Knockoff procedure for false discovery rate control in high-dimensional data streams

Abstract

Motivated by applications to root-cause identification of faults in high-dimensional data streams that may have very limited samples after faults are detected, we consider multiple testing in models for multivariate statistical process control (SPC). With quick fault detection, only small portion of data streams being out-of-control (OC) can be assumed. It is a long standing problem to identify those OC data streams while controlling the number of false discoveries. It is challenging due to the limited number of OC samples after the termination of the process when faults are detected. Although several false discovery rate (FDR) controlling methods have been proposed, people may prefer other methods for quick detection. With a recently developed method called Knockoff filtering, we propose a knockoff procedure that can combine with other fault detection methods in the sense that the knockoff procedure does not change the stopping time, but may identify another set of faults to control FDR. A theorem for the FDR control of the proposed procedure is provided. Simulation studies show that the proposed procedure can control FDR while maintaining high power. We also illustrate the performance in an application to semiconductor manufacturing processes that motivated this development.