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The paper considers the problem of identifying the sparse differentcomponents between two high dimensional means of column-wise dependent randomvectors. We show that the dependence can be utilized to lower theidentification boundary for signal recovery. Moreover, an optimal convergencerate for the marginal false non-discovery rate (mFNR) is established under thedependence. The convergence rate is faster than the optimal rate withoutdependence. To recover the sparse signal bearing dimensions, we propose aDependence-Assisted Thresholding and Excising (DATE) procedure, which is shownto be rate optimal for the mFNR with the marginal false discovery rate (mFDR)controlled at a pre-specified level. Simulation studies and case study aregiven to demonstrate the performance of the proposed signal identificationprocedure.

A rate optimal procedure for sparse signal recovery under dependence