A1079
Title: Degree heterogeneity in higher-order networks: Inference in the hypergraph beta-model
Authors: Sagnik Nandy - University of Chicago (United States) [presenting]
Bhaswar Bhattacharya - University of Pennsylvania (United States)
Abstract: The aim is to introduce a multilayer hypergraph beta-model, extending the standard beta-model to networks with multi-way interactions and varying hyperedge sizes across layers. The statistical properties of this novel model are rigorously studied. First, the convergence rates of the maximum likelihood (ML) estimate are established, and their minimax optimality is proven. The ML estimate's limiting distribution is also determined, and asymptotically valid confidence intervals are constructed for model parameters. Next, the goodness-of-fit problem is addressed by analyzing the likelihood ratio (LR) test. Its asymptotic normality is derived under the null hypothesis, its detection threshold is determined, and its limiting power is analyzed. Notably, this detection threshold is minimax optimal, meaning no test can perform better below it. These theoretical findings are supported by numerical experiments. This not only develops a comprehensive framework for multilayer hypergraph beta-models but also addresses existing gaps in the graph beta-model literature, particularly concerning ML estimate minimax optimality and non-null LR test properties.
