Learning with centered reproducing kernels

Abstract

In the past twenty years, reproducing kernels and the kernel-based learning algorithms have been widely and successfully applied to many areas of scientific research and industry, and are extensively studied. Many of these algorithms take the form of an optimization problem. Typically, the objective function consists of a fidelity term for fitting the observations, and a regularization term for preventing over-fitting. Examples include the support vector machines for classification, and the regularized least squares for regression. However, in many regression problems, the constant component should be treated differently in the regression function, and the existing kernel methods are not perfect tools to model this difference. Examples include score-based ranking function regression. In this thesis, we study a class of Centered Reproducing Kernels (CRKs), which separate the constant component from the reproducing kernel Hilbert spaces. We provide the non-asymptotic convergence analysis of the empirical CRK-based regularized least squares.