A pseudo knockoff filter for correlated features
In Barber & Candès (2015, Ann. Statist., 43, 2055–2085), the authors introduced a new variable selection procedure called the knockoff filter to control the false discovery rate (FDR) and proved that this method achieves exact FDR control. Inspired by the work by Barber & Candès (2015, Ann. Statist., 43, 2055–2085), we propose a pseudo knockoff filter that inherits some advantages of the original knockoff filter and has more flexibility in constructing its knockoff matrix. Moreover, we perform a number of numerical experiments that seem to suggest that the pseudo knockoff filter with the half Lasso statistic has FDR control and offers more power than the original knockoff filter with the Lasso Path or the half Lasso statistic for the numerical examples that we consider in this paper. Although we cannot establish rigourous FDR control for the pseudo knockoff filter, we provide some partial analysis of the pseudo knockoff filter with the half Lasso statistic and establish a uniform false discovery proportion bound and an expectation inequality.
© 2018 The Author(s). Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model). Received on 30 August 2017; revised on 14 May 2018; accepted on 7 June 2018. Published: 17 July 2018. The research of J.C. was performed during his visit to ACM at Caltech. We would like to thank Professor Emmanuel Candes for his many valuable comments and suggestions to our work. We would also like to thank Professor Lucas Janson for his interest and comments on the earlier version of this manuscript and Dr. Pengfei Liu for the discussions on the pseudo knockoff. Funding: National Science Foundation (DMS 1318377 and DMS 1613861).
Submitted - 1708.09305.pdf