  Discovering the causality from observational data is a crucial task in
various scientific domains. With increasing awareness of privacy, data are not
allowed to be exposed, and it is very hard to learn causal graphs from
dispersed data, since these data may have different distributions. In this
paper, we propose a federated causal discovery strategy (FedCausal) to learn
the unified global causal graph from decentralized heterogeneous data. We
design a global optimization formula to naturally aggregate the causal graphs
from client data and constrain the acyclicity of the global graph without
exposing local data. Unlike other federated causal learning algorithms,
FedCausal unifies the local and global optimizations into a complete directed
acyclic graph (DAG) learning process with a flexible optimization objective. We
prove that this optimization objective has a high interpretability and can
adaptively handle homogeneous and heterogeneous data. Experimental results on
synthetic and real datasets show that FedCausal can effectively deal with
non-independently and identically distributed (non-iid) data and has a superior
performance.
