This paper focuses on parameter selection issues of kernel ridge regression (KRR). Due to special spectral properties of KRR, we find that delicate subdivision of the parameter interval shrinks the difference between two successive KRR estimates. Based on this observation, we develop an early-stopping type parameter selection strategy for KRR according to the so-called Lepskii-type principle. Theoretical verifications are presented in the framework of learning theory to show that KRR equipped with the proposed parameter selection strategy succeeds in achieving optimal learning rates and adapts to different norms, providing a new record of parameter selection for kernel methods.

翻译：本文聚焦于核岭回归（KRR）中的参数选择问题。由于KRR特殊的谱性质，我们发现对参数区间进行精细划分可以缩小相邻两个KRR估计之间的差异。基于这一发现，我们依据所谓的Lepskii型原则，为KRR发展了一种早停型参数选择策略。在学习理论框架下进行的理论验证表明，采用所提出参数选择策略的KRR能够实现最优学习率，并适应不同范数，为核方法的参数选择提供了新的基准。