  Federated Semi-Supervised Learning (FSSL) leverages both labeled and
unlabeled data on clients to collaboratively train a model.In FSSL, the
heterogeneous data can introduce prediction bias into the model, causing the
model's prediction to skew towards some certain classes. Existing FSSL methods
primarily tackle this issue by enhancing consistency in model parameters or
outputs. However, as the models themselves are biased, merely constraining
their consistency is not sufficient to alleviate prediction bias. In this
paper, we explore this bias from a Bayesian perspective and demonstrate that it
principally originates from label prior bias within the training data. Building
upon this insight, we propose a debiasing method for FSSL named FedDB. FedDB
utilizes the Average Prediction Probability of Unlabeled Data (APP-U) to
approximate the biased prior.During local training, FedDB employs APP-U to
refine pseudo-labeling through Bayes' theorem, thereby significantly reducing
the label prior bias. Concurrently, during the model aggregation, FedDB uses
APP-U from participating clients to formulate unbiased aggregate weights,
thereby effectively diminishing bias in the global model. Experimental results
show that FedDB can surpass existing FSSL methods. The code is available at
https://github.com/GuogangZhu/FedDB.
