Least squares regression with l1-regularizer in sum space

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:261

Article

Xu, Yong-Li¹  Han, Min²  Dong, Xue-mei³  Wang, Min⁴ 

[1] Beijing Univ Chem Technol, Dept Math, Beijing 100029, Peoples R China

[2] Beijing Univ Technol, Coll Appl Sci, Beijing 100024, Peoples R China

[3] Zhejiang Gongshang Univ, Sch Math & Stat, Hangzhou 310018, Zhejiang, Peoples R China

[4] Natl Assoc Financial Market Inst Investors, Beingjing, Peoples R China

关键词: Learning theory;    Least square regression;    Regularization scheme;    Sum space;    Error analysis;   

DOI  :  10.1016/j.cam.2013.11.029

来源: Elsevier

【 摘 要 】

In this paper, we propose a least squares regularized regression algorithm with l(1)-regularizer in a sum space of some base hypothesis spaces. This sum space contains more functions than single base hypothesis space and therefore has stronger approximation capability. We establish an excess error bound for this algorithm under some assumptions on the kernels, the input space, the marginal distribution and the regression function. For error analysis, the excess error is decomposed into the sample error, hypothesis error and regularization error, which are estimated respectively. From the excess error bound, convergency and a learning rate can be derived by choosing a suitable value of the regularization parameter. The utility of this method is illustrated with two simulated data sets and one real life database. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

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