A lower bound based smoothed quasi-Newton algorithm for group bridge penalized regression

作者：Cao, Yongxiu; Huang, Jian; Jiao, Yuling; Liu, Yanyan^*

来源：Communications in Statistics - Simulation and Computation, 2017, 46(6): 4694-4707.

DOI：10.1080/03610918.2015.1129409

• Lower bound rule
• Group bridge
• Penalized least squares
• Quasi-Newton algorithm

In this paper, we propose a lower bound based smoothed quasi-Newton algorithm for computing the solution paths of the group bridge estimator in linear regression models. Our method is based on the quasi-Newton algorithm with a smoothed group bridge penalty in combination with a novel data-driven thresholding rule for the regression coefficients. This rule is derived based on a necessary KKT condition of the group bridge optimization problem. It is easy to implement and can be used to eliminate groups with zero coefficients. Thus, it reduces the dimension of the optimization problem. The proposed algorithm removes the restriction of groupwise orthogonal condition needed in coordinate descent and LARS algorithms for group variable selection. Numerical results show that the proposed algorithm outperforms the coordinate descent based algorithms in both efficiency and accuracy.

• 出版日期2017
• 单位武汉大学; 上海财经大学; 中南财经政法大学