**统计与管理学院****2017****年学术报告第****50****期**【主 题】

**Model-free Knockoffs for High-dimensional Controlled Variable Selection**【报告人】Fan Yingying, 副教授

University of Southern California

【时 间】 2017年07月05日（星期三）15:00－16:00

【地 点】 上海财经大学统计与管理学院大楼1208室

【摘 要】A common problem in modern statistical applications is to select, from a large set of candidates, a subset of variables which are important for determining an outcome of interest. For instance, the outcome may be disease status and the variables may be hundreds of thousands of single nucleotide polymorphisms on the genome. For data coming from low-dimensional n> p linear homoscedastic models, the knockoff procedure recently introduced by Barber and Candes solves the problem by performing variable selection while controlling the false discovery rate (FDR). The present paper extends the knockoff framework to arbitrary (and unknown) conditional models and any dimensions, including n<p, allowing it to solve a much broader array of problems. This extension requires the design matrix be random (independent and identically distributed rows) with a covariate distribution that is known, although we show our procedure to be robust to unknown/estimated distributions. To our knowledge, no other procedure solves the variable selection problem in such generality, but in the restricted settings where competitors exist, we demonstrate the superior power of knockoffs through simulations. Finally, we apply our procedure to data from a case-control study of Crohn's disease in the United Kingdom, making twice as many discoveries as the original analysis of the same data.

【邀请人】 黄涛