Efficient Estimation for Longitudinal Networks via Adaptive Merging

Longitudinal networks consist of sequences of temporal edges among multiple nodes, where the temporal edges are observed in real-time. They have become ubiquitous with the rise of online social platforms and e-commerce, but largely under-investigated in the literature. In this paper, we propose an efficient estimation framework for longitudinal networks, leveraging strengths of adaptive network merging, tensor decomposition, and point processes. It merges neighboring sparse networks so as to enlarge the number of observed edges and reduce estimation variance, whereas the estimation bias introduced by network merging is controlled by exploiting local temporal structures for adaptive network neighborhood. A projected gradient descent algorithm is proposed to facilitate estimation, where the upper bound of the estimation error in each iteration is established. A thorough analysis is conducted to quantify the asymptotic behavior of the proposed method, which shows that it can significantly reduce the estimation error and also provides a guideline for network merging under various scenarios. We further demonstrate the advantage of the proposed method through extensive numerical experiments on synthetic datasets and a militarized interstate dispute dataset.