Year: 2021
Author: Mingwei Dai, Shuyang Dai, Junjun Huang, Lican Kang, Xiliang Lu
Communications in Computational Physics, Vol. 30 (2021), Iss. 1 : pp. 190–209
Abstract
Truncated $L_1$ regularization proposed by Fan in [5], is an approximation to the $L_0$ regularization in high-dimensional sparse models. In this work, we prove the non-asymptotic error bound for the global optimal solution to the truncated $L_1$ regularized linear regression problem and study the support recovery property. Moreover, a primal dual active set algorithm (PDAS) for variable estimation and selection is proposed. Coupled with continuation by a warm-start strategy leads to a primal dual active set with continuation algorithm (PDASC). Data-driven parameter selection rules such as cross validation, BIC or voting method can be applied to select a proper regularization parameter. The application of the proposed method is demonstrated by applying it to simulation data and a breast cancer gene expression data set (bcTCGA).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2020-0250
Communications in Computational Physics, Vol. 30 (2021), Iss. 1 : pp. 190–209
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: High-dimensional linear regression sparsity truncated $L_1$ regularization primal dual active set algorithm.
Author Details
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