Learning convolution operators on compact Abelian groups

2025/01/09 by Emilia Magnani, Magnani, Emilia, Ernesto De Vito +5
Computer Science · #42B10 #47A52 #62J07 #68T05 #F.2.1 #FOS: Computer and information sciences #G.3 #I.2.6 #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.2501.05279

openalex publication_date 2025/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

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