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, attainin...
| Main Authors: | , , , |
|---|---|
| Language: | en_US |
| Published: |
2005
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/30548 |
| _version_ | 1826199511993679872 |
|---|---|
| author | Caponnetto, Andrea Rosasco, Lorenzo Vito, Ernesto De Verri, Alessandro |
| author_facet | Caponnetto, Andrea Rosasco, Lorenzo Vito, Ernesto De Verri, Alessandro |
| author_sort | Caponnetto, Andrea |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T11:21:05Z |
| id | mit-1721.1/30548 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:21:05Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | mit-1721.1/305482019-04-11T06:23:29Z Empirical Effective Dimension and Optimal Rates for Regularized Least Squares Algorithm Caponnetto, Andrea Rosasco, Lorenzo Vito, Ernesto De Verri, Alessandro AI optimal rates effective dimension semi-supervised learning 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. 2005-12-22T02:29:53Z 2005-12-22T02:29:53Z 2005-05-27 MIT-CSAIL-TR-2005-036 AIM-2005-019 CBCL-252 http://hdl.handle.net/1721.1/30548 en_US Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory 14 p. 11158573 bytes 526018 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | AI optimal rates effective dimension semi-supervised learning Caponnetto, Andrea Rosasco, Lorenzo Vito, Ernesto De Verri, Alessandro Empirical Effective Dimension and Optimal Rates for Regularized Least Squares Algorithm |
| title | Empirical Effective Dimension and Optimal Rates for Regularized Least Squares Algorithm |
| title_full | Empirical Effective Dimension and Optimal Rates for Regularized Least Squares Algorithm |
| title_fullStr | Empirical Effective Dimension and Optimal Rates for Regularized Least Squares Algorithm |
| title_full_unstemmed | Empirical Effective Dimension and Optimal Rates for Regularized Least Squares Algorithm |
| title_short | Empirical Effective Dimension and Optimal Rates for Regularized Least Squares Algorithm |
| title_sort | empirical effective dimension and optimal rates for regularized least squares algorithm |
| topic | AI optimal rates effective dimension semi-supervised learning |
| url | http://hdl.handle.net/1721.1/30548 |
| work_keys_str_mv | AT caponnettoandrea empiricaleffectivedimensionandoptimalratesforregularizedleastsquaresalgorithm AT rosascolorenzo empiricaleffectivedimensionandoptimalratesforregularizedleastsquaresalgorithm AT vitoernestode empiricaleffectivedimensionandoptimalratesforregularizedleastsquaresalgorithm AT verrialessandro empiricaleffectivedimensionandoptimalratesforregularizedleastsquaresalgorithm |