Multiparameter regularization and aggregation in the context of polynomial functional regression

TL;DR

This paper introduces a novel multi-parameter regularization algorithm for polynomial functional regression, enabling model aggregation and demonstrating promising results on synthetic and medical data.

Contribution

It extends existing single-parameter regularization methods by developing a multi-parameter approach with a theoretical framework for parameter handling.

Findings

Effective model aggregation with multiple regularization parameters

Promising results on synthetic data

Positive outcomes on real-world medical data

Abstract

Most of the recent results in polynomial functional regression have been focused on an in-depth exploration of single-parameter regularization schemes. In contrast, in this study we go beyond that framework by introducing an algorithm for multiple parameter regularization and presenting a theoretically grounded method for dealing with the associated parameters. This method facilitates the aggregation of models with varying regularization parameters. The efficacy of the proposed approach is assessed through evaluations on both synthetic and some real-world medical data, revealing promising results.