Group sparse structural smoothing recovery: model, statistical properties and algorithm

In this paper, we propose an innovative group sparse structural smoothing recovery model and explore its statistical properties. Specifically, the nonconvex group norm and a new inner-group total variation regularizer are established to capture the group and smooth structures of variables. Under a regularization condition, we analyze the statistical properties of the proposed model, including the global recovery bound for estimation error and prediction error. To tackle the proposed nonconvex and nonsmooth problem, an efficient Bregman alternative direction method of multipliers (Bregman ADMM) is designed. We demonstrate that the sequence produced by the proposed Bregman ADMM converges to a stationary point under certain assumptions. Extensive numerical experiments and the application of comparative genomic hybridization data and large-scale breast cancer gene expression data demonstrate that the proposed method improves estimation accuracy and produces better sparsity and smoothness than other group variable selection models.