论文标题
与社区估计和变更点分析相关的网络评估流程的集中不平等
Concentration inequalities for correlated network-valued processes with applications to community estimation and changepoint analysis
论文作者
论文摘要
网络值时间序列是当前的网络数据的常见形式。然而，研究由网络价值随机过程产生的网络序列的总体行为相对较少。大多数现有的研究都集中在简单的设置上，其中网络在整个时间内是独立的（或有条件独立的），并且所有边缘在每个时间步骤均同步更新。在本文中，我们研究了聚集的邻接矩阵的浓度特性和与懒惰网络值随机过程产生的网络序列相关的相应的拉普拉斯矩阵，在该过程中，边缘异步不断地更新，并且每个边缘都遵循与其他边缘独立于其他边缘更新的懒惰随机过程。我们证明了这些集中度的有用性，导致证明标准估计量在社区估计和变更点估计问题中的一致性。我们还进行了一项仿真研究，以证明懒惰参数的影响，该参数控制时间相关的程度，对社区和变化点估计的准确性。
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.
