Partition-based ultrahigh-dimensional variable screening

• 成果类型: Article
• 署名作者: Kang, Jian; Hong, Hyokyoung G.; Li, Yi
• 署名单位: University of Michigan System; University of Michigan; Michigan State University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asx052
• 发表日期: 2017
• 页码: 785800
• 关键词: GENERALIZED LINEAR-MODELS; adaptive lasso; selection; regularization; index

摘要

Traditional variable selection methods are compromised by overlooking useful information on covariates with similar functionality or spatial proximity, and by treating each covariate independently. Leveraging prior grouping information on covariates, we propose partition-based screening methods for ultrahigh-dimensional variables in the framework of generalized linear models. We show that partition-based screening exhibits the sure screening property with a vanishing false selection rate, and we propose a data-driven partition screening framework with unavailable or unreliable prior knowledge on covariate grouping and investigate its theoretical properties. We consider two special cases: correlation-guided partitioning and spatial location-guided partitioning. In the absence of a single partition, we propose a theoretically justified strategy for combining statistics from various partitioning methods. The utility of the proposed methods is demonstrated via simulation and analysis of functional neuroimaging data.