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Distributed Gaussian Mean Testing Under Communication Constraints: Messages, Samples, and Coins

Authors Clément L. Canonne , Nimitt

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LIPIcs.APPROX-RANDOM.2026.36.pdf
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  • 20 pages

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Subject Classification

ACM Subject Classification
  • Theory of computation → Communication complexity
  • Theory of computation → Distributed algorithms
  • Theory of computation → Randomness, geometry and discrete structures
Keywords
  • Distribution Testing
  • Property Testing
  • Distributed Algorithms
  • Communication Constraints

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Abstract

We revisit the problem of Gaussian mean testing in a distributed, communication constrained setting, where each of n users independently observes samples from an unknown d-dimensional spherical Gaussian distribution 𝒢(μ,𝕀_d), and can communicate up to 𝓁 bits to a central referee. The referee’s goal is then to distinguish between cases (i) ‖μ‖₂ = 0 versus (ii) ‖μ‖₂ ≥ ε. This problem has been considered in the private- and public-coin settings, when each user holds exactly one sample, or more generally when each holds exactly m samples. In this work, we significantly generalize the question in three directions: when the users only share a small number s of random bits, when each user holds a different number of samples m_k, and when each user can send a different number of bits 𝓁_k to the referee.

Cite As Get BibTex

Clément L. Canonne and Nimitt. Distributed Gaussian Mean Testing Under Communication Constraints: Messages, Samples, and Coins. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 36:1-36:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.36

Author Details

Clément L. Canonne
  • University of Sydney, Australia
Nimitt
  • IIT Gandhinagar, India

Acknowledgements

The authors thank the anonymous reviewers for their helpful suggestions.

References

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  2. Jayadev Acharya, Clément L. Canonne, Ziteng Sun, and Himanshu Tyagi. Unified lower bounds for interactive high-dimensional estimation under information constraints. In NeurIPS, 2023. Google Scholar
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