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

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

Bibtex Paper Supplemental


Tin Sum Cheng, Aurelien Lucchi, Anastasis Kratsios, Ivan Dokmanić, David Belius


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 a number of 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.