Nonconvex truncated conditional value at risk-based sparse linear regression

IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Boyi Xie, Zhongming Wu, Min Li
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引用次数: 0

Abstract

Conditional value at risk (CVaR) is a widely recognized risk measure used to manage data uncertainty within risk management. In this paper, we study a class of sparse linear regression models based on truncated CVaR measure and 0-norm regularization. Due to the nonconvexity and nonsmoothness of the objective functions, as well as the NP-hardness of the problem with the 0-norm regularization, we propose an approximation model that employs a tight relaxation of the 0-norm. The solution equivalence between the proposed model and its approximation model is explored. To efficiently solve the approximation model, we develop a semismooth Newton-based proximal majorization-minimization algorithm. Furthermore, the convergence analysis of the proposed algorithm is presented, and the convergence rate for the reduced CVaR-based sparse linear regression model is established. Moreover, extensive numerical experiments conducted on both synthetic and real datasets validate the stability and effectiveness of the proposed algorithm, demonstrating significant improvements in both sparsity and accuracy compared to existing state-of-the-art methods.
基于风险的稀疏线性回归的非凸截断条件值
条件风险值(CVaR)是一种被广泛认可的风险度量,用于管理风险管理中的数据不确定性。本文研究了一类基于截断CVaR测度和0范数正则化的稀疏线性回归模型。由于目标函数的非凸性和非光滑性,以及具有0范数正则化问题的np -硬度,我们提出了一个采用0范数严格松弛的近似模型。探讨了该模型与其近似模型的解等价性。为了有效地求解近似模型,我们提出了一种半光滑的基于牛顿的近端最大化-最小化算法。在此基础上,对该算法进行了收敛性分析,建立了基于约简cvar的稀疏线性回归模型的收敛速率。此外,在合成和真实数据集上进行的大量数值实验验证了所提出算法的稳定性和有效性,与现有最先进的方法相比,在稀疏性和准确性方面都有显着提高。
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来源期刊
European Journal of Operational Research
European Journal of Operational Research 管理科学-运筹学与管理科学
CiteScore
11.90
自引率
9.40%
发文量
786
审稿时长
8.2 months
期刊介绍: The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.
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