On regularized polynomial functional regression
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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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 6 of its 37 references that are in the map. First posted on arXiv 6 Nov 2023.
Builds on
6 of 37 references.
References · 6
- 2018Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spacescited by 59
- 2016Distributed learning with regularized least squarescited by 42
- 2022Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problemcited by 27
- 2021Deep Learning for Functional Data Analysis with Adaptive Basis Layerscited by 17
- 2022Capacity dependent analysis for functional online learning algorithmscited by 10
- 2022Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regressioncited by 8
Built on by
Citing papers per year: 2024: 1.
1 paper.