Nonparametric Modeling of Higher-Order Interactions via Hypergraphons
This work addresses the challenge of efficiently estimating hypergraph models for complex network data, representing an incremental improvement in hypergraphon methodology.
The authors tackled the problem of modeling higher-order interactions in large hypergraphs by introducing a restricted class of Simple Lipschitz Hypergraphons (SLH) that enables practical estimation, achieving optimal convergence rates for this class as validated by simulations.
We study statistical and algorithmic aspects of using hypergraphons, that are limits of large hypergraphs, for modeling higher-order interactions. Although hypergraphons are extremely powerful from a modeling perspective, we consider a restricted class of Simple Lipschitz Hypergraphons (SLH), that are amenable to practically efficient estimation. We also provide rates of convergence for our estimator that are optimal for the class of SLH. Simulation results are provided to corroborate the theory.