2020/06/11 by Xinyu Zhang, Zhang, Xinyu · 1 citation
Decision Sciences · Engineering · Mathematics · #Algorithm #Artificial intelligence #Computation #Computation (stat.CO) #Computer science #Dual (grammatical number) #FOS: Computer and information sciences #FOS: Mathematics #Feature selection #Mathematical optimization #Mathematics #Multi-Criteria Decision Making #Norm (philosophy) #Optimization and Control (math.OC) #Regularization (linguistics) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #math.OC #stat.CO
paper · pdf · doi:10.48550/arxiv.2006.06172
published in arXiv (Cornell University) (Cornell University) · merge with Error Bounds for Generalized Group Sparsity
openalex publication_date 2020/06/11 · arxiv created 2021/09/24 · arxiv updated 2021/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a high-dimensional setting, sparse model has shown its power in computational and statistical efficiency. We consider variables selection problem with a broad class of simultaneous sparsity regularization, enforcing both feature-wise and group-wise sparsity at the same time. The analysis leverages an introduction of εq-norm in vector space, which is proved to has close connection with the mixture regularization and naturally leads to a dual formulation. Properties of primal/dual optimal solution and optimal values are discussed, which motivates the design of screening rules. We several fast safe screening rules in the general framework, rules that discard inactive features/groups at an early stage that are guaranteed to be inactive in the exact solution, leading to a significant gain in computation speed.