  The false discovery rate (FDR)---the expected fraction of spurious
discoveries among all the discoveries---provides a popular statistical
assessment of the reproducibility of scientific studies in various disciplines.
In this work, we introduce a new method for controlling the FDR in
meta-analysis of many decentralized linear models. Our method targets the
scenario where many research groups---possibly the number of which is
random---are independently testing a common set of hypotheses and then sending
summary statistics to a coordinating center in an online manner. Built on the
knockoffs framework introduced by Barber and Candes (2015), our procedure
starts by applying the knockoff filter to each linear model and then aggregates
the summary statistics via one-shot communication in a novel way. This method
gives exact FDR control non-asymptotically without any knowledge of the noise
variances or making any assumption about sparsity of the signal. In certain
settings, it has a communication complexity that is optimal up to a logarithmic
factor.
