Personalized Federated Hierarchical Gaussian Processes for Privacy-Preserving Modeling of Heterogeneous Distributed Systems

Abstract: We present Personalized Federated Hierarchical Gaussian Processes (pFedHGP) for probabilistic regression and classification when data are distributed across heterogeneous clients. Each client's latent function decomposes into (i) a shared global component, (ii) a client-specific deviation that shares the global kernel structure, and (iii) a flexible local residual. Sparse inducing-variable approximations and federated variational inference keep raw data local while the server synchronizes only low-dimensional statistics for the shared component. Full predictive distributions support uncertainty-aware decisions. In application studies, pFedHGP attains perfect fault classification in press tonnage monitoring using 13.77% of labeled cycles and recovers geographic zones in federated air-quality modeling without centralizing station-level time series. An Instantaneous Linear Mixing Model viewpoint links the hierarchy to multi-output Gaussian processes for correlated sensors.