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

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.