期刊
ANALYSIS AND APPLICATIONS
卷 17, 期 6, 页码 931-946出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0219530519500039
关键词
Nystrom subsampling; kernel learning; low smoothness; learning rate
资金
- NSFC [91730304]
- Shanghai Municipal Education Commission [16SG01]
- Program of Shanghai Academic/Technology Research Leader [19XD1420500]
- Special Funds for Major State Basic Research Projects of China [2015CB856003]
- Austrian Science Fund (FWF) [P 29514-N32]
This paper studies a Nystrom-type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproducing kernel Hilbert space generated by the underlying kernel. This case is less understood in spite of its practical importance. To model such a case, the smoothness of target functions is described in terms of general source conditions. It is surprising that almost for the whole range of the source conditions, describing the misspecified case, the corresponding learning rate bounds can be achieved with just one value of the regularization parameter. This observation allows a formulation of mild conditions under which the plain Nystrom subsampling can be realized with subquadratic cost maintaining the guaranteed learning rates.
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