Regularized least squares learning with heavy-tailed noise is minimax optimal

• URL: http://arxiv.org/abs/2505.14214v2
• Date: Thu, 22 May 2025 14:25:20 GMT
• Title: Regularized least squares learning with heavy-tailed noise is minimax optimal
• Authors: Mattes Mollenhauer, Nicole Mücke, Dimitri Meunier, Arthur Gretton,
• Abstract summary: This paper examines the performance of ridge regression in kernel Hilbert spaces in the presence of noise that exhibits a finite number of reproducing higher moments.<n>We establish risk bounds consisting of subgaussian and excess terms based on the well known integral operator framework.
• Score: 23.16162334363017
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper examines the performance of ridge regression in reproducing kernel Hilbert spaces in the presence of noise that exhibits a finite number of higher moments. We establish excess risk bounds consisting of subgaussian and polynomial terms based on the well known integral operator framework. The dominant subgaussian component allows to achieve convergence rates that have previously only been derived under subexponential noise - a prevalent assumption in related work from the last two decades. These rates are optimal under standard eigenvalue decay conditions, demonstrating the asymptotic robustness of regularized least squares against heavy-tailed noise. Our derivations are based on a Fuk-Nagaev inequality for Hilbert-space valued random variables.

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