Temporal network has become ubiquitous with the rise of online social platform and e-commerce, but largely under investigated in literature. In this paper, we propose a statistical framework for temporal network analysis, leveraging strengths of adaptive network merging, tensor decomposition and point process. A two-step embedding procedure and a regularized maximum likelihood estimate based on Poisson point process is developed, where the initial estimate is based on equal spaced time intervals while the final estimate on the adaptively merging time intervals. A projected gradient descent algorithm is proposed to facilitate estimation, where the upper bound of the tensor estimation error in each iteration is established. Through analysis, it is shown that the tensor estimation error is significantly reduced by the proposed method. Extensive numerical experiments also validate this phenomenon, as well as its advantage over other existing competitors. The proposed method is also applied to analyze a militarized interstate dispute dataset, where not only the prediction accuracy increases, but the adaptively merged intervals also lead to clear interpretation.
翻译:随着在线社会平台和电子商务的兴起,时间网络已变得无处不在,但大部分文献对此进行了调查。在本文件中,我们提出了一个时间网络分析统计框架,利用适应性网络合并、高分解和点进程的力量。根据 Poisson点进程,制定了一个双步嵌入程序和定期最大可能性估计,初步估计基于相等的间距,而适应性合并时间间隔的最后估计则基于相等的间距。提出了一个预测梯度下行算法,以便利估算,因为每次迭代中都确定了高压估计误差的上限。通过分析,我们发现,通过拟议方法,高压估计误差显著减少。广泛的数字实验也验证了这一现象,以及它与其他现有竞争者相比的优势。还应用了拟议方法来分析军事化国家间争端数据集,其中不仅预测精确度增加,而且适应性合并的间距还导致清晰的解释。