Improved Communication Efficiency for Distributed Mean Estimation with Side Information

TL;DR

This paper introduces a new distributed mean estimation method that leverages side information at both the server and clients, improving accuracy without probabilistic data assumptions.

Contribution

It presents a practical estimator that jointly exploits client-server and inter-client data correlations, extending previous work which only used server-side side information.

Findings

Derives an upper bound on estimation error for the proposed estimator.

Provides algorithms for optimal parameter selection based on the error bound.

Characterizes parameter regions where the new estimator outperforms previous methods.

Abstract

In this paper, we consider the distributed mean estimation problem where the server has access to some side information, e.g., its local computed mean estimation or the received information sent by the distributed clients at the previous iterations. We propose a practical and efficient estimator based on an r-bit Wynzer-Ziv estimator proposed by Mayekar et al., which requires no probabilistic assumption on the data. Unlike Mayekar's work which only utilizes side information at the server, our scheme jointly exploits the correlation between clients' data and server' s side information, and also between data of different clients. We derive an upper bound of the estimation error of the proposed estimator. Based on this upper bound, we provide two algorithms on how to choose input parameters for the estimator. Finally, parameter regions in which our estimator is better than the previous one are characterized.