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March 2019 Multilayer knockoff filter: Controlled variable selection at multiple resolutions
Eugene Katsevich, Chiara Sabatti
Ann. Appl. Stat. 13(1): 1-33 (March 2019). DOI: 10.1214/18-AOAS1185


We tackle the problem of selecting from among a large number of variables those that are “important” for an outcome. We consider situations where groups of variables are also of interest. For example, each variable might be a genetic polymorphism, and we might want to study how a trait depends on variability in genes, segments of DNA that typically contain multiple such polymorphisms. In this context, to discover that a variable is relevant for the outcome implies discovering that the larger entity it represents is also important. To guarantee meaningful results with high chance of replicability, we suggest controlling the rate of false discoveries for findings at the level of individual variables and at the level of groups. Building on the knockoff construction of Barber and Candès [Ann. Statist. 43 (2015) 2055–2085] and the multilayer testing framework of Barber and Ramdas [J. Roy. Statist. Soc. Ser. B 79 (2017) 1247–1268], we introduce the multilayer knockoff filter (MKF). We prove that MKF simultaneously controls the FDR at each resolution and use simulations to show that it incurs little power loss compared to methods that provide guarantees only for the discoveries of individual variables. We apply MKF to analyze a genetic dataset and find that it successfully reduces the number of false gene discoveries without a significant reduction in power.


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Eugene Katsevich. Chiara Sabatti. "Multilayer knockoff filter: Controlled variable selection at multiple resolutions." Ann. Appl. Stat. 13 (1) 1 - 33, March 2019.


Received: 1 August 2017; Revised: 1 April 2018; Published: March 2019
First available in Project Euclid: 10 April 2019

zbMATH: 07057418
MathSciNet: MR3937419
Digital Object Identifier: 10.1214/18-AOAS1185

Keywords: $p$-filter , false discovery rate (FDR) , genomewide association study (GWAS) , group FDR , knockoff filter , multiresolution , Variable selection

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.13 • No. 1 • March 2019
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