RELAXING THE ASSUMPTIONS OF KNOCKOFFS BY CONDITIONING

• 成果类型: Article
• 署名作者: Huang, Dongming; Janson, Lucas
• 署名单位: Harvard University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1920
• 发表日期: 2020
• 页码: 3021-3042
• 关键词: false discovery rate; Post-selection Inference; confidence-intervals; statistics; parameters; estimators; regression; tests

摘要

The recent paper Candes et al. (J. R. Stat. Soc. Ser. B. Stat. Methodol. 80 (2018) 551-577) introduced model-X knockoffs, a method for variable selection that provably and nonasymptotically controls the false discovery rate with no restrictions or assumptions on the dimensionality of the data or the conditional distribution of the response given the covariates. The one requirement for the procedure is that the covariate samples are drawn independently and identically from a precisely-known (but arbitrary) distribution. The present paper shows that the exact same guarantees can be made without knowing the covariate distribution fully, but instead knowing it only up to a parametric model with as many as Omega (n*p) parameters, where p is the dimension and n* is the number of covariate samples (which may exceed the usual sample size n of labeled samples when unlabeled samples are also available). The key is to treat the covariates as if they are drawn conditionally on their observed value for a sufficient statistic of the model. Although this idea is simple, even in Gaussian models conditioning on a sufficient statistic leads to a distribution supported on a set of zero Lebesgue measure, requiring techniques from topological measure theory to establish valid algorithms. We demonstrate how to do this for three models of interest, with simulations showing the new approach remains powerful under the weaker assumptions.