文献类型：期刊文献

英文题名：An efficient method for the support vector machine with minimax concave penalty in high dimensions

作者：Yang, Jin[1];Zhang, Ning[2];Zhang, Yi[3]

机构：[1]Beijing Univ Posts & Telecommun, Sch Math Sci, Beijing 100876, Peoples R China;[2]Dongguan Univ Technol, Sch Comp Sci & Technol, Dongguan 523808, Peoples R China;[3]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2025

卷号：12

期号：1

外文期刊名：COMPLEX & INTELLIGENT SYSTEMS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001623691100009)】；

基金：The research of Ning Zhang was supported by the National Natural Science Foundation of China (12271095, 11901083) and the Guangdong Basic and Applied Basic Research Foundation (2022A1515010088). The research of Yi Zhang was supported by the National Natural Science Foundation of China (12171153).

语种：英文

外文关键词：Minimax concave penalty; Sparse Newton method; One step convergence property

摘要：Support vector machines (SVMs) are powerful approaches for achieving accurate and well-generalized classification on high-dimensional datasets. However, considering all dimensions will lead to computational difficulties and overfitting. In this study, our focus lies in establishing the numerical theory for solving minimax concave penalty penalized SVMs, with the aim of providing sparse optimization and statistical guarantees. We develop a novel convergence theory proving that the difference-of-convex algorithm (DCA), without any proximal regularization, achieves linear convergence to directional-stationary points. More strikingly, in high-dimensional regimes, the DCA provably achieves convergence to the oracle estimator with high probability after a single iteration. To overcome computational bottlenecks inherent in existing algorithms, we propose a highly efficient second-order information-based algorithm for solving the subproblems of DCA. Numerical experiments substantiate computational efficiency and model accuracy of the proposed approach.