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High-dimensional data pose challenges in statistical learning and modeling.Sometimes the predictors can be naturally grouped where pursuing thebetween-group sparsity is desired. Collinearity may occur in real-worldhigh-dimensional applications where the popular $l_1$ technique suffers fromboth selection inconsistency and prediction inaccuracy. Moreover, the problemsof interest often go beyond Gaussian models. To meet these challenges,nonconvex penalized generalized linear models with grouped predictors areinvestigated and a simple-to-implement algorithm is proposed for computation. Arigorous theoretical result guarantees its convergence and provides tightpreliminary scaling. This framework allows for grouped predictors and nonconvexpenalties, including the discrete $l_0$ and the `$l_0+l_2$' type penalties.Penalty design and parameter tuning for nonconvex penalties are examined.Applications of super-resolution spectrum estimation in signal processing andcancer classification with joint gene selection in bioinformatics show theperformance improvement by nonconvex penalized estimation.

An Iterative Algorithm for Fitting Nonconvex Penalized Generalized Linear Models with Grouped Predictors