Radial kernels and their reproducing kernel Hilbert spaces |
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Authors: | Clint Scovel Don Hush Ingo Steinwart James Theiler |
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Affiliation: | Los Alamos National Laboratory, United States |
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Abstract: | We describe how to use Schoenberg’s theorem for a radial kernel combined with existing bounds on the approximation error functions for Gaussian kernels to obtain a bound on the approximation error function for the radial kernel. The result is applied to the exponential kernel and Student’s kernel. To establish these results we develop a general theory regarding mixtures of kernels. We analyze the reproducing kernel Hilbert space (RKHS) of the mixture in terms of the RKHS’s of the mixture components and prove a type of Jensen inequality between the approximation error function for the mixture and the approximation error functions of the mixture components. |
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Keywords: | RKHS Reproducing kernel Hilbert space Schoenberg theorem Approximation error |
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