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CROSS-VALIDATION BASED ADAPTATION FOR REGULARIZATION OPERATORS IN LEARNING THEORY.
- Source :
- Analysis & Applications; Apr2010, Vol. 8 Issue 2, p161-183, 23p
- Publication Year :
- 2010
-
Abstract
- 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 cross-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 this broad class of methods which includes regularized least-squares, truncated SVD, Landweber iteration and ν-method. [ABSTRACT FROM AUTHOR]
- Subjects :
- REGRESSION analysis
ALGORITHMS
STOCHASTIC convergence
LEAST squares
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 02195305
- Volume :
- 8
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 49505141
- Full Text :
- https://doi.org/10.1142/S0219530510001564