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.

翻译：我们研究使用超高光谱的统计和算法方面,这些高光谱是大型高光谱的极限,用来模拟高光谱的相互作用。 尽管高光谱从模型的角度来说非常强大,但我们认为有一定的有限类别简单的Lipschitz超光谱(SLH),可以进行实际有效的估计。我们还为我们的测算员提供了最佳的SLH等级的趋同率。提供了模拟结果来证实这一理论。