Federated Expectation Maximization with heterogeneity mitigation and variance reduction

TL;DR

This paper introduces FedEM, a federated extension of the EM algorithm that efficiently handles heterogeneity and partial participation in distributed datasets, with variance reduction and theoretical guarantees.

Contribution

It presents the first federated EM algorithm, FedEM, incorporating communication efficiency, heterogeneity robustness, and variance reduction, with finite-time complexity analysis.

Findings

FedEM is communication-efficient and robust to data heterogeneity.

The variance reduction extension improves convergence.

Numerical results validate theoretical bounds and application effectiveness.

Abstract

The Expectation Maximization (EM) algorithm is the default algorithm for inference in latent variable models. As in any other field of machine learning, applications of latent variable models to very large datasets make the use of advanced parallel and distributed architectures mandatory. This paper introduces FedEM, which is the first extension of the EM algorithm to the federated learning context. FedEM is a new communication efficient method, which handles partial participation of local devices, and is robust to heterogeneous distributions of the datasets. To alleviate the communication bottleneck, FedEM compresses appropriately defined complete data sufficient statistics. We also develop and analyze an extension of FedEM to further incorporate a variance reduction scheme. In all cases, we derive finite-time complexity bounds for smooth non-convex problems. Numerical results are presented to support our theoretical findings, as well as an application to federated missing values imputation for biodiversity monitoring.