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.

翻译：有向无环图（DAG）被广泛用于表示一组收集节点之间的方向性关系。然而，单一研究中的可用数据往往有限，难以实现准确的DAG重构，而多个相关研究可能会收集到异质性数据。如何整合这些异质性数据以改善目标研究中的DAG结构重构，仍是一个悬而未决的问题。本文首先引入一组新颖的DAG结构相似性度量，进而提出一个迁移DAG学习框架，通过有效利用来自不同相似度水平的辅助DAG的信息，实现更优的结构重构。理论分析表明，即使在所有辅助DAG与目标DAG整体相似度不高的情况下，本文方法仍能显著提升目标研究中的DAG重构性能，这与多数现有迁移学习方法形成鲜明对比。通过基于合成数据和多站点脑功能连接网络数据的广泛数值实验，进一步验证了所提出的迁移DAG学习的优势。