We study the problem of estimating at a central server the mean of a set of vectors distributed across several nodes (one vector per node). When the vectors are high-dimensional, the communication cost of sending entire vectors may be prohibitive, and it may be imperative for them to use sparsification techniques. While most existing work on sparsified mean estimation is agnostic to the characteristics of the data vectors, in many practical applications such as federated learning, there may be spatial correlations (similarities in the vectors sent by different nodes) or temporal correlations (similarities in the data sent by a single node over different iterations of the algorithm) in the data vectors. We leverage these correlations by simply modifying the decoding method used by the server to estimate the mean. We provide an analysis of the resulting estimation error as well as experiments for PCA, K-Means and Logistic Regression, which show that our estimators consistently outperform more sophisticated and expensive sparsification methods.

翻译：我们研究在中央服务器上估计分布于多个节点(每个节点一个矢量)的一组矢量平均值的问题。当矢量为高维时,发送整个矢量的通信成本可能令人望而却步,它们可能必须使用静电技术。虽然大部分关于封闭平均估计的现有工作对数据矢量的特性是不可知的,但在诸如联结学习等许多实际应用中,可能存在空间相关性(不同节点发送的矢量的相似性),或数据矢量中的时间相关性(单一节点发送的数据与算法不同迭代值的相似性)。我们只是通过修改服务器使用的解码方法来利用这些关联性来估计平均值。我们对由此产生的估计错误以及五氯苯、K-Means和物流回归实验进行了分析,这些分析表明我们的估计者一贯地超越了更为复杂和昂贵的通缩方法。