# On regularized polynomial functional regression

arXiv: https://arxiv.org/abs/2311.03036 · HTML: https://mlsanity.com/paper/2311.03036/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 6 Nov 2023.

## Builds on (most cited first, 6 of 6)

- [Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces](https://mlsanity.com/paper/1801.06720/) (2018)
- [Distributed learning with regularized least squares](https://mlsanity.com/paper/1608.03339/) (2016)
- [Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem](https://mlsanity.com/paper/2211.08875/) (2022)
- [Deep Learning for Functional Data Analysis with Adaptive Basis Layers](https://mlsanity.com/paper/2106.10414/) (2021)
- [Capacity dependent analysis for functional online learning algorithms](https://mlsanity.com/paper/2209.12198/) (2022)
- [Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regression](https://mlsanity.com/paper/2211.10968/) (2022)

## Built on by (most cited first, 1 of 1)

- [Multiparameter regularization and aggregation in the context of polynomial functional regression](https://mlsanity.com/paper/2405.04147/) (2024)

## Abstract (arXiv)

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.