# Dual Accuracy-Quality-Driven Neural Network for Prediction Interval Generation

arXiv: https://arxiv.org/abs/2212.06370 · HTML: https://mlsanity.com/paper/2212.06370/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 47 references that are in the map.
- First posted on arXiv 13 Dec 2022.

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

- [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)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [High-Quality Prediction Intervals for Deep Learning: A Distribution-Free, Ensembled Approach](https://mlsanity.com/paper/1802.07167/) (2018)
- [Plex: Towards Reliability using Pretrained Large Model Extensions](https://mlsanity.com/paper/2207.07411/) (2022)
- [Subspace Inference for Bayesian Deep Learning](https://mlsanity.com/paper/1907.07504/) (2019)
- [Analysis of Explainers of Black Box Deep Neural Networks for Computer Vision: A Survey](https://mlsanity.com/paper/1911.12116/) (2019)
- [Quality of Uncertainty Quantification for Bayesian Neural Network Inference](https://mlsanity.com/paper/1906.09686/) (2019)
- [Can stable and accurate neural networks be computed? -- On the barriers of deep learning and Smale's 18th problem](https://mlsanity.com/paper/2101.08286/) (2021)
- [Deep and Confident Prediction for Time Series at Uber](https://mlsanity.com/paper/1709.01907/) (2017)
- [Radial Bayesian Neural Networks: Beyond Discrete Support In Large-Scale Bayesian Deep Learning](https://mlsanity.com/paper/1907.00865/) (2019)
- [Prediction Intervals: Split Normal Mixture from Quality-Driven Deep Ensembles](https://mlsanity.com/paper/2007.09670/) (2020)
- [PIVEN: A Deep Neural Network for Prediction Intervals with Specific Value Prediction](https://mlsanity.com/paper/2006.05139/) (2020)
- [The Two-Piece Normal, Binormal, or Double Gaussian Distribution: Its Origin and Rediscoveries](https://mlsanity.com/paper/1405.4995/) (2014)
- [Two-dimensional Deep Regression for Early Yield Prediction of Winter Wheat](https://mlsanity.com/paper/2111.08069/) (2021)

## Built on by (most cited first, 5 of 5)

- [Conformal Loss-Controlling Prediction](https://mlsanity.com/paper/2301.02424/) (2023)
- [Adaptive Sampling to Reduce Epistemic Uncertainty Using Prediction Interval-Generation Neural Networks](https://mlsanity.com/paper/2412.10570/) (2024)
- [Large width penalization for neural network-based prediction interval estimation](https://mlsanity.com/paper/2411.19181/) (2024)
- [Neutrino Oscillation Parameter Estimation Using Structured Hierarchical Transformers](https://mlsanity.com/paper/2603.22342/) (2026)
- [Barrier-enforced multi-objective optimization for direct point and sharp interval forecasting](https://mlsanity.com/paper/2604.18492/) (2026)

## Abstract (arXiv)

Accurate uncertainty quantification is necessary to enhance the reliability of deep learning models in real-world applications. In the case of regression tasks, prediction intervals (PIs) should be provided along with the deterministic predictions of deep learning models. Such PIs are useful or "high-quality" as long as they are sufficiently narrow and capture most of the probability density. In this paper, we present a method to learn prediction intervals for regression-based neural networks automatically in addition to the conventional target predictions. In particular, we train two companion neural networks: one that uses one output, the target estimate, and another that uses two outputs, the upper and lower bounds of the corresponding PI. Our main contribution is the design of a novel loss function for the PI-generation network that takes into account the output of the target-estimation network and has two optimization objectives: minimizing the mean prediction interval width and ensuring the PI integrity using constraints that maximize the prediction interval probability coverage implicitly. Furthermore, we introduce a self-adaptive coefficient that balances both objectives within the loss function, which alleviates the task of fine-tuning. Experiments using a synthetic dataset, eight benchmark datasets, and a real-world crop yield prediction dataset showed that our method was able to maintain a nominal probability coverage and produce significantly narrower PIs without detriment to its target estimation accuracy when compared to those PIs generated by three state-of-the-art neural-network-based methods. In other words, our method was shown to produce higher-quality PIs.