Transfer learning in high-dimensional semiparametric graphical models with application to brain connectivity analysis

Transfer learning has drawn growing attention with the target of improving statistical efficiency of one study (dataset) by digging up information from similar and related auxiliary studies (datasets). In this article, we consider transfer learning problem in estimating undirected semiparametric graphical model. We propose an algorithm called Trans-Copula-CLIME for estimating an undirected graphical model while uncovering information from similar auxiliary studies, characterizing the similarity between the target graph and each auxiliary graph by the sparsity of a divergence matrix. The proposed method relaxes the restrictive Gaussian distribution assumption, which deviates from reality for the fMRI dataset related to attention deficit hyperactivity disorder (ADHD) considered here. Nonparametric rank-based correlation coefficient estimators are utilized in the Trans-Copula-CLIME procedure to achieve robustness against normality. We establish the convergence rate of the Trans-Copula-CLIME estimator under some mild conditions, which demonstrates that if the similarity between the auxiliary studies and the target study is sufficiently high and the number of informative auxiliary samples is sufficiently large, the Trans-Copula-CLIME estimator shows great advantage over the existing non-transfer-learning ones. Simulation studies also show that Trans-Copula-CLIME estimator has better performance especially when data are not from Gaussian distribution. Finally, the proposed method is applied to infer functional brain connectivity pattern for ADHD patients in the target Beijing site by leveraging the fMRI datasets from some other sites.