Autoregressive Networks
Autoregressive Networks
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发表时间：
2020-10
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通讯作者：
Binyan Jiang;Jialiang Li;Q. Yao
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作者：
Binyan Jiang;Jialiang Li;Q. Yao
我们提出了一个一阶自回归模型的动态网络过程中，边随时间变化，而节点保持不变。该模型明确地描述了动态变化。它也便于简单和有效的统计推断，如极大似然估计被证明是（一致）一致和渐近正态的。模型诊断检查可以很容易地使用置换测试来进行。该模型适用于任何具有不同底层结构的Erd\“os-Renyi网络过程。作为一个例子，自回归随机块模型进行了深入的研究，其特征的潜在社区的转移概率随时间的推移。%，而不是传统的（静态）连接概率。这导致了一个更有效的谱聚类算法来识别潜在的社区。变点的推断被纳入自回归随机块模型，以应付可能的结构变化。发达的渐近理论以及仿真研究肯定了所提出的方法的性能。三个真实的数据集的应用说明了所提出的模型的相关性和实用性。
We propose a first-order autoregressive model for dynamic network processes in which edges change over time while nodes remain unchanged. The model depicts the dynamic changes explicitly. It also facilitates simple and efficient statistical inference such as the maximum likelihood estimators which are proved to be (uniformly) consistent and asymptotically normal. The model diagnostic checking can be carried out easily using a permutation test. The proposed model can apply to any Erd\"os-Renyi network processes with various underlying structures. As an illustration, an autoregressive stochastic block model has been investigated in depth, which characterizes the latent communities by the transition probabilities over time. % instead of conventional (static) connection probabilities. This leads to a more effective spectral clustering algorithm for identifying the latent communities. Inference for a change-point is incorporated into the autoregressive stochastic block model to cater for possible structure changes. The developed asymptotic theory as well as the simulation study affirm the performance of the proposed methods. Application with three real data sets illustrates both relevance and usefulness of the proposed models.