Group Structure Influence on Group Lasso Consistency

Group Lasso is a recently proposed regression method that can be used to select group variables. When studying the consistency condition of the regularization path of group Lasso, we assume that the groupings of the univariate variables are known and fixed, that is, the group structure is given. In this paper, we address the issue of the influence of group structure on the group Lasso consistency. Based on the analysis of the consistency condition, we argue that the sparsity patterns is the determinant, the different group structures can lead to different consistencies, and the degree of the correlation between the relevant groups and the irrelevant groups is the key factor. Experimental results also demonstrate that the group Lasso is consistent under low correlation conditions.