Longitudinal network consists of a sequence of temporal edges among multiple nodes, where the temporal edges are observed in real time. It has become ubiquitous with the rise of online social platform and e-commerce, but largely under-investigated in literature. In this paper, we propose an efficient estimation framework for longitudinal network, leveraging strengths of adaptive network merging, tensor decomposition and point process. 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 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.
翻译:长期网络由多个节点之间的时间序列边组成,其中时间序列边在实时中观察到。随着在线社交平台和电子商务的兴起,长期网络已变得司空见惯,但现有文献中关注不足。本文提出了一种基于自适应网络合并、张量分解和点过程的高效估计框架,用于长期网络。该方法合并相邻的稀疏网络,以放大观测到的边的数量和减少估计的方差,同时通过利用局部时间结构控制网络合并引入的估计偏差。提出了一种投影梯度下降算法来促进估计,其中在每次迭代中建立了估计误差的上界。对所提出的方法的渐近行为进行了彻底的分析,表明它可以显着减少估计误差,并为各种情况下的网络合并提供指导。通过对合成数据集和军事冲突数据集的广泛数值实验,我们进一步展示了所提出方法的优势。