Adaptivity for Regularized Kernel Methods by Lepskii's Principle

Understand

We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression.

• More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$.
• In practical applications, an important task is to choose the regularization parameter $\lam$ appropriately, i.e.
• based only on the given data and independently on unknown structural assumptions on the regression function.