Modeling Hypergraphs with Diversity and Heterogeneous Popularity
本文提出一种基于行列式点过程的超图潜变量模型，利用超边内的多样性和节点流行度来建模多元关系，适用于无限制的超边基数和多重性，并证明了参数估计的一致性和渐近正态性。
While relations among individuals make an important part of data with scientific and business interests, existing statistical modeling of relational data has mainly been focusing on dyadic relations, that is, those between two individuals.This article addresses the less studied, though commonly encountered, polyadic relations that can involve more than two individuals.In particular, we propose a new latent space model for hypergraphs using determinantal point processes, which is driven by the diversity within hyperedges and each node's popularity.This model mechanism is in contrast to existing hypergraph models, which are predominantly driven by similarity rather than diversity.Additionally, the proposed model accommodates broad types of hypergraphs, with no restriction on the cardinality and multiplicity of hyperedges, which previous models often have.Consistency and asymptotic normality of the maximum likelihood estimates of the model parameters have been established.The proof is challenging, owing to the special configuration of the parameter space.Further, we apply the projected accelerated gradient descent algorithm to obtain the parameter estimates, and we show its effectiveness in simulation studies.We also demonstrate an application of the proposed model on the What's Cooking data and present the embedding of food ingredients learned from cooking recipes using the model.Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.