Unbalanced distributed estimation and inference for the precision matrix in Gaussian graphical models

This paper studies the estimation of Gaussian graphical models in the unbalanced distributed framework. It provides an effective approach when the available machines are of different powers or when the existing dataset comes from different sources with different sizes and cannot be aggregated in one single machine. In this paper, we propose a new aggregated estimator of the precision matrix and justify such an approach by both theoretical and practical arguments. The limit distribution and convergence rate for this estimator are provided under sparsity conditions on the true precision matrix and controlling for the number of machines. Furthermore, a procedure for performing statistical inference is proposed. On the practical side, using a simulation study and a real data example, we show that the performance of the distributed estimator is similar to that of the non-distributed estimator that uses the full data.