Network EM Algorithm for Gaussian Mixture Model in Decentralized Federated Learning

• URL: http://arxiv.org/abs/2411.05591v1
• Date: Fri, 08 Nov 2024 14:25:46 GMT
• Title: Network EM Algorithm for Gaussian Mixture Model in Decentralized Federated Learning
• Authors: Shuyuan Wu, Bin Du, Xuetong Li, Hansheng Wang,
• Abstract summary: We study various network Expectation-Maximization (EM) algorithms for the Gaussian mixture model. We introduce a momentum network EM (MNEM) algorithm, which uses a momentum parameter to combine information from both the current and historical estimators. We also develop a semi-supervised MNEM algorithm, which leverages partially labeled data.
• Score: 1.4549461207028445
• License:
• Abstract: We systematically study various network Expectation-Maximization (EM) algorithms for the Gaussian mixture model within the framework of decentralized federated learning. Our theoretical investigation reveals that directly extending the classical decentralized supervised learning method to the EM algorithm exhibits poor estimation accuracy with heterogeneous data across clients and struggles to converge numerically when Gaussian components are poorly-separated. To address these issues, we propose two novel solutions. First, to handle heterogeneous data, we introduce a momentum network EM (MNEM) algorithm, which uses a momentum parameter to combine information from both the current and historical estimators. Second, to tackle the challenge of poorly-separated Gaussian components, we develop a semi-supervised MNEM (semi-MNEM) algorithm, which leverages partially labeled data. Rigorous theoretical analysis demonstrates that MNEM can achieve statistical efficiency comparable to that of the whole sample estimator when the mixture components satisfy certain separation conditions, even in heterogeneous scenarios. Moreover, the semi-MNEM estimator enhances the convergence speed of the MNEM algorithm, effectively addressing the numerical convergence challenges in poorly-separated scenarios. Extensive simulation and real data analyses are conducted to justify our theoretical findings.

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