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

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.