Optimal Distributed Composite Testing in High-Dimensional Gaussian Models With 1-Bit Communication

Botond Szabó, Lasse Vuursteen, Harry van Zanten

Abstract: In this paper we study the problem of signal detection in Gaussian noise in a distributed setting where the local machines in the star topology can communicate a single bit of information. We derive a lower bound on the Euclidian norm that the signal needs to have in order to be detectable. Moreover, we exhibit optimal distributed testing strategies that attain the lower bound.