RaSE: A Variable Screening Framework via Random Subspace Ensembles

• Published in: Journal of the American Statistical Association Vol. 118; no. 541; pp. 457 - 468
• Main Authors: Tian, Ye, Feng, Yang
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 02.01.2023; Taylor & Francis Ltd
• Subjects: Americans; Data analysis; design; dimensions; Ensemble learning; High-dimensional data; Independent variables; Random subspace method; Rank consistency; Regression analysis; Screening; Simulation; Statistical methods; Statistics; Subspaces; Sure screening property; Variable screening; Variable selection
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2021.1938084

Variable screening methods have been shown to be effective in dimension reduction under the ultra-high dimensional setting. Most existing screening methods are designed to rank the predictors according to their individual contributions to the response. As a result, variables that are marginally independent but jointly dependent with the response could be missed. In this work, we propose a new framework for variable screening, random subspace ensemble (RaSE), which works by evaluating the quality of random subspaces that may cover multiple predictors. This new screening framework can be naturally combined with any subspace evaluation criterion, which leads to an array of screening methods. The framework is capable to identify signals with no marginal effect or with high-order interaction effects. It is shown to enjoy the sure screening property and rank consistency. We also develop an iterative version of RaSE screening with theoretical support. Extensive simulation studies and real-data analysis show the effectiveness of the new screening framework.