The nature of statistical learning theory
The nature of statistical learning theory
An introduction to support Vector Machines: and other kernel-based learning methods
An introduction to support Vector Machines: and other kernel-based learning methods
Kernel Methods for Pattern Analysis
Kernel Methods for Pattern Analysis
Constructing Kernel Functions for Binary Regression
IEICE - Transactions on Information and Systems
An introduction to kernel-based learning algorithms
IEEE Transactions on Neural Networks
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Kernel machines are widely known as powerful tools in various fields of information science. One of central topics 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 investigated 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 unknown target function to be estimated.