Theoretical analyses on a class of nested RKHS's

One of central topics of kernel machines in the field of machine learning is a model selection, especially a selection of a kernel or its parameters. In our previous work, we discussed a class of kernels forming a class of nested reproducing kernel Hilbert spaces with an invariant metric; and proved that the kernel corresponding to the smallest reproducing kernel Hilbert space, including an unknown true function, gives the optimal model. In this paper, we consider a class of kernels forming a class of nested reproducing kernel Hilbert spaces whose metrics are not always invariant and show that a similar result to the invariant case is not obtained by providing a counter example using a class of Gaussian kernels.

• Type: Journal
• Year: 2011
• Where: ICASSP
• Authors: Akira Tanaka, Hideyuki Imai, Mineichi Kudo, Masaaki Miyakoshi
• Keywords: ICASSP 2011, Kernel Hilbert, Kernel Hilbert Space, Signal Processing, Unknown True Function