the benefit of group sparsity

• DOI: 10.48550/arxiv.0901.2962
• Publication Date: 2010-08-01
• Authors: Huang, Junzhou; Zhang, T.
• Keywords: FOS: Computer and information sciences; Variable selection; L_1 regularization; Mathematics - Statistics Theory; Machine Learning (stat.ML); Statistics Theory (math.ST); 02 engineering and technology; 62J05; Statistics - Machine Learning; Parameter estimation; FOS: Mathematics; 0202 electrical engineering, electronic engineering, information engineering; 62G05; Group sparsity; group Lasso; sparsity; Regression; Group Lasso; group sparsity; regression; Lasso; parameter estimation; Sparsity; L1 regularization; variable selection

This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.