Time‐Varying Degree‐Corrected Stochastic Block Models
提出一种时变度修正随机块模型，用于分析随时间演化的动态网络，能同时估计节点连接概率、社区归属和度参数，并给出渐近理论保证。
ABSTRACT Recent interest has emerged in community detection for dynamic networks, which are observed along a trajectory of points in time. In this paper, we present a time‐varying (t‐v) degree‐corrected stochastic block model to fit a dynamic network which allows evolving heterogeneity in the degrees of nodes within a community over time. In order to aggregate network information over time via a sliding window, we propose a smoothing‐based method that simultaneously allows to recover the: (i) t‐v node connection probabilities; (ii) t‐v community memberships; and (iii) t‐v node degree parameters. As a novelty compared to existing literature, we provide asymptotic theory for all of these three goals, that is, we derive rates of consistency of our smooth estimators for degree parameters and communities using a time‐localized profile‐likelihood approach as well as strong consistency of community membership estimation at every time point. Extensive simulation studies and applications to two different real data sets complete our work.