A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression

• URL: http://arxiv.org/abs/2310.00987v2
• Date: Tue, 3 Oct 2023 16:00:34 GMT
• Title: A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression
• Authors: Tin Sum Cheng, Aurelien Lucchi, Ivan Dokmani\'c, Anastasis Kratsios and David Belius
• Abstract summary: finite-rank kernels naturally appear in several machine learning problems, e.g. when fine-tuning a pre-trained deep neural network's last layer to adapt it to a novel task. We address this gap by deriving sharp non-asymptotic upper and lower bounds for the KRR test error of any finite-rank KRR. Our bounds are tighter than previously derived bounds on finite-rank KRR, and unlike comparable results, they also remain valid for any regularization parameters.
• Score: 23.156642467474995
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a pre-trained deep neural network's last layer to adapt it to a novel task when performing transfer learning. We address this gap for finite-rank kernel ridge regression (KRR) by deriving sharp non-asymptotic upper and lower bounds for the KRR test error of any finite-rank KRR. Our bounds are tighter than previously derived bounds on finite-rank KRR, and unlike comparable results, they also remain valid for any regularization parameters.

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