Adaptive Kernel Methods Using the Balancing Principle
The regularization parameter choice is a fundamental problem in Learning Theory since the performance of most supervised algorithms crucially depends on the choice of one or more of such parameters. In particular a main theoretical issue regards the amount of prior knowledge needed to choose the regularization parameter in order to obtain good learning rates. In this paper we present a parameter choice strategy, called the balancing principle, to choose the regularization parameter without knowledge of the regularity of the target function. Such a choice adaptively achieves the best error rate. Our main result applies to regularization algorithms in reproducing kernel Hilbert space with the square loss, though we also study how a similar principle can be used in other situations. As a straightforward corollary we can immediately derive adaptive parameter choices for various kernel methods recently studied. Numerical experiments with the proposed parameter choice rules are also presented.
learning theory model selection adaptive regularization inverse problems