Optimal distributed composite testing in high-dimensional Gaussian models with 1-bit communication

TL;DR

This paper investigates the limits of detecting signals in high-dimensional Gaussian noise within a distributed system constrained to 1-bit communication per node, proposing optimal testing strategies that meet theoretical bounds.

Contribution

It establishes a lower bound on signal strength for detection and introduces optimal distributed testing methods achieving this bound.

Findings

Derived a lower bound on signal norm for detection

Proposed optimal distributed testing strategies

Achieved theoretical bounds in high-dimensional Gaussian models

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.