Nonparametric Modeling of Higher-Order Interactions via Hypergraphons

TL;DR

This paper introduces a practical approach to modeling higher-order interactions using a restricted class of hypergraphons, providing efficient estimation methods with optimal convergence rates, supported by simulations.

Contribution

It proposes Simple Lipschitz Hypergraphons (SLH) for practical estimation of hypergraph limits, with proven optimal convergence rates and empirical validation.

Findings

Efficient estimation algorithms for SLH hypergraphons.

Optimal convergence rates for the proposed estimators.

Simulation results confirming theoretical predictions.

Abstract

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.