Chapter 11 - Learning in Reproducing Kernel Hilbert Spaces

Abstract

This chapter is dedicated to nonparametric modeling of nonlinear functions in reproducing kernel Hilbert spaces (RKHS). The basic definitions and concepts behind RKHSs are presented, including positive definite kernels, reproducing kernels, kernel matrices, and the kernel trick. Cover's theorem and the representer theorem are introduced. Then, kernel ridge regression, support vector regression, and support vector machines are studied. The concept of random Fourier features for kernel approximation is introduced and its application to online and distributed learning is discussed. The notion of multiple kernel learning is presented and a discussion on sparse modeling for nonparametric models in the context of additive models is provided. The chapter closes with a case study for text authorship identification via the use of string kernels.