Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control
Sai Li, Tony Cai, and Hongzhe Li
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-task setting. Furthermore, we introduce a universal debiasing method which can be coupled with many initial graph estimators and can be analytically computed in one step. Applying such a debiasing method, a debiased Trans-CLIME estimator is obtained and is shown to be element-wise asymptotically normal. We use the latter fact 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.