Adaptive Parameter Selection for Kernel Ridge Regression
This provides a new record for parameter selection in kernel methods, addressing a specific issue for machine learning practitioners.
The paper tackles the problem of parameter selection in kernel ridge regression by developing an early-stopping strategy based on a Lepskii-type principle, achieving optimal learning rates and adapting to different norms.
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.