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

Botond Szabo; Lasse Vuursteen; Harry Van Zanten

doi:10.1109/TIT.2022.3150599

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

Botond Szabo
, Lasse Vuursteen^*
, Harry Van Zanten

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

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 language	English
Pages (from-to)	4070-4084
Number of pages	15
Journal	IEEE Transactions on Information Theory
Volume	68
Issue number	6
Early online date	9 Feb 2022
DOIs	https://doi.org/10.1109/TIT.2022.3150599
Publication status	Published - Jun 2022

Bibliographical note

Publisher Copyright:
© 1963-2012 IEEE.

Keywords

distributed algorithms
federated learning
Gaussian noise
hypothesis testing
minimax lower bounds
Testing

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10.1109/TIT.2022.3150599

http://arxiv.org/abs/2012.04957

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KW - Gaussian noise

KW - hypothesis testing

KW - minimax lower bounds

KW - Testing

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

Abstract

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Keywords

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