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.
Adaptive Dimension Reduction for Overlapping Group Sparsity
School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）；Mathematics Institute, University of Warwick（华威大学数学研究所）；Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学自然研究院）
A Safe Screening Rule with Bi-level Optimization of $ν$ Support Vector Machine
College of Statistics and Mathematics, Yunnan University of Finance and Economics（云南财经大学统计与数学学院）；College of Science, China Agricultural University（中国农业大学理学院）
