On regularized polynomial functional regression

Markus Holzleitner, Sergei Pereverzyev
11/6/2023
math.NAcs.LGmath.ST

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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.

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Cite this paper

@article{holzleitner2023regularized,
  title  = {On regularized polynomial functional regression},
  author = {Markus Holzleitner and Sergei Pereverzyev},
  year   = {2023},
  eprint = {2311.03036},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2311.03036v2}
}

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