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.

翻译：现有的通用核回归器的统计学习保证在使用有限秩核时往往产生宽松的界。然而，有限秩核在多个机器学习问题中自然出现，例如在迁移学习过程中微调预训练深度神经网络的最后一层以适应新任务时。我们针对有限秩核岭回归（KRR）解决了这一空白，通过推导任意有限秩KRR测试误差的尖锐非渐近上界和下界。我们的界比先前推导的有限秩KRR界更紧，且与同类结果不同，它们对于任何正则化参数仍然成立。