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The convergence rates of Shannon sampling learning algorithms
- Source :
- Science China Mathematics. 55:1243-1256
- Publication Year :
- 2012
- Publisher :
- Springer Science and Business Media LLC, 2012.
-
Abstract
- In the present paper, we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space (RKHS) derived by a Mercer kernel and a determined net. We show that if the sample is taken according to the determined set, then, the sample error can be bounded by the Mercer matrix with respect to the samples and the determined net. The regularization error may be bounded by the approximation order of the reproducing kernel Hilbert space interpolation operator. The paper is an investigation on a remark provided by Smale and Zhou.
- Subjects :
- Representer theorem
Kernel embedding of distributions
General Mathematics
Bounded function
Mathematical analysis
Regularization perspectives on support vector machines
Applied mathematics
Sampling error
Regularization (mathematics)
Kernel principal component analysis
Mathematics
Reproducing kernel Hilbert space
Subjects
Details
- ISSN :
- 18691862 and 16747283
- Volume :
- 55
- Database :
- OpenAIRE
- Journal :
- Science China Mathematics
- Accession number :
- edsair.doi...........2a1296c6b389c78dec930ae66aff7f4b