Sharp learning rates of coefficient-based l q -regularized regression with indefinite kernels

Abstract

Learning with coefficient-based regularization has attracted a considerable amount of attention in recent years, on both theoretical analysis and applications. In this paper, we study coefficient-based learning scheme (CBLS) for regression problem with lq-regularizer (1 < q ⩽ 2). Our analysis is conducted under more general conditions, and particularly the kernel function is not necessarily positive definite. This paper applies concentration inequality with l2-empirical covering numbers to present an elaborate capacity dependence analysis for CBLS, which yields sharper estimates than existing bounds. Moreover, we estimate the regularization error to support our assumptions in error analysis, also provide an illustrative example to further verify the theoretical results.