Optimal Distributed Composite Testing in High-dimensional Gaussian Models with 1-bit Communication

Botond Szabo, Lasse Vuursteen, Harry Van Zanten

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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.

Original languageEnglish
JournalIEEE Transactions on Information Theory
DOIs
Publication statusE-pub ahead of print - 2022

Keywords

  • distributed algorithms
  • Gaussian noise
  • hypothesis testing
  • minimax lower bounds
  • Testing

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