On regularized polynomial functional regression

Markus Holzleitner, Sergei Pereverzyev

Abstract: This article offers a comprehensive treatment of polynomial functional regression, cul- minating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity conditions, and reg- ularization 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.