# A Novel Smoothed Loss and Penalty Function for Noncrossing Composite Quantile Estimation via Deep Neural Networks

arXiv: https://arxiv.org/abs/1909.12122 · HTML: https://mlsanity.com/paper/1909.12122/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2019.

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

- [The Earth Mover's Pinball Loss: Quantiles for Histogram-Valued Regression](https://mlsanity.com/paper/2106.02051/) (2021)
- [Composite Quantile Regression With XGBoost Using the Novel Arctan Pinball Loss](https://mlsanity.com/paper/2406.02293/) (2024)

## Abstract (arXiv)

Uncertainty analysis in the form of probabilistic forecasting can significantly improve decision making processes in the smart power grid when integrating renewable energy sources such as wind. Whereas point forecasting provides a single expected value, probabilistic forecasts provide more information in the form of quantiles, prediction intervals, or full predictive densities. Traditionally quantile regression is applied for such forecasting and recently quantile regression neural networks have become popular for weather and renewable energy forecasting. However, one major shortcoming of composite quantile estimation in neural networks is the quantile crossover problem. This paper analyzes the effectiveness of a novel smoothed loss and penalty function for neural network architectures to prevent the quantile crossover problem. Its efficacy is examined on the wind power forecasting problem. A numerical case study is conducted using publicly available wind data from the Global Energy Forecasting Competition 2014. Multiple quantiles are estimated to form 10%, to 90% prediction intervals which are evaluated using a quantile score and reliability measures. Benchmark models such as the persistence and climatology distributions, multiple quantile regression, and support vector quantile regression are used for comparison where results demonstrate the proposed approach leads to improved performance while preventing the problem of overlapping quantile estimates.