Adaptation for Regularization Operators in Learning Theory
Author(s)Caponnetto, Andrea; Yao, Yuan
Center for Biological and Computational Learning (CBCL)
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We consider learning algorithms induced by regularization methods in the regression setting. We show that previously obtained error bounds for these algorithms using a-priori choices of the regularization parameter, can be attained using a suitable a-posteriori choice based on validation. In particular, these results prove adaptation of the rate of convergence of the estimators to the minimax rate induced by the "effective dimension" of the problem. We also show universal consistency for theses class methods.
Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory
optimal rates, Learning, regularization methods, adaptation, cross-validation