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The identification of the dependent components in multiple data sets is afundamental problem in many practical applications. The challenge in theseapplications is that often the data sets are high-dimensional with fewobservations or available samples and contain latent components with unknownprobability distributions. A novel mathematical formulation of this problem isproposed, which enables the inference of the underlying correlation structurewith strict false positive control. In particular, the false discovery rate iscontrolled at a pre-defined threshold on two levels simultaneously. Thedeployed test statistics originate in the sample coherence matrix. The requiredprobability models are learned from the data using the bootstrap. Local falsediscovery rates are used to solve the multiple hypothesis testing problem.Compared to the existing techniques in the literature, the developed techniquedoes not assume an a priori correlation structure and work well when the numberof data sets is large while the number of observations is small. In addition,it can handle the presence of distributional uncertainties, heavy-tailed noise,and outliers.

Identifying the Complete Correlation Structure in Large-Scale High-Dimensional Data Sets with Local False Discovery Rates