# Optimal Uncertainty-guided Neural Network Training

arXiv: https://arxiv.org/abs/1912.12761 · HTML: https://mlsanity.com/paper/1912.12761/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2019.

## Built on by (most cited first, 7 of 7)

- [Towards a mathematical framework to inform Neural Network modelling via Polynomial Regression](https://mlsanity.com/paper/2102.03865/) (2021)
- [A Comprehensive Study on Torchvision Pre-trained Models for Fine-grained Inter-species Classification](https://mlsanity.com/paper/2110.07097/) (2021)
- [Confidence-Guided Learning Process for Continuous Classification of Time Series](https://mlsanity.com/paper/2208.06883/) (2022)
- [Reduction of Class Activation Uncertainty with Background Information](https://mlsanity.com/paper/2305.03238/) (2023)
- [Interval Load Forecasting for Individual Households in the Presence of Electric Vehicle Charging](https://mlsanity.com/paper/2306.03010/) (2023)
- [Uncertainty Aware Neural Network from Similarity and Sensitivity](https://mlsanity.com/paper/2304.14925/) (2023)
- [Beyond Prediction: Interval Neural Networks for Uncertainty-Aware System Identification](https://mlsanity.com/paper/2605.11460/) (2026)

## Abstract (arXiv)

The neural network (NN)-based direct uncertainty quantification (UQ) methods have achieved the state of the art performance since the first inauguration, known as the lower-upper-bound estimation (LUBE) method. However, currently-available cost functions for uncertainty guided NN training are not always converging and all converged NNs are not generating optimized prediction intervals (PIs). Moreover, several groups have proposed different quality criteria for PIs. These raise a question about their relative effectiveness. Most of the existing cost functions of uncertainty guided NN training are not customizable and the convergence of training is uncertain. Therefore, in this paper, we propose a highly customizable smooth cost function for developing NNs to construct optimal PIs. The optimized average width of PIs, PI-failure distances and the PI coverage probability (PICP) are computed for the test dataset. The performance of the proposed method is examined for the wind power generation and the electricity demand data. Results show that the proposed method reduces variation in the quality of PIs, accelerates the training, and improves convergence probability from 99.2% to 99.8%.