  Transfer learning for high-dimensional Gaussian graphical models (GGMs) is
studied with the goal of estimating the target GGM by utilizing the data from
similar and related auxiliary studies. The similarity between the target graph
and each auxiliary graph is characterized by the sparsity of a divergence
matrix. An estimation algorithm, Trans-CLIME, is proposed and shown to attain a
faster convergence rate than the minimax rate in the single study setting.
Furthermore, a debiased Trans-CLIME estimator is introduced and shown to be
element-wise asymptotically normal. It is used to construct a multiple testing
procedure for edge detection with false discovery rate control. The proposed
estimation and multiple testing procedures demonstrate superior numerical
performance in simulations and are applied to infer the gene networks in a
target brain tissue by leveraging the gene expressions from multiple other
brain tissues. A significant decrease in prediction errors and a significant
increase in power for link detection are observed.
