Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4609098 | Journal of Complexity | 2010 | 20 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Clint Scovel, Don Hush, Ingo Steinwart, James Theiler,