A statistical view of column subset selection

• 成果类型: Article; Early Access
• 署名作者: Sood, Anav; Hastie, Trevor
• 署名单位: Stanford University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf023
• 发表日期: 2025
• 关键词: Principal component analysis; revealing qr factorizations; Matrix decomposition; variable selection; band selection; rank; algorithms; personality; CLASSIFICATION; computation

摘要

We consider the problem of selecting a small subset of representative variables from a large dataset. In the computer science literature, this dimensionality reduction problem is typically formalized as column subset selection (CSS). Meanwhile, the typical statistical formalization is to find an information-maximizing set of principal variables. This paper shows that these two approaches are equivalent, and moreover, both can be viewed as maximum-likelihood estimation within a certain semi-parametric model. Within this model, we establish suitable conditions under which the CSS estimate is consistent in high dimensions, specifically in the proportional asymptotic regime where the number of variables over the sample size converges to a constant. Using these connections, we show how to efficiently (1) perform CSS using only summary statistics from the original dataset; (2) perform CSS in the presence of missing and/or censored data; and (3) select the subset size for CSS in a hypothesis testing framework.