Efficient Distributed Transfer Learning for Large‐Scale Gaussian Graphic Models

ABSTRACT A transfer learning for the large‐scale Gaussian graphical models (GGMs) is considered in a distributed architecture for fitting these target and auxiliary studies scattered across multiple sites. A distributed transfer learning algorithm, DisPower‐Trans‐CLIME, is proposed to learn the target GGMs by incorporating the data from similar and related auxiliary studies. The algorithm is communication efficient via the distributed power method for matrix decomposition. We show that DisPower‐Trans‐CLIME has a fast convergence rate comparable to the centred Trans‐CLIME algorithm. A debiased DisPower‐Trans‐CLIME is constructed and is proved to be element‐wise asymptotically normal for statistical inference. Thus, a multiple testing procedure is developed to detect edge of GGMs with false discovery rate (FDR) control. Extensive simulation experiments have been conducted to demonstrate superior numerical performance of our proposed learning algorithm on estimation and edge detection. It is also applied to infer the regional connection networks in brain regions of interest (ROIs) based on a target hospital site by leveraging the graph from multiple other hospital sites for autism spectrum disorder. We observe that the degrees of regional connectivity in the right brain are balanced, while the ones of the left brain region are extremely uneven because of the presence of multiple strong connections. However, the specific association, between the degrees of connectivity of these regions and ASD disease, is unknown.