Optimal Kernel in a Class of Kernels with an Invariant Metric

Learning based oil kernel machines is widely known as a, powerful tool for various fields of information science such as pattern recog nition and regression estimation. One of central topics of kernel machines is model selection, especially selection of a kernel or its parameters. In this paper, we consider a. class of kernels that forms a monotonic classes of reproducing kernel Hilbert spaces with an invariant metric and show that the kernel corresponding to the smallest reproducing kernel Hilbert space including an unknown true function gives the optimal model for the unknown true function.