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While supervised federated learning approaches have enjoyed significantsuccess, the domain of unsupervised federated learning remains relativelyunderexplored. Several federated EM algorithms have gained popularity inpractice, however, their theoretical foundations are often lacking. In thispaper, we first introduce a federated gradient EM algorithm (FedGrEM) designedfor the unsupervised learning of mixture models, which supplements the existingfederated EM algorithms by considering task heterogeneity and potentialadversarial attacks. We present a comprehensive finite-sample theory that holdsfor general mixture models, then apply this general theory on specificstatistical models to characterize the explicit estimation error of modelparameters and mixture proportions. Our theory elucidates when and how FedGrEMoutperforms local single-task learning with insights extending to existingfederated EM algorithms. This bridges the gap between their practical successand theoretical understanding. Our numerical results validate our theory, anddemonstrate FedGrEM's superiority over existing unsupervised federated learningbenchmarks.

Towards the Theory of Unsupervised Federated Learning: Non-asymptotic Analysis of Federated EM Algorithms