Reproducible Feature Selection for High-Dimensional Measurement Error Models

The literature has witnessed an upsurge of interest in dealing with corrupted data in diverse operations research and optimization applications. Despite the substantial progress of feature selection, how to control the false discovery rate (FDR) under measurement errors remains largely unexplored, especially in the knockoffs framework. In this paper, we extend the recently developed knockoff procedures designed for clean data sets to deal with corrupted data. To be specific, we propose a new method called the double projection knockoff filter (DP-knockoff) for reproducible feature selection under additive measurement errors in the high-dimensional setup. Our key contribution is to show that the FDR of the proposed DP-knockoff can be asymptotically controlled within a user-specified level. This is nontrivial because there is no way to obtain the exact knockoff copies due to the unobservable measurement errors. We address this issue by resorting to certain bias-corrected test statistics. Our numerical studies and real data analysis demonstrate the effectiveness of the proposed procedure.