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Optimal distributed composite testing in high-dimensional Gaussian models with 1-bit communication (2012.04957v2)
Published 9 Dec 2020 in cs.IT, math.IT, math.ST, stat.ML, and stat.TH
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.
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