超高维数据的特征筛选方法研究  

Research on Feature Screening Approach of Ultrahigh Dimensional Data

作　　者：闫彤 刘祎 Yan Tong;Liu Yi(School of Mathematical Science,Ocean University of China,Qingdao Shandong 266100,China)

机构地区：[1]中国海洋大学数学科学学院,山东青岛266100

出　　处：《统计与决策》2025年第5期43-48,共6页Statistics & Decision

基　　金：国家自然科学基金资助项目(11801567);山东省自然科学基金资助项目(ZR2024QA018)。

摘　　要：文章首先针对超高维数据建立了新的边际筛选方法(FMAS-SIS)。该方法采用切片-融合技术,将连续变量切片转化为离散变量,并对不同切片方案进行融合,可以有效地处理分类、离散、连续的响应变量;其次,在一定的正则性条件下,证明了该方法的确定筛选性和排序一致性;最后,基于数值模拟和实际案例,将所提方法与其他筛选方法进行比较,展示了所提方法的有限样本性能。综合来看,FMAS-SIS具有以下优势:第一,该方法是一种非参数特征筛选方法,不依赖于模型假设;第二,只涉及条件分布函数的经验估计,计算简单、易于实现;第三,即使预测变量、随机误差是重尾的,或预测变量是强相关的,或存在异常值,依然具有优良的筛选性能;第四,对切片方案不敏感。This paper firstly proposes a new marginal screening method(FMAS-SIS)for ultrahigh dimensional data.In the method,slice-fusion technology is used to transform continuous variable slices into discrete variables,and different slicing schemes are fused,which can effectively deal with classified,discrete and continuous response variables.Secondly,under certain regularity conditions,the sure screening property and ordering consistency of the method is proved.Finally,based on numerical simulation and practical cases,the proposed method is compared with other screening methods to demonstrate the limited sample performance of the proposed method.Comprehensively,FMAS-SIS has the following advantages:First,it is a nonparametric model-free method that do not depend on model assumptions;second,only involving empirical estimation of conditional distribution functions,the calculation is simple and easy to implement;third,it still has excellent screening performance even if the predictor variables,random errors are heavy-tailed,or the predictor variables are strongly correlated,or outliers are presented;fourth,it is unsensitive to the slicing scheme.

关 键 词：超高维数据 特征筛选 切片-融合技术 确定筛选性 

分 类 号：O212[理学—概率论与数理统计]