论文标题
通用组稀疏的错误界限
Error Bounds for Generalized Group Sparsity
论文作者
论文摘要
在高维统计推论中，稀疏性正规化显示了系数估计的一致性和收敛速率的优势。我们考虑了稀疏组套索的广义版本，该版本同时捕获了元素的稀疏性和小组的稀疏性。我们陈述了一个通用定理，该定理被证明可以根据不同形式的双重稀疏正规化的一致性和收敛速率获得结果。结果的普遍性在于单个正则化案例（例如Lasso和Group Lasso）的各种收敛速率的概括，以及稀疏组套索等双重正则化案例。我们的分析确定了$ε$ -Norm的广义规范，该规范为我们的双重稀疏正则化提供了双重配方。
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.
