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

Federated prognostics enable clients (e.g., companies, factories, and production lines) to collaboratively develop a failure time prediction model while keeping each client's data local and confidential. However, traditional federated models often assume homogeneity in the degradation processes across clients, an assumption that may not hold in many industrial settings. To overcome this, this paper proposes a personalized federated prognostic model designed to accommodate clients with heterogeneous degradation processes, allowing them to build tailored prognostic models. The prognostic model iteratively facilitates the underlying pairwise collaborations between clients with similar degradation patterns, which enhances the performance of personalized federated learning. To estimate parameters jointly using decentralized datasets, we develop a federated parameter estimation algorithm based on proximal gradient descent. The proposed approach addresses the limitations of existing federated prognostic models by simultaneously achieving model personalization, preserving data privacy, and providing comprehensive failure time distributions. The superiority of the proposed model is validated through extensive simulation studies and a case study using the turbofan engine degradation dataset from the NASA repository.

Federated learning enables collaborative model training without sharing raw data, but its performance can degrade substantially under heterogeneous client data distributions. A single global model often cannot satisfy diverse client requirements, so personalized federated learning has therefore been explored to improve client specific performance while preserving global generalization. Existing PFL methods often face a fundamental tradeoff in which stronger global sharing can undermine local specialization, whereas stronger local adaptation can lead to overfitting under limited data, label imbalance, and missing class scenarios. In this work, we propose PGFedSplit, a personalized federated learning framework that improves both personalization and global generalization under severe client heterogeneity. PGFedSplit adopts a split architecture and performs adaptive aggregation scheduling tailored to the roles of different model components, enabling stable knowledge sharing while maintaining client specific adaptation. Each client further leverages a mixture of locally extracted representations and synthetic representations generated from server side Gaussian statistics, improving robustness under label imbalance and missing class conditions. Extensive experiments on Fashion MNIST, CIFAR 10, CIFAR 100, and Tiny ImageNet demonstrate consistent improvements over state of the art PFL methods, with stable convergence and superior personalization in highly heterogeneous settings.

Federated Learning (FL) facilitates collaborative model training across decentralized clients while preserving data privacy by avoiding raw data exchange. Despite its potential, FL performance is often compromised by data heterogeneity across clients. To address this, Clustered Federated Learning (CFL) groups clients with similar data distributions to improve model performance, but constrained by intra-cluster heterogeneity. Conversely, Personalized Federated Learning (PFL) tailors models to individual clients, but usually neglects the underlying structural similarities among clients. In this work, we investigate a probabilistic mixture (PM) scenario, where each client's local data distribution is modeled as a convex combination of several shared inherent distributions. To effectively model this structure, we propose FedGMI, a framework that utilizes Variational Autoencoders (VAEs) as generative density estimators to represent these inherent distributions and infer the mixture components of clients' local data distributions. This approach enables structured personalization without sacrificing the benefits of collaborative learning. Extensive experiments demonstrate that FedGMI effectively characterizes and discriminate the inherent distributions, as well as accurately estimates mixture proportions. Furthermore, FedGMI maintains robust performance even under communication cost constraints.