Learning with coefficient-based regularization and ℓ1 -penalty

Zheng-Chu Guo, Lei Shi

Abstract: The least-square regression problem is considered by coefficient-based regularization schemes with ℓ1 −penalty. The learning algorithm is analyzed with samples drawn from unbounded sampling processes. The purpose of this paper is to present an elaborate concentration estimate for the algorithms by means of a novel stepping stone technique. The learning rates derived from our analysis can be achieved in a more general setting. Our refined analysis will lead to satisfactory learning rates even for non-smooth kernels.