On regularized polynomial functional regression

TL;DR

This paper develops a comprehensive theoretical framework for polynomial functional regression, establishing a new finite sample bound, and demonstrates that higher order polynomials can enhance predictive performance.

Contribution

It introduces a novel finite sample bound for polynomial functional regression that generalizes previous linear models and incorporates regularization and smoothness conditions.

Findings

Higher order polynomial terms can improve model performance.

Theoretical bounds encompass smoothness, capacity, and regularization.

Extends linear functional regression results to polynomial cases.

Abstract

This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity conditions, and regularization techniques. In doing so, it extends and generalizes several findings from the context of linear functional regression as well. We also provide numerical evidence that using higher order polynomial terms can lead to an improved performance.