Abstract

This paper considers the change-point problem for finite sequences of networks. To avoid the difficulty of computing the normalization coefficient in the models such as Exponential Random Graphical Model (ERGM) and Markov networks, we construct a finite measure space with measure ratio statistics. A new performance measure of detection delay is proposed to detect the changes in distribution of the network data. And under the performance measure we defined, an optimal sequential test is presented. The good performance of the optimal sequential test is illustrated numerically on ERGM and Erdős–Rényi network sequences.

中文翻译：

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用于检测有限测量空间下有限网络序列变化的最佳序列测试

摘要

本文考虑网络有限序列的变点问题。为了避免在指数随机图形模型（ERGM）和马尔可夫网络等模型中计算归一化系数的困难，我们构建了一个具有测度比统计的有限测度空间。提出了一种新的检测延迟性能度量来检测网络数据分布的变化。在我们定义的性能度量下，提出了一个最佳的顺序测试。最佳序列测试的良好性能在 ERGM 和 Erdős-Rényi 网络序列上进行了数值说明。