Autoregressive Networks
Binyan Jiang, Jialiang Li, Qiwei Yao; 24(227):1−69, 2023.
Abstract
This study introduces a first-order autoregressive (AR(1)) model to represent dynamic network processes, where edges change over time while nodes remain unchanged. The model explicitly captures the dynamic changes and facilitates simple and efficient statistical inference methods, including a permutation test for diagnostic checking of the fitted network models. The proposed model can be applied to network processes with various underlying structures but with independent edges. As an example, we investigate an AR(1) stochastic block model that characterizes latent communities through transition probabilities over time. This leads to a new and more effective spectral clustering algorithm for identifying the latent communities. We also derive a finite sample condition for achieving perfect recovery of the community structure using the newly defined spectral clustering algorithm. Additionally, we incorporate inference for a change point into the AR(1) stochastic block model to account for possible structure changes. We provide explicit error rates for the maximum likelihood estimator of the change-point. The application of the proposed AR(1) models and associated inference methods is illustrated using three real data sets, highlighting their relevance and usefulness.
[abs]