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Empirical Effective Dimension and Optimal Rates for Regularized Least Squares Algorithm

This paper presents an approach to model selection for regularized least-squares on reproducing kernel Hilbert spaces in the semi-supervised setting. The role of effective dimension was recently shown to be crucial in the definition of a rule for the choice of the regularization parameter, attaining asymptotic optimal performances in a minimax sense. The main goal of the present paper is showing how the effective dimension can be replaced by an empirical counterpart while conserving optimality. The empirical effective dimension can be computed from independent unlabelled samples. This makes the approach particularly appealing in the semi-supervised setting.

Identiferoai:union.ndltd.org:MIT/oai:dspace.mit.edu:1721.1/30548
Date27 May 2005
CreatorsCaponnetto, Andrea, Rosasco, Lorenzo, Vito, Ernesto De, Verri, Alessandro
Source SetsM.I.T. Theses and Dissertation
Languageen_US
Detected LanguageEnglish
Format14 p., 11158573 bytes, 526018 bytes, application/postscript, application/pdf
RelationMassachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory

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