Accuracy and stability of Artificial Neural Networks for HP-Splines frequency parameter selection

TL;DR

This paper investigates neural network methods for stable, data-driven selection of HP-spline frequency parameters, linking classical spline theory with modern deep learning for improved signal processing models.

Contribution

It introduces a neural network framework for predicting HP-spline parameters, combining approximation theory, stability analysis, and complexity control.

Findings

Neural networks can accurately predict optimal HP-spline parameters.

The proposed method achieves high accuracy and stability in numerical experiments.

Theoretical analysis links deep neural networks with classical spline approximation.

Abstract

This paper explores the use of artificial neural networks for the stable and data-driven selection of the frequency parameter in hyperbolic polynomial penalized splines (HP-splines). This parameter defines the underlying spline space and is essential for adapting the model to exponential patterns in the data, such as those encountered in signal processing. The theoretical approximation properties of deep neural network architectures are investigated to establish a connection between classical spline-based regression and modern data-driven learning methods. Based on this analysis, a neural network is designed to predict optimal HP-spline parameters by balancing approximation accuracy, stability analysis, and complexity control, thereby producing neural architectures that are both expressive and stable. Numerical experiments confirm that the proposed approach achieves both high accuracy and stable performance, validating the theoretical findings.