Network-valued time series are currently a common form of network data. However, the study of the aggregate behavior of network sequences generated from network-valued stochastic processes is relatively rare. Most of the existing research focuses on the simple setup where the networks are independent (or conditionally independent) across time, and all edges are updated synchronously at each time step. In this paper, we study the concentration properties of the aggregated adjacency matrix and the corresponding Laplacian matrix associated with network sequences generated from lazy network-valued stochastic processes, where edges update asynchronously, and each edge follows a lazy stochastic process for its updates independent of the other edges. We demonstrate the usefulness of these concentration results in proving consistency of standard estimators in community estimation and changepoint estimation problems. We also conduct a simulation study to demonstrate the effect of the laziness parameter, which controls the extent of temporal correlation, on the accuracy of community and changepoint estimation.

中文翻译：

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用于社区估计和变化点分析的相关网络价值过程的集中不等式

网络值时间序列是目前一种常见的网络数据形式。然而，对由网络值随机过程生成的网络序列的聚合行为的研究相对较少。大多数现有研究都集中在简单的设置上，其中网络在时间上是独立的（或条件独立的），并且所有边在每个时间步同步更新。在本文中，我们研究了聚合邻接矩阵和与网络序列相关的相应拉普拉斯矩阵的集中特性，这些网络序列由惰性网络值随机过程生成，其中边异步更新，并且每条边遵循惰性随机过程进行更新，独立于其他边缘。我们证明了这些集中结果在证明标准估计量在社区估计和变化点估计问题中的一致性方面的有用性。我们还进行了一项模拟研究，以证明控制时间相关程度的惰性参数对社区和变化点估计的准确性的影响。