On regularized polynomial functional regression
Markus Holzleitner Sergei Pereverzyev
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.