  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.
