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The false discovery rate (FDR)---the expected fraction of spuriousdiscoveries among all the discoveries---provides a popular statisticalassessment of the reproducibility of scientific studies in various disciplines.In this work, we introduce a new method for controlling the FDR inmeta-analysis of many decentralized linear models. Our method targets thescenario where many research groups---possibly the number of which israndom---are independently testing a common set of hypotheses and then sendingsummary statistics to a coordinating center in an online manner. Built on theknockoffs framework introduced by Barber and Candes (2015), our procedurestarts by applying the knockoff filter to each linear model and then aggregatesthe summary statistics via one-shot communication in a novel way. This methodgives exact FDR control non-asymptotically without any knowledge of the noisevariances or making any assumption about sparsity of the signal. In certainsettings, it has a communication complexity that is optimal up to a logarithmicfactor.

Communication-Efficient False Discovery Rate Control via Knockoff Aggregation