Learning convolution operators on compact Abelian groups
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Abstract (arXiv)
We consider the problem of learning convolution operators associated to compact Abelian groups. We study a regularization-based approach and provide corresponding learning guarantees under natural regularity conditions on the convolution kernel. More precisely, we assume the convolution kernel is a function in a translation invariant Hilbert space and analyze a natural ridge regression (RR) estimator. Building on existing results for RR, we characterize the accuracy of the estimator in terms of finite sample bounds. Interestingly, regularity assumptions which are classical in the analysis of RR, have a novel and natural interpretation in terms of space/frequency localization. Theoretical results are illustrated by numerical simulations.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 10 of its 47 references that are in the map. First posted on arXiv 9 Jan 2025.
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References · 10
- 2021Neural Operator: Learning Maps Between Function Spacescited by 414
- 2022Physics-Informed Deep Neural Operator Networkscited by 113
- 2014Learning to Deblurcited by 66
- 2015Operator-valued Kernels for Learning from Functional Response Datacited by 60
- 2021Convergence Rates for Learning Linear Operators from Noisy Datacited by 55
- 2022Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problemcited by 28
- 2022Learning Green's functions associated with time-dependent partial differential equationscited by 26
- 2014On the Sample Complexity of Subspace Learningcited by 7
- 2019Learning Schatten--von Neumann Operatorscited by 7
- 2018Bayesian inverse problems with unknown operatorscited by 4
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