A Theoretical Analysis of the Test Error of Finite-Rank Kernel Ridge Regression
This work provides improved theoretical guarantees for finite-rank kernels, which are relevant in applications like transfer learning with pre-trained neural networks, but it is incremental as it builds on prior bounds.
The authors derived sharp non-asymptotic upper and lower bounds for the test error of finite-rank kernel ridge regression, addressing the gap of loose existing guarantees for such kernels, with results that are tighter and valid for any regularization parameters.
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.