Personalised Federated Learning at Scale: Hierarchical Boosting with Bayesian Fusion

The Industrial Internet of Things (IIoT) generates heterogeneous, high-volume data across diverse devices, posing challenges for anomaly detection while preserving privacy. Traditional federated learning approaches struggle with nonIID data, limited edge resources, and a lack of device-specific adaptation. These limitations often result in suboptimal bias handling, poor personalisation, and unstable convergence in complex IIoT environments. To address these challenges, this paper proposes a novel theoretical Hierarchical Boosting with Bayesian Fusion (HBBF) framework that extends the conventional federated learning paradigm into a three-tier architecture, with multiple devices per edge layer and edge nodes aggregated via a global server layer. Within this hierarchy, each device performs sequential boosting with bias fixation, ensuring that local LightGBM models progressively correct residual errors while maintaining personalised adaptation. The resulting leaf one-hot encoded embeddings from each device/edge are then blended at the edge layer, allowing correlated local knowledge to be synthesised before global Bayesian Aggregation. At the global layer, Bayesian Aggregation fuses the edge-level embeddings and uncertainties, providing a principled probabilistic integration of distributed knowledge. Through this hierarchical design, HBBF enhances robustness and accuracy under heterogeneous data conditions, reduces residual variance through structured bias fixation, and maintains communication efficiency and privacy. Compared to conventional methods like FedAvg and FedPer, HBBF achieves scalable, stable, and high-accuracy federated learning.