  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.
