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Finite rank kernels for multi-task learning |
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| Authors: | Jianqiang Liu Charles A Micchelli Rui Wang Yuesheng Xu |
| Institution: | 1. Department of Mathematics and Computer Science, Ningxia University, Yinchuan, 750021, People’s Republic of China 2. Department of Mathematics and Statistics, State University of New York, The University at Albany, Albany, New York, 12222, USA 3. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong 4. College of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China 5. Department of Mathematics, Syracuse University, Syracuse, NY, 13244, USA 6. Guangdong Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China |
| Abstract: | Motivated by the importance of kernel-based methods for multi-task learning, we provide here a complete characterization of multi-task finite rank kernels in terms of the positivity of what we call its associated characteristic operator. Consequently, we are led to establishing that every continuous multi-task kernel, defined on a cube in an Euclidean space, not only can be uniformly approximated by multi-task polynomial kernels, but also can be extended as a multi-task kernel to all of the Euclidean space. Finally, we discuss the interpolation of multi-task kernels by multi-task finite rank kernels. |
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