  Traditionally, Bayesian network structure learning is often carried out at a
central site, in which all data is gathered. However, in practice, data may be
distributed across different parties (e.g., companies, devices) who intend to
collectively learn a Bayesian network, but are not willing to disclose
information related to their data owing to privacy or security concerns. In
this work, we present a federated learning approach to estimate the structure
of Bayesian network from data that is horizontally partitioned across different
parties. We develop a distributed structure learning method based on continuous
optimization, using the alternating direction method of multipliers (ADMM),
such that only the model parameters have to be exchanged during the
optimization process. We demonstrate the flexibility of our approach by
adopting it for both linear and nonlinear cases. Experimental results on
synthetic and real datasets show that it achieves an improved performance over
the other methods, especially when there is a relatively large number of
clients and each has a limited sample size.
