Autoregressive Hypergraph
提出了首个有理论保证的动态超图自回归模型，能刻画超边随时间演化的规律，并给出推断、社区检测和变点估计方法，适用于多实体交互数据的时序分析。
ABSTRACT Traditional graph representations are insufficient for modelling real‐world phenomena involving multi‐entity interactions, such as collaborative projects or protein complexes, necessitating the use of hypergraphs. While hypergraphs preserve the intrinsic nature of such complex relationships, existing models often overlook temporal evolution in relational data. To address this, we introduce a first‐order autoregressive (i.e., AR(1)) model for dynamic nonuniform hypergraphs. This is the first dynamic hypergraph model with provable theoretical guarantees, explicitly defining the temporal evolution of hyperedge presence through transition probabilities that govern persistence and change dynamics. This framework provides closed‐form expressions for key probabilistic properties and facilitates straightforward maximum‐likelihood inference with uniform error bounds and asymptotic normality, along with a permutation‐based diagnostic test. We also consider an AR(1) hypergraph stochastic block model (HSBM), where a novel Laplacian enables exact and efficient latent community recovery via a spectral clustering algorithm. Furthermore, we develop a likelihood‐based change‐point estimator for the HSBM to detect structural breaks. The efficacy and practical value of our methods are comprehensively demonstrated through extensive simulation studies and compelling applications to a primary school interaction data set and the Enron email corpus, revealing insightful community structures and significant temporal changes.