Statistics and Biostatistics seminar series
Emma Zhang
Emory University
Room: M3 3127
Modeling Hypergraphs Using Determinantal Point Processes
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.