Graph-Regularized Learning of Gaussian Mixture Models

Abstract--We present a graph-regularized learning of Gaussian Mixture Models (GMMs) in distributed settings with heterogeneous and limited local data. The method exploits a provided similarity graph to guide parameter sharing among nodes, avoiding the transfer of raw data. The resulting model allows for flexible aggregation of neighbors' parameters and outperforms both centralized and locally trained GMMs in heterogeneous, low-sample regimes. We propose GraphFed-EM, a federated Gaussian Mixture Model in which local nodes collaboratively learn a personalized probabilistic model through graph-based regularization, without exchanging raw data. The algorithm is adapted for decentralized settings, incorporating an aggregation step that promotes parameter similarity among connected nodes.