  Federated learning (FL) has emerged with increasing popularity to collaborate
distributed medical institutions for training deep networks. However, despite
existing FL algorithms only allow the supervised training setting, most
hospitals in realistic usually cannot afford the intricate data labeling due to
absence of budget or expertise. This paper studies a practical yet challenging
FL problem, named \textit{Federated Semi-supervised Learning} (FSSL), which
aims to learn a federated model by jointly utilizing the data from both labeled
and unlabeled clients (i.e., hospitals). We present a novel approach for this
problem, which improves over traditional consistency regularization mechanism
with a new inter-client relation matching scheme. The proposed learning scheme
explicitly connects the learning across labeled and unlabeled clients by
aligning their extracted disease relationships, thereby mitigating the
deficiency of task knowledge at unlabeled clients and promoting discriminative
information from unlabeled samples. We validate our method on two large-scale
medical image classification datasets. The effectiveness of our method has been
demonstrated with the clear improvements over state-of-the-arts as well as the
thorough ablation analysis on both tasks\footnote{Code will be made available
at \url{https://github.com/liuquande/FedIRM}}.
