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.

中文翻译：

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核岭回归的自适应参数选择


本文重点研究核岭回归（KRR）的参数选择问题。由于 KRR 的特殊谱特性，我们发现参数区间的精细细分缩小了两个连续 KRR 估计之间的差异。基于这一观察，我们根据所谓的 Lepskii 型原理开发了一种 KRR 的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，配备所提出的参数选择策略的KRR成功实现了最优学习率并适应不同的规范，为核方法的参数选择提供了新的记录。