Autoregressive Networks

Abstract

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 Erdös-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.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.

Networks with Correlated Edge Processes

“…A blockmodel varying in time is less frequently discussed, since this may make the model non-identifiable [20] if at the same time the nodes are allowed to change cluster. However, [15] proposes an autoregressive network model with changepoints over time in the blockmodel, and [30] discusses the theoretical properties of models with smoothly varying connectivity probabilities. Finally, to obtain interesting dynamics, one can also relax the conditional independence in the generation of the Bernoulli variables A ij over time.…”

“…The rising ubiquity of dynamic graphs has been matched by technical innovation for their analysis, see for example [21,19,30,15,29]. Simultaneously, the realisation that networks should be described directly in terms of observed interactions or edges rather than in terms of describing the interactions between nodes, in a nodal view, has been gaining considerable traction [8].…”

“…Currently, there are many proposed methods to perform inference on dynamic networks, say for example [20,21,19,30,15,26], each method coming with either explicit or implicit modelling assumptions. Most of these approaches use the stochastic blockmodel imposing clustering structure on the nodes (SBM; [14,12,4,34]) to model the underlying dynamic structure of the network, with clear choices on how parameters change or evolve across time.…”

“…. Exceptions to the description applied in those SBM-based papers cited above are [15] and [19], where the former constructs correlated graphs by adding correlated noise that may erase or construct edges, that is, introduces correlation at the observed process. The latter models community membership by a switching process, and directly imposes correlation on the edge variables.…”

Rank determination in tensor factor model

“…These studies all focus on panel (vector) time series. Recently there is a growing interest in analyzing matrix-or tensor-valued time series, as such time series is encountered more and more frequently in applications, including Fama-French 10 by 10 series (Wang, Liu and Chen, 2019), a set of economic indicator series among a set of countries (Chen, Xiao and Yang, 2021), multi-category international trading volume series Chen, 2019, Hoff, 2011), multitype international action counts among a group of countries (Hoff, 2015), sequence of realized covariance matrices (Kim andFan, 2019, Lunde, Shephard andSheppard, 2016), sequence of gray-scale face recognition images (Chen and Fan, 2021), dynamic networks (Barabási andAlbert, 1999, Jiang, Li andYao, 2020), dynamic human brain transcriptome data (Liu, Yuan and Zhao, 2017), multivariate spatial-temporal climate series (Chen et al, 2020), neuroimaging data (Zhang, 2019, Zhou, Li andZhu, 2013). Factor model is again developed as an effective dimension reduction tool (Chen, Yang and Zhang, 2021, Wang, Liu and Chen, 2019.…”