Leveraging Spatial and Temporal Correlations in Sparsified Mean Estimation

TL;DR

This paper introduces a novel approach to mean estimation in distributed high-dimensional data by exploiting spatial and temporal correlations, improving accuracy over existing sparsification methods.

Contribution

It proposes a simple modification to decoding that leverages data correlations, providing theoretical analysis and empirical validation across multiple machine learning tasks.

Findings

Outperforms existing sparsification methods in estimation accuracy

Effective in PCA, K-Means, and Logistic Regression tasks

Reduces communication costs while maintaining high estimation quality

Abstract

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.