FedEBM: Robust graph federated learning via energy-based model

Graph Federated Learning (GFL), as a vital component of graph neural networks, has found extensive applications in real-world scenarios. However, real-world graph data often suffers from label noise due to factors such as mislabeled data or malicious attacks. Existing methods for handling noisy labels primarily focus on centralized approaches, which perform poorly when directly applied to distributed settings and struggle to operate effectively on large-scale datasets. To address noisy labels in GFL, we propose a novel method called FedEBM. First, recognizing that clients in GFL often exhibit suboptimal learning capabilities under adverse conditions such as sample sparsity or label imbalance, we innovatively apply an Energy-Based Model (EBM) to tackle the noisy label problem. The EBM discriminates between clean and noisy samples based on their energy score. Even when clean samples are scarce, it implicitly delineates the energy region boundary by elevating the energy score of noisy samples, thereby separating clean and noisy samples. Furthermore, the energy score across categories in the EBM does not necessitate changes in other categories' energy score, avoiding probability competition on minority classes and enhancing sensitivity to minority class features. Comparative experiments across multiple public datasets demonstrate that FedEBM outperforms six baseline methods under various noise rates, noise types, and client numbers. Specifically, FedEBM outperforms the second-best method by an average margin of 5.43% on small-scale datasets and 12.58% on large-scale datasets.