QuTE: decentralized multiple testing on sensor networks with false discovery rate control

This paper designs methods for decentralized multiple hypothesis testing on graphs that are equipped with provable guarantees on the false discovery rate (FDR). We consider the setting where distinct agents reside on the nodes of an undirected graph, and each agent possesses p-values corresponding to one or more hypotheses local to its node. Each agent must individually decide whether to reject one or more of its local hypotheses by only communicating with its neighbors, with the joint aim that the global FDR over the entire graph must be controlled at a predefined level. We propose a simple decentralized family of Query-Test-Exchange (QuTE) algorithms and prove that they can control FDR under independence or positive dependence of the p-values. Our algorithm reduces to the Benjamini-Hochberg (BH) algorithm when after graph-diameter rounds of communication, and to the Bonferroni procedure when no communication has occurred or the graph is empty. To avoid communicating real-valued p-values, we develop a quantized BH procedure, and extend it to a quantized QuTE procedure. QuTE works seamlessly in streaming data settings, where anytime-valid p-values may be continually updated at each node. Last, QuTE is robust to arbitrary dropping of packets, or a graph that changes at every step, making it particularly suitable to mobile sensor networks involving drones or other multi-agent systems. We study the power of our procedure using a simulation suite of different levels of connectivity and communication on a variety of graph structures, and also provide an illustrative real-world example.