Communication-Efficient False Discovery Rate Control via Knockoff Aggregation

TL;DR

This paper presents a new communication-efficient method for controlling the false discovery rate in decentralized linear models, enabling exact FDR control with minimal communication and no assumptions on noise or sparsity.

Contribution

It introduces a novel knockoff aggregation technique for meta-analysis that achieves exact FDR control with one-shot communication in decentralized settings.

Findings

Exact FDR control without noise variance knowledge

Optimal communication complexity up to a logarithmic factor

Applicable to decentralized linear models in meta-analysis

Abstract

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.