Acharya, J and Canonne, CL and Tyagi, H (2020) Inference under Information Constraints II: Communication Constraints and Shared Randomness. In: IEEE Transactions on Information Theory, 66 (12). pp. 7856-7877.
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Abstract
A central server needs to perform statistical inference based on samples that are distributed over multiple users who can each send a message of limited length to the center. We study problems of distribution learning and identity testing in this distributed inference setting and examine the role of shared randomness as a resource. We propose a general-purpose simulate-and-infer strategy that uses only private-coin communication protocols and is sample-optimal for distribution learning. This general strategy turns out to be sample-optimal even for distribution testing among private-coin protocols. Interestingly, we propose a public-coin protocol that outperforms simulate-and-infer for distribution testing and is, in fact, sample-optimal. Underlying our public-coin protocol is a random hash that when applied to the samples minimally contracts the chi-squared distance of their distribution to the uniform distribution. © 1963-2012 IEEE.
| Item Type: | Journal Article |
|---|---|
| Publication: | IEEE Transactions on Information Theory |
| Publisher: | Institute of Electrical and Electronics Engineers Inc. |
| Additional Information: | The copyright for this article belongs to The Author(s). |
| Keywords: | Cryptocurrency, Central servers; Communication constraints; Distributed inference; Distribution testing; Identity testing; Multiple user; Statistical inference; Uniform distribution, Random processes |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 10 Jan 2023 05:04 |
| Last Modified: | 10 Jan 2023 05:04 |
| URI: | https://eprints.iisc.ac.in/id/eprint/78969 |
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