False discovery and its control in low rank estimation

• 成果类型: Article
• 署名作者: Taeb, Armeen; Shah, Parikshit; Chandrasekaran, Venkat
• 署名单位: California Institute of Technology; Yahoo! Inc
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12387
• 发表日期: 2020
• 页码: 997-1027
• 关键词: selection; number

摘要

Models specified by low rank matrices are ubiquitous in contemporary applications. In many of these problem domains, the row-column space structure of a low rank matrix carries information about some underlying phenomenon, and it is of interest in inferential settings to evaluate the extent to which the row-column spaces of an estimated low rank matrix signify discoveries about the phenomenon. However, in contrast with variable selection, we lack a formal framework to assess true or false discoveries in low rank estimation; in particular, the key source of difficulty is that the standard notion of a discovery is a discrete notion that is ill suited to the smooth structure underlying low rank matrices. We address this challenge via ageometricreformulation of the concept of a discovery, which then enables a natural definition in the low rank case. We describe and analyse a generalization of the stability selection method of Meinshausen and Buhlmann to control for false discoveries in low rank estimation, and we demonstrate its utility compared with previous approaches via numerical experiments.