  Directed acyclic graph (DAG) has been widely employed to represent
directional relationships among a set of collected nodes. Yet, the available
data in one single study is often limited for accurate DAG reconstruction,
whereas heterogeneous data may be collected from multiple relevant studies. It
remains an open question how to pool the heterogeneous data together for better
DAG structure reconstruction in the target study. In this paper, we first
introduce a novel set of structural similarity measures for DAG and then
present a transfer DAG learning framework by effectively leveraging information
from auxiliary DAGs of different levels of similarities. Our theoretical
analysis shows substantial improvement in terms of DAG reconstruction in the
target study, even when no auxiliary DAG is overall similar to the target DAG,
which is in sharp contrast to most existing transfer learning methods. The
advantage of the proposed transfer DAG learning is also supported by extensive
numerical experiments on both synthetic data and multi-site brain functional
connectivity network data.

Machine Learning;Machine Learning;Methodology