大规模数据的L_(1)惩罚分位数回归方法研究--基于特征筛选和随机抽样方法  

L_(1) Penalty Quantile Regression Model for Large-scale Data Based on Feature Screening and Sampling

作　　者：蔡超[1] 王康宁 CAI Chao;WANG Kang-ning(School of Statistics,Shandong Technology and Business University,Yantai 264005,China)

机构地区：[1]山东工商学院统计学院,山东烟台264005

出　　处：《数理统计与管理》2022年第1期63-78,共16页Journal of Applied Statistics and Management

基　　金：国家自然科学基金(11901356);国家社会科学基金(20BTJ052);山东省社会科学规划研究项目(20CTJJ01,19BYSJ40);全国统计科学研究项目(2019320).

摘　　要：为解决大规模数据在进行回归分析时存在的计算内存不足和运行时间较长的问题,提出两个新的回归分析方法:先筛选后抽样的大规模数据L_(1)惩罚分位数回归方法(FSSLQR)和先抽样后筛选的大规模数据L_(1)惩罚分位数回归方法(SFSLQR),其数值模拟和实际应用结果表明:FSSLQR和SFSLQR方法不仅能够显著降低计算内存和运行时间,而且其估计预测和变量选择的结果与全量L_(1)惩罚分位数回归基本一致。此外,与Xu等(2018)提出的大规模数据的L1惩罚分位数回归方法(SLQR)相比,FSSLQR和SFSLQR方法在估计预测、变量选择和运行时间等方面都更具优势。Regression analysis becomes infeasible on large-scale data due to the limitations of primary memory and running time in computers.To address this issue,we propose two novel FSSLQR and SFSLQR method to implement L_(1) penalty quantile regression analysis on large-scale data.Both numerical simulations and a real-world application show that the proposed method not only significantly reduces the required amount of primary memory and computation time,but also the resulting estimator is as efficient as the L_(1) penalty quantile regression on entire dataset in terms of fitting effect and forecasting ability,and variable selection.In addition,the proposed method significantly superior to the SLQR method proposed Xu et al.(2018)in fitting effect and forecasting ability,variable selection and running time.

关 键 词：L_(1)惩罚分位数回归 大规模数据 特征筛选 随机抽样 

分 类 号：O212[理学—概率论与数理统计]