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Center for Nonlinear Studies |
Gaussian kernels have been popular in Learning Theory for some time. However it is only recently that they have been shown to allow efficient learning. However, they can suffer numerically since they may be evaluated by the computer as having only values $0$ and $1$. Consequently, other radial kernels, such as the exponential kernel and Student's kernel, are often used. However, the analysis of learning rates has yet to be developed for these kernels. In this talk we will describe our progress in developing a comprehensive learning theory for radial kernels. We provide an introduction to Reproducing Kernel Hilbert Spaces (RKHS), their use in learning theory, and describe how to use Schoenberg's Theorem to describe the RKHS associated with a radial kernel in terms of the well understood RKHSs associated with the Gaussian kernels.
Host: Garrett Kenyon