Inference under Information Constraints II: Communication Constraints and Shared Randomness
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.
Cite
@article{arxiv.1905.08302,
title = {Inference under Information Constraints II: Communication Constraints and Shared Randomness},
author = {Jayadev Acharya and Clément L. Canonne and Himanshu Tyagi},
journal= {arXiv preprint arXiv:1905.08302},
year = {2020}
}
Comments
To appear in IEEE Transactions on Information Theory. An abridged version of this work appeared in the 2019 International Conference on Machine Learning (ICML)