Sparse generalized linear model with L0 approximation for feature selection and prediction with big omics data

Zhenqiu Liu, Fengzhu Sun, Dermot P. McGovern

Feature selection and prediction are the most important tasks for big data mining. The common strategies for feature selection in big data mining are L1, SCAD and MC+. However, none of the existing algorithms optimizes L0, which penalizes the number of nonzero features directly. In this paper, we develop a novel sparse generalized linear model (GLM) with L0 approximation for feature selection and prediction with big omics data. The proposed approach approximate the L0 optimization directly. Even though the original L0 problem is non-convex, the problem is approximated by sequential convex optimizations with the proposed algorithm. The proposed method is easy to implement with only several lines of code. Novel adaptive ridge algorithms (L0ADRIDGE) for L0 penalized GLM with ultra high dimensional big data are developed. The proposed approach outperforms the other cutting edge regularization methods including SCAD and MC+ in simulations. When it is applied to integrated analysis of mRNA, microRNA, and methylation data from TCGA ovarian cancer, multilevel gene signatures associated with suboptimal debulking are identified simultaneously. The biological significance and potential clinical importance of those genes are further explored. The developed Software L0ADRIDGE in MATLAB is available at https://github.com/liuzqx/L0adridge.