A. Tanaka, H. Imai, J. Toyama, M. Kudo, and M. Miyakoshi (Japan)
kernel machine, kernel function, reproducing kernel Hilbert space, metric, Wiener restoration
Kernel machines are widely known as powerful tools in various fields of information science. One of central top ics of kernel machines is a selection of a kernel function or its parameters. In terms of generalization ability, many methods, represented by cross-validation, have been used for the selection. However, the mathematical analyses of the role of the kernels in kernel machines are not inves tigated sufficiently. The difficulty of the analyses lies on the fact that the metric of the reproducing kernel Hilbert space corresponding to the adopted kernel depends on the kernel itself, which implies that we do not have a unified (or kernel-independent) framework for the formulation of learning problems. In this paper, we construct a unified framework of learning problems and show that the kernel plays a role to specify the correlation structure of an un known target function to be estimated.
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