Efficient Regularized Regression with L0 Penalty for Variable Selection and Network Construction

Zhenqiu Liu, Gang Li

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


Variable selections for regression with high-dimensional big data have found many applications in bioinformatics and computational biology. One appealing approach is the L0 regularized regression which penalizes the number of nonzero features in the model directly. However, it is well known that L0 optimization is NP-hard and computationally challenging. In this paper, we propose efficient EM (L0EM) and dual L0EM (DL0EM) algorithms that directly approximate the L0 optimization problem. While L0EM is efficient with large sample size, DL0EM is efficient with high-dimensional (n≪m) data. They also provide a natural solution to all Lp p[0,2] problems, including lasso with p=1 and elastic net with p[1,2]. The regularized parameter can be determined through cross validation or AIC and BIC. We demonstrate our methods through simulation and high-dimensional genomic data. The results indicate that L0 has better performance than lasso, SCAD, and MC+, and L0 with 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.

Original languageEnglish (US)
Article number3456153
JournalComputational and Mathematical Methods in Medicine
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • Applied Mathematics


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