Learning with coefficient-based regularization and ℓ1 −penalty

ZC Guo, L Shi - Advances in Computational Mathematics, 2013 - Springer
ZC Guo, L Shi
Advances in Computational Mathematics, 2013Springer
The least-square regression problem is considered by coefficient-based regularization
schemes with ℓ 1− 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.
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.
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