Communication efficient distributed mean estimation is an important primitive that arises in many distributed learning and optimization scenarios such as federated learning. Without any probabilistic assumptions on the underlying data, we study the problem of distributed mean estimation where the server has access to side information. We propose \emph{Wyner-Ziv estimators}, which are communication and computationally efficient and near-optimal when an upper bound for the distance between the side information and the data is known. As a corollary, we also show that our algorithms provide efficient schemes for the classic Wyner-Ziv problem in information theory. In a different direction, when there is no knowledge assumed about the distance between side information and the data, we present an alternative Wyner-Ziv estimator that uses correlated sampling. This latter setting offers {\em universal recovery guarantees}, and perhaps will be of interest in practice when the number of users is large and keeping track of the distances between the data and the side information may not be possible.

中文翻译：

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Wyner-Ziv估计器：带有辅助信息的高效分布式均值估计

通信有效的分布式均值估计是在许多分布式学习和优化方案（例如联合学习）中出现的重要原语。在不对基础数据进行任何概率假设的情况下，我们研究了服务器可以访问辅助信息的分布式均值估计问题。我们提出\ emph {Wyner-Ziv估计量}，当边信息和数据之间的距离的上限已知时，它们通信效率高，计算效率高且接近最佳。作为推论，我们还证明了我们的算法为信息论中的经典Wyner-Ziv问题提供了有效的方案。在另一个方向上，如果没有假设有关辅助信息和数据之间的距离的知识，我们提出了一种使用相关采样的Wyner-Ziv估计器。后一种设置提供{\ em通用恢复保证}，并且在实践中，当用户数量很大并且可能无法跟踪数据与辅助信息之间的距离时，可能会引起人们的兴趣。