  Cross-silo Federated learning (FL) has become a promising tool in machine
learning applications for healthcare. It allows hospitals/institutions to train
models with sufficient data while the data is kept private. To make sure the FL
model is robust when facing heterogeneous data among FL clients, most efforts
focus on personalizing models for clients. However, the latent relationships
between clients' data are ignored. In this work, we focus on a special non-iid
FL problem, called Domain-mixed FL, where each client's data distribution is
assumed to be a mixture of several predefined domains. Recognizing the
diversity of domains and the similarity within domains, we propose a novel
method, FedDAR, which learns a domain shared representation and domain-wise
personalized prediction heads in a decoupled manner. For simplified linear
regression settings, we have theoretically proved that FedDAR enjoys a linear
convergence rate. For general settings, we have performed intensive empirical
studies on both synthetic and real-world medical datasets which demonstrate its
superiority over prior FL methods.
