论文标题
使用有效的原始偶算法的最佳子集选择
Best Subset Selection with Efficient Primal-Dual Algorithm
论文作者
论文摘要
最佳子集选择被认为是许多稀疏学习问题的“黄金标准”。已经提出了多种优化技术来攻击这一非凸和NP障碍问题。在本文中，我们研究了$ \ ell_0 $登记的问题的双重形式。基于原始问题和双重问题结构已经开发了一种有效的原始偶对偶方法。通过利用双重范围估计以及增量策略，我们的算法有可能减少冗余计算并改善最佳子集选择的解决方案。关于合成和现实世界数据集的理论分析和实验验证了所提出的解决方案的效率和统计特性。
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-convex and NP-hard problem. In this paper, we investigate the dual forms of a family of $\ell_0$-regularized problems. An efficient primal-dual method has been developed based on the primal and dual problem structures. By leveraging the dual range estimation along with the incremental strategy, our algorithm potentially reduces redundant computation and improves the solutions of best subset selection. Theoretical analysis and experiments on synthetic and real-world datasets validate the efficiency and statistical properties of the proposed solutions.
