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This research advances federated learning by introducing generalized total variation minimization to enable soft clustering across devices with private data. The study rigorously compares different discrepancy measures, including KL divergence and maximum mean discrepancy, to improve robustness against data heterogeneity without requiring component matching. These methodological contributions are significant for optimizing distributed machine learning architectures in privacy-sensitive environments.
Federated Soft Clustering via Generalized Total Variation Minimization
arXiv:2609.19202v1 Announce Type: cross Abstract: We study federated soft clustering over federated learning (FL) networks of devices that each hold a private local dataset and fit a personalized Gaussian mixture model (GMM). Generalized total variation minimization (GTVMin) couples the local maximum likelihood problems through a graph regularizer that penalizes a discrepancy between the models of connected nodes. The choice of discrepancy measure is a key design decision: we compare a squared Euclidean distance between model parameters, which requires component matching, with two measures that compare the local model distributions directly and hence need no matching: a Monte-Carlo approximated Kullback-Leibler (KL) divergence and a closed-form maximum mean discrepancy (MMD). All three resulting GTVMin instances are optimized by synchronous projected gradient updates; for the smooth MMD instance we provide a convergence guarantee to stationary points. We characterize their computational cost and evaluate their robustness to data heterogeneity.
Abstract:We study federated soft clustering over federated learning (FL) networks of devices that each hold a private local dataset and fit a personalized Gaussian mixture model (GMM). Generalized total variation minimization (GTVMin) couples the local maximum likelihood problems through a graph regularizer that penalizes a discrepancy between the models of connected nodes. The choice of discrepancy measure is a key design decision: we compare a squared Euclidean distance between model parameters, which requires component matching, with two measures that compare the local model distributions directly and hence need no matching: a Monte-Carlo approximated Kullback-Leibler (KL) divergence and a closed-form maximum mean discrepancy (MMD). All three resulting GTVMin instances are optimized by synchronous projected gradient updates; for the smooth MMD instance we provide a convergence guarantee to stationary points. We characterize their computational cost and evaluate their robustness to data heterogeneity.
Machine Learning (stat.ML); Machine Learning (cs.LG)
I.5.3; I.2.6; G.3; C.2.4
arXiv:2609.19202 [stat.ML]
(or arXiv:2609.19202v1 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2609.19202 Focus to learn more arXiv-issued DOI via DataCite
https://doi.org/10.5281/zenodo.22791733 Focus to learn more DOI(s) linking to related resources
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