Aggregating Knockoffs for Controlling the False Discovery Rate with One-Shot Communication

We introduce a new method for controlling the false discovery rate (FDR)---the expected fraction of spurious discoveries among all the discoveries---in the context of 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. Based on the knockoffs framework introduced by Barber and Cand\`es (2014), 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.