Mathematical Interpretations of Kernel Ridge Regression
Akira Tanaka · AIP conference proceedings · 2006
Learning based on kernel machines is widely known as a powerful tool for various fields of information science. The kernel ridge regression is one of simple and classical kernel machines and it gives a foundation for other kernel machines such as the support vector machine. However, it has some problems such as arbitrariness of the model and theoretical validity of an ad hoc kernelization of the ridge regression. The essence of using a kernel in learning problems is that the unknown target is representable by a function belonging to the reproducing kernel Hilbert space corresponding to the adopted kernel. In this paper, on the basis of the essence, we give two identical interpretations, whose theoretical grounds are clarified, for the kernel ridge regression. One is the ridge regression on the reproducing kernel Hilbert space and the other is the parametric projection learning with a specific condition.