Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks feature higher-order interactions involving multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a natural representation for these networks, with each hyperedge representing a set of nodes. The majority of existing hypergraph models assume uniform hyperedges, that is, edges are of the same size, or are driven by diversity amongst nodes. In this work, we propose a new hypergraph model formulated based on non-symmetric determinantal point processes. The proposed model naturally accommodates non-uniform hyperedges, has tractable probability mass functions, and allows for node similarity or diversity in hyperedges. For model estimation, we maximize the likelihood function under constraints via a computationally efficient projected adaptive gradient descent algorithm and establish the consistency and asymptotic normality of the estimator. Simulation studies confirm the efficacy of the proposed model, and its utility is further demonstrated through edge predictions on several real-world datasets.

Short bio: 

Emma Jingfei Zhang is the Goizueta Foundation Term Associate Professor of Information Systems & Operations Management at the Goizueta Business School of Emory University, with a secondary appointment in Biostatistics and Bioinformatics at the Rollins School of Public Health. Dr. Zhang’s research focuses on analyzing large networks, tensors and point processes, with applications in business, public health and biomedical research. She is an elected member of the International Statistical Institute. She is currently serving as associate editors at Journal of the American Statistical Association, Annals of Applied Statistics, Statistica Sinica, and Journal of Computational and Graphical Statistics.