Adaptive Kernel Methods Using the Balancing Principle |
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Authors: | E De Vito S Pereverzyev L Rosasco |
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Institution: | 1. DSA, Università di Genova and INFN, Genova, Italy 2. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstrasse 69, 4040, Linz, Austria 3. Center for Biological and Computational Learning, Massachusetts Institute of Technology, Cambridge, MA, USA 4. DISI, Università di Genova, Genova, Italy
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Abstract: | 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. |
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