Name
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s10444-011-9244-x | Adv. Comput. Math. |
Keywords | Field | DocType |
Multi-task polynomial kernels,Characteristic operator,Weierstrass approximation theorem,Continuous kernel extension,41A05,41A10,46E22 | Kernel (linear algebra),Discrete mathematics,Mathematical optimization,Polynomial,Kernel embedding of distributions,Mathematical analysis,Euclidean space,Polynomial kernel,Stone–Weierstrass theorem,String kernel,Variable kernel density estimation,Mathematics | Journal |
Volume | Issue | ISSN |
38 | 2 | 1019-7168 |
Citations | PageRank | References |
0 | 0.34 | 19 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jianqiang Liu | 1 | 0 | 0.34 |
| Charles A. Micchelli | 2 | 1579 | 224.81 |
| Rui Wang | 3 | 8 | 5.36 |
| Yuesheng Xu | 4 | 559 | 75.46 |