Error Bounds for Generalized Group Sparsity
This provides theoretical guarantees for sparsity methods in high-dimensional data analysis, but it appears incremental as it extends existing results from single to double regularizations.
The paper tackles the problem of high-dimensional statistical inference by analyzing a generalized Sparse-Group Lasso that combines element-wise and group-wise sparsity, proving a universal theorem to derive consistency and convergence rates for such double sparsity regularizations.
In high-dimensional statistical inference, sparsity regularizations have shown advantages in consistency and convergence rates for coefficient estimation. We consider a generalized version of Sparse-Group Lasso which captures both element-wise sparsity and group-wise sparsity simultaneously. We state one universal theorem which is proved to obtain results on consistency and convergence rates for different forms of double sparsity regularization. The universality of the results lies in an generalization of various convergence rates for single regularization cases such as LASSO and group LASSO and also double regularization cases such as sparse-group LASSO. Our analysis identifies a generalized norm of $ε$-norm, which provides a dual formulation for our double sparsity regularization.