Least Square Regularized Regression for Multitask Learning
The study of multitask learning algorithms is one of very important issues. This paper proposes a least-square regularized regression algorithm for multi-task learning with hypothesis space being the union of a sequence of Hilbert spaces. The algorithm consists of two steps of selecting the optimal...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/715275 |
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| author | Yong-Li Xu Di-Rong Chen Han-Xiong Li |
| author_facet | Yong-Li Xu Di-Rong Chen Han-Xiong Li |
| author_sort | Yong-Li Xu |
| collection | DOAJ |
| description | The study of multitask learning algorithms is one of very important issues. This paper proposes a least-square regularized regression algorithm for multi-task learning with
hypothesis space being the union of a sequence of Hilbert spaces. The algorithm consists of two steps of selecting the optimal Hilbert space and searching for the optimal function. We assume that the distributions of different tasks are related to a set of transformations under which any Hilbert space in the hypothesis space is norm invariant. We prove that under the above assumption the optimal prediction function of every task is in the same Hilbert space. Based on this result, a pivotal error decomposition is founded, which can use samples of related tasks to bound excess error of the target task. We obtain an upper bound for the sample error of related tasks, and based on this bound, potential faster learning rates are obtained compared to single-task learning algorithms. |
| format | Article |
| id | doaj-art-861f73b4b1e44db7a1de42c4d28c647a |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-861f73b4b1e44db7a1de42c4d28c647a2025-08-20T03:37:42ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/715275715275Least Square Regularized Regression for Multitask LearningYong-Li Xu0Di-Rong Chen1Han-Xiong Li2Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, ChinaDepartment of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100091, ChinaDepartment of Systems Engineering and Engineering Management, City University of Hong Kong, Hong KongThe study of multitask learning algorithms is one of very important issues. This paper proposes a least-square regularized regression algorithm for multi-task learning with hypothesis space being the union of a sequence of Hilbert spaces. The algorithm consists of two steps of selecting the optimal Hilbert space and searching for the optimal function. We assume that the distributions of different tasks are related to a set of transformations under which any Hilbert space in the hypothesis space is norm invariant. We prove that under the above assumption the optimal prediction function of every task is in the same Hilbert space. Based on this result, a pivotal error decomposition is founded, which can use samples of related tasks to bound excess error of the target task. We obtain an upper bound for the sample error of related tasks, and based on this bound, potential faster learning rates are obtained compared to single-task learning algorithms.http://dx.doi.org/10.1155/2013/715275 |
| spellingShingle | Yong-Li Xu Di-Rong Chen Han-Xiong Li Least Square Regularized Regression for Multitask Learning Abstract and Applied Analysis |
| title | Least Square Regularized Regression for Multitask Learning |
| title_full | Least Square Regularized Regression for Multitask Learning |
| title_fullStr | Least Square Regularized Regression for Multitask Learning |
| title_full_unstemmed | Least Square Regularized Regression for Multitask Learning |
| title_short | Least Square Regularized Regression for Multitask Learning |
| title_sort | least square regularized regression for multitask learning |
| url | http://dx.doi.org/10.1155/2013/715275 |
| work_keys_str_mv | AT yonglixu leastsquareregularizedregressionformultitasklearning AT dirongchen leastsquareregularizedregressionformultitasklearning AT hanxiongli leastsquareregularizedregressionformultitasklearning |