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

Abstract

Background: 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.

Results: 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.

Conclusions: The developed Software L₀ADRIDGE in MATLAB is available at https://github.com/liuzqx/L0adridge.

Keywords: Big data mining; Classification; GLM; L0 penalty; Multi-omics data; Sparse modeling; Suboptimal debulking.

Fig. 1

Gene signatures associated with suboptimal debulking, where nodes in red: mRNA signatures; nodes in green: microRNA signatures; nodes in pink: methylation signatures, and edges in red: positive partial correlation; edges in blue: negative partial correlation

Fig. 2

Predictive AUCs for integrated data, mRNA expression only, microRNA expression only, and methylation only