Truncated L1 Regularized Linear Regression:Theory and Algorithm

作     者：Mingwei Dai Shuyang Dai Junjun Huang Lican Kang Xiliang Lu 

作者机构：Center of Statistical Research and School of StatisticsSouthwestern University of Finance and EconomicsChengduP.R.China School of Mathematics and StatisticsWuhan UniversityWuhanP.R.China Hubei Key Laboratory of Computational ScienceWuhan UniversityWuhanP.R.China. 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2021年第30卷第6期

页      面：190-209页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：National Natural Science Foundation of China, NSFC, (11871385) National Natural Science Foundation of China, NSFC Natural Science Foundation of Hubei Province, (2019CFA007) Natural Science Foundation of Hubei Province National Key Research and Development Program of China, NKRDPC, (12071363, 2020YFA0714200) National Key Research and Development Program of China, NKRDPC theNatural Science Foundation of Hubei Province 

主　　题：High-dimensional linear regression sparsity truncated L1 regularization primal dual active set algorithm 

摘      要：Truncated L1 regularization proposed by Fan in[5],is an approximation to the L0 regularization in high-dimensional sparse *** this work,we prove the non-asymptotic error bound for the global optimal solution to the truncated L1 regularized linear regression problem and study the support recovery ***,a primal dual active set algorithm(PDAS)for variable estimation and selection is *** 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 *** application of the proposed method is demonstrated by applying it to simulation data and a breast cancer gene expression data set(bcTCGA).