Kernel partial least squares regression for functional nonlinear models

TL;DR

This paper introduces a kernel functional partial least squares (KFPLS) method for modeling nonlinear relationships in functional data, providing a flexible alternative to linear models with demonstrated effectiveness through simulations and real data applications.

Contribution

The paper develops a novel KFPLS method that handles nonlinear functional regression without strict structural assumptions, extending the applicability of functional data analysis.

Findings

Effective in various nonlinear models

Outperforms linear methods in simulations

Shows superiority in real-world data

Abstract

Functional regression is very crucial in functional data analysis and a linear relationship between scalar response and functional predictor is often assumed. However, the linear assumption may not hold in practice, which makes the methods for linear models invalid. To gain more flexibility, we focus on functional nonlinear models and aim to develop new method that requires no strict constraint on the nonlinear structure. Inspired by the idea of the kernel method in machine learning, we propose a kernel functional partial least squares (KFPLS) method for the functional nonlinear models. The innovative algorithm works on the prediction of the scalar response and is accompanied by R package KFPLS for implementation. The simulation study demonstrates the effectiveness of the proposed method for various types of nonlinear models. Moreover, the real world application also shows the superiority of the proposed KFPLS method.