Multi-Output Learning via Spectral Filtering
In this paper we study a class of regularized kernel methods for vector-valued learning which are based on filtering the spectrum of the kernel matrix. The considered methods include Tikhonov regularization as a special case, as well as interesting alternatives such as vector-valued extensions of L2...
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2011
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| Online Access: | http://hdl.handle.net/1721.1/60875 |
| _version_ | 1811081925752782848 |
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| author | Baldassarre, Luca Rosasco, Lorenzo Barla, Annalisa Verri, Alessandro |
| author2 | Tomaso Poggio |
| author_facet | Tomaso Poggio Baldassarre, Luca Rosasco, Lorenzo Barla, Annalisa Verri, Alessandro |
| author_sort | Baldassarre, Luca |
| collection | MIT |
| description | In this paper we study a class of regularized kernel methods for vector-valued learning which are based on filtering the spectrum of the kernel matrix. The considered methods include Tikhonov regularization as a special case, as well as interesting alternatives such as vector-valued extensions of L2 boosting. Computational properties are discussed for various examples of kernels for vector-valued functions and the benefits of iterative techniques are illustrated. Generalizing previous results for the scalar case, we show finite sample bounds for the excess risk of the obtained estimator and, in turn, these results allow to prove consistency both for regression and multi-category classification. Finally, we present some promising results of the proposed algorithms on artificial and real data. |
| first_indexed | 2024-09-23T11:54:36Z |
| id | mit-1721.1/60875 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T11:54:36Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | mit-1721.1/608752019-04-10T21:58:16Z Multi-Output Learning via Spectral Filtering Baldassarre, Luca Rosasco, Lorenzo Barla, Annalisa Verri, Alessandro Tomaso Poggio Center for Biological and Computational Learning (CBCL) Computational Learning, Multi-Output Learning, Spectral Methods In this paper we study a class of regularized kernel methods for vector-valued learning which are based on filtering the spectrum of the kernel matrix. The considered methods include Tikhonov regularization as a special case, as well as interesting alternatives such as vector-valued extensions of L2 boosting. Computational properties are discussed for various examples of kernels for vector-valued functions and the benefits of iterative techniques are illustrated. Generalizing previous results for the scalar case, we show finite sample bounds for the excess risk of the obtained estimator and, in turn, these results allow to prove consistency both for regression and multi-category classification. Finally, we present some promising results of the proposed algorithms on artificial and real data. 2011-02-01T20:00:05Z 2011-02-01T20:00:05Z 2011-01-24 http://hdl.handle.net/1721.1/60875 MIT-CSAIL-TR-2011-004 CBCL-296 37 p. application/pdf |
| spellingShingle | Computational Learning, Multi-Output Learning, Spectral Methods Baldassarre, Luca Rosasco, Lorenzo Barla, Annalisa Verri, Alessandro Multi-Output Learning via Spectral Filtering |
| title | Multi-Output Learning via Spectral Filtering |
| title_full | Multi-Output Learning via Spectral Filtering |
| title_fullStr | Multi-Output Learning via Spectral Filtering |
| title_full_unstemmed | Multi-Output Learning via Spectral Filtering |
| title_short | Multi-Output Learning via Spectral Filtering |
| title_sort | multi output learning via spectral filtering |
| topic | Computational Learning, Multi-Output Learning, Spectral Methods |
| url | http://hdl.handle.net/1721.1/60875 |
| work_keys_str_mv | AT baldassarreluca multioutputlearningviaspectralfiltering AT rosascolorenzo multioutputlearningviaspectralfiltering AT barlaannalisa multioutputlearningviaspectralfiltering AT verrialessandro multioutputlearningviaspectralfiltering |