论文标题
通过自适应合并对纵向网络的有效估计
Efficient Estimation for Longitudinal Networks via Adaptive Merging
论文作者
论文摘要
纵向网络由多个节点之间的一系列时间边组成，其中实时观察到时间边缘。随着在线社交平台和电子商务的兴起，它已经变得无处不在，但在文献中的评价很大。在本文中，我们为纵向网络提出了一个有效的估计框架，利用自适应网络合并的优势，张量分解和点过程。它融合了相邻的稀疏网络，以扩大观察到的边缘的数量并减少估计差异，而通过网络合并引入的估计偏差通过利用自适应网络邻居的局部时间结构来控制。提出了一种预测的梯度下降算法来促进估计，其中建立了每种迭代中估计误差的上限。进行了彻底的分析来量化所提出方法的渐近行为，这表明它可以显着减少估计误差，并为在各种情况下的网络合并提供指南。我们通过在合成数据集和军事化的州际争端数据集上进行了广泛的数值实验来证明所提出的方法的优势。
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.
