Decentralized EM Algorithm for Gaussian Mixtures under Data Heterogeneity and Partial Labeling

Abstract:We systematically study several network-based Expectation-Maximization (EM) algorithms for the Gaussian mixture model within decentralized federated learning (DFL). Our theoretical investigation shows that directly extending the classic EM algorithm to DFL leads to a biased estimator when data are heterogeneously distributed across sites. To address this, we introduce a momentum network EM (MNEM) algorithm, which integrates information from both current and historical estimators from previous DFL iterations. We further develop a semi-supervised MNEM (semi-MNEM) algorithm, which utilizes information provided by partially labeled data. Rigorous theoretical analysis demonstrates that the MNEM estimator can achieve the same asymptotic efficiency as the whole-sample estimator under appropriate regularity conditions, even with heterogeneous data. Moreover, the semi-MNEM estimator significantly improves the convergence speed of the MNEM algorithm, even if different mixture components are poorly separated. Extensive simulations are conducted, and a widely used chest X-ray dataset is analyzed to demonstrate the finite-sample performance of the proposed methods.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2411.05591 [stat.ML]

(or arXiv:2411.05591v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2411.05591 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.