Learning convolution operators on compact Abelian groups
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916682280206336 |
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| author | Magnani, Emilia De Vito, Ernesto Hennig, Philipp Rosasco, Lorenzo |
| author_facet | Magnani, Emilia De Vito, Ernesto Hennig, Philipp Rosasco, Lorenzo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05279 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning convolution operators on compact Abelian groups Magnani, Emilia De Vito, Ernesto Hennig, Philipp Rosasco, Lorenzo Machine Learning 68T05, 47A52, 42B10, 62J07 I.2.6; F.2.1; G.3 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. |
| title | Learning convolution operators on compact Abelian groups |
| topic | Machine Learning 68T05, 47A52, 42B10, 62J07 I.2.6; F.2.1; G.3 |
| url | https://arxiv.org/abs/2501.05279 |