Risk Bounds for Regularized Least-squares Algorithm with Operator-valued kernels
We show that recent results in [3] on risk bounds for regularized least-squares on reproducing kernel Hilbert spaces can be straightforwardly extended to the vector-valued regression setting. We first briefly introduce central concepts on operator-valued kernels. Then we show how risk bounds can b...
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| Language: | en_US |
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2005
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| Online Access: | http://hdl.handle.net/1721.1/30543 |
| _version_ | 1811085379862790144 |
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| author | Vito, Ernesto De Caponnetto, Andrea |
| author_facet | Vito, Ernesto De Caponnetto, Andrea |
| author_sort | Vito, Ernesto De |
| collection | MIT |
| description | We show that recent results in [3] on risk bounds for regularized least-squares on reproducing kernel Hilbert spaces can be straightforwardly extended to the vector-valued regression setting. We first briefly introduce central concepts on operator-valued kernels. Then we show how risk bounds can be expressed in terms of a generalization of effective dimension. |
| first_indexed | 2024-09-23T13:08:40Z |
| id | mit-1721.1/30543 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:08:40Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | mit-1721.1/305432019-04-11T06:23:28Z Risk Bounds for Regularized Least-squares Algorithm with Operator-valued kernels Vito, Ernesto De Caponnetto, Andrea AI optimal rates reproducing kernel Hilbert space effective dimension We show that recent results in [3] on risk bounds for regularized least-squares on reproducing kernel Hilbert spaces can be straightforwardly extended to the vector-valued regression setting. We first briefly introduce central concepts on operator-valued kernels. Then we show how risk bounds can be expressed in terms of a generalization of effective dimension. 2005-12-22T02:28:54Z 2005-12-22T02:28:54Z 2005-05-16 MIT-CSAIL-TR-2005-031 AIM-2005-015 CBCL-249 http://hdl.handle.net/1721.1/30543 en_US Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory 17 p. 12090406 bytes 642646 bytes application/postscript application/pdf application/postscript application/pdf |
| spellingShingle | AI optimal rates reproducing kernel Hilbert space effective dimension Vito, Ernesto De Caponnetto, Andrea Risk Bounds for Regularized Least-squares Algorithm with Operator-valued kernels |
| title | Risk Bounds for Regularized Least-squares Algorithm with Operator-valued kernels |
| title_full | Risk Bounds for Regularized Least-squares Algorithm with Operator-valued kernels |
| title_fullStr | Risk Bounds for Regularized Least-squares Algorithm with Operator-valued kernels |
| title_full_unstemmed | Risk Bounds for Regularized Least-squares Algorithm with Operator-valued kernels |
| title_short | Risk Bounds for Regularized Least-squares Algorithm with Operator-valued kernels |
| title_sort | risk bounds for regularized least squares algorithm with operator valued kernels |
| topic | AI optimal rates reproducing kernel Hilbert space effective dimension |
| url | http://hdl.handle.net/1721.1/30543 |
| work_keys_str_mv | AT vitoernestode riskboundsforregularizedleastsquaresalgorithmwithoperatorvaluedkernels AT caponnettoandrea riskboundsforregularizedleastsquaresalgorithmwithoperatorvaluedkernels |