems. Good prediction intervals should be both correct, containing the actual value between the lower and upper bound at least a target percentage of the time; and tight, having a small mean width of the bounds. Many prior techniques for generating prediction intervals make assumptions on the distribution of error, which causes them to work poorly for problems with asymmetric distributions. This paper presents Expanded Interval Minimization (EIM), a novel loss function for generating prediction intervals using neural networks. This loss function uses minibatch statistics to estimate the coverage and optimize the width of the prediction intervals. It does not make the same assumptions on the distributions of data and error as prior work. We compare to three published techniques and show EIM produces on average 1.37x tighter prediction intervals and in the worst case 1.06x tighter intervals across two large real-world datasets and varying coverage levels.