Structural transfer learning of non-Gaussian DAG

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.

Transfer learning for tensor Gaussian graphical models

Tensor Gaussian graphical models (GGMs), interpreting conditional independence structures within tensor data, have important applications in numerous areas. Yet, the available tensor data in one single study is often limited due to high acquisition costs. Although relevant studies can provide additional data, it remains an open question how to pool such heterogeneous data. In this paper, we propose a transfer learning framework for tensor GGMs, which takes full advantage of informative auxiliary domains even when non-informative auxiliary domains are present, benefiting from the carefully designed data-adaptive weights. Our theoretical analysis shows substantial improvement of estimation errors and variable selection consistency on the target domain under much relaxed conditions, by leveraging information from auxiliary domains. Extensive numerical experiments are conducted on both synthetic tensor graphs and a brain functional connectivity network data, which demonstrates the satisfactory performance of the proposed method.