title: Efficient Regularized Regression withL0Penalty for Variable Selection and Network Construction.
abstract: Variable selections for regression with high-dimensional big data have found many applications in bioinformatics and computational biology. One appealing approach is theL0regularized regression which penalizes the number of nonzero features in the model directly. However, it is well known thatL0optimization is NP-hard and computationally challenging. In this paper, we propose efficient EM (L0EM) and dualL0EM (DL0EM) algorithms that directly approximate theL0optimization problem. WhileL0EM is efficient with large sample size, DL0EM is efficient with high-dimensional (n≪m) data. They also provide a natural solution to allLpp∈ [0,2] problems, including lasso withp= 1 and elastic net withp∈ [1,2]. The regularized parameterλcan be determined through cross validation or AIC and BIC. We demonstrate our methods through simulation and high-dimensional genomic data. The results indicate thatL0has better performance than lasso, SCAD, and MC+, andL0with AIC or BIC has similar performance as computationally intensive cross validation. The proposed algorithms are efficient in identifying the nonzero variables with less bias and constructing biologically important networks with high-dimensional big data.
authors.affiliation: Samuel Oschin Comprehensive Cancer Institute, Cedars-Sinai Medical Center, Los Angeles, CA 90048, USA.
authors.forename: Zhenqiu
authors.identifier: 0000-0003-1535-4322
authors.initials: Z
authors.lastname: Liu
authors.affiliation: Department of Biostatistics, School of Public Health, University of California at Los Angeles, Los Angeles, CA 90095-1772, USA.
authors.forename: Gang
authors.identifier: 0000-0002-4753-9420
authors.initials: G
authors.lastname: Li
mesh_terms: D000465:Algorithms; D019540:Area Under Curve; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D003625:Data Collection; D005260:Female; D020869:Gene Expression Profiling; D015972:Gene Expression Regulation, Neoplastic; D023281:Genomics / Q000379:methods*; D006801:Humans; D015233:Models, Statistical; D016011:Normal Distribution; D010051:Ovarian Neoplasms / Q000235:genetics* / Q000378:metabolism; D025941:Protein Interaction Mapping; D012044:Regression Analysis; D018401:Sample Size