Abstract:
A distributed estimation and statistical inference framework is introduced for the sparse precision matrix in the (covariate-adjusted) Gaussian graphical models under the unbalanced splitting setting. This type of splitting arises when the datasets from different sources cannot be aggregated on one single machine or when the available machines are of different powers. A de-biased estimator of the precision matrix on every single machine is proposed, and theoretical guarantees are provided. Moreover, a new de-biased estimator that is pooled across the machines using a composite likelihood approach is proposed. It is shown to enjoy consistency and asymptotic normality, and we provide statistical inference strategies based on it. The performance of this estimator is investigated via simulation studies and real data examples. It is shown that the performance of this estimator is close to the non-distributed estimator, which uses the entire dataset.