Efficient Distributed Differential Network Estimation

ABSTRACT Differential network is an essential tool to reveal structural changes across two populations. However, existing single‐machine methods for estimating differential network face computational and storage limitations when dealing with large‐scale data sets. To address this issue, this paper develops a distributed estimation algorithm, which divides the estimation of differential network into several small‐scale node‐wise regression tasks and reduces local estimation bias through a debiasing technique. After aggregating debiased estimators, a global estimator is constructed efficiently. Theoretical analysis shows that the proposed distributed estimator can achieve global estimation consistency under mild conditions, with a convergence rate comparable to that of the single‐machine method, while also facilitating support set recovery. Finally, we provide extensive numerical experiments to demonstrate the superior performance of our estimator compared to several baselines.