From robust neural networks toward robust nonlinear quantile estimation

• Published in: Sequential analysis Vol. 44; no. 3; pp. 326 - 350
• Main Author: Kalina, Jan
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 03.07.2025
• Subjects: Neural networks; outliers; quantiles; regression; robust statistics; sequential example selection
• ISSN: 0747-4946; 1532-4176
• DOI: 10.1080/07474946.2025.2498933

Regression quantiles provide a flexible framework for modeling the conditional distribution of a response variable by estimating different parts of its distribution, thereby offering valuable insights into the relationship between predictors and outcomes. However, existing nonlinear regression quantile methods may be sensitive to the presence of severe outliers in the data. This paper starts with investigating robust versions of neural networks. The study includes a proposal of a sequential outlier detection procedure based on sequential example selection for robust neural networks. Further, robust quantile estimators for nonlinear regression is introduced. The proposed quantiles are inspired by least weighted squares regression. To enhance robustness to outliers, they assign implicit weights to individual samples and are specifically tailored for multilayer perceptrons, radial basis function networks, and regularized networks. Numerical experiments demonstrate that the robust quantiles improve generalization and outlier resistance. Simulations confirm that the proposed method outperforms traditional (non-robust) quantiles.