Distribution-Level AirComp for Bayesian FL
Conventional federated learning (FL) methods face critical challenges in realistic wireless edge networks, where training data are often limited and heterogeneous, which can lead to unstable training and poor generalization. To address these challenges in a principled manner, we propose a novel Bayesian wireless FL framework grounded in Bayesian inference. By explicitly modeling uncertainty, the proposed framework mitigates local overfitting and client drift, thereby enabling more reliable inference. Nevertheless, adopting Bayesian FL increases communication overhead due to the need to transmit richer model information and fundamentally changes the aggregation process beyond simple averaging. To overcome this limitation, we design a dedicated over-the-air computation (AirComp) scheme tailored to Bayesian FL, which efficiently aggregates local posterior distributions at the distribution level by exploiting the superposition property of wireless channels. Simulations validate the proposed framework, demonstrating significant gains in test accuracy over conventional FL methods, particularly in data-scarce and heterogeneous environments.