# Nonparametric Modeling of Higher-Order Interactions via Hypergraphons

arXiv: https://arxiv.org/abs/2105.08678 · HTML: https://mlsanity.com/paper/2105.08678/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 79 references that are in the map.
- First posted on arXiv 18 May 2021.

## Builds on (most cited first, 30 of 30)

- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Networks beyond pairwise interactions: structure and dynamics](https://mlsanity.com/paper/2006.01764/) (2020)
- [Consistency of spectral clustering in stochastic block models](https://mlsanity.com/paper/1312.2050/) (2013)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [Multilayer Networks](https://mlsanity.com/paper/1309.7233/) (2013)
- [Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval](https://mlsanity.com/paper/1803.07726/) (2018)
- [Spectral redemption: clustering sparse networks](https://mlsanity.com/paper/1306.5550/) (2013)
- [Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants](https://mlsanity.com/paper/1612.02099/) (2016)
- [Stochastic blockmodel approximation of a graphon: Theory and consistent estimation](https://mlsanity.com/paper/1311.1731/) (2013)
- [A Consistent Histogram Estimator for Exchangeable Graph Models](https://mlsanity.com/paper/1402.1888/) (2014)
- [Community Detection in Degree-Corrected Block Models](https://mlsanity.com/paper/1607.06993/) (2016)
- [Estimating network edge probabilities by neighborhood smoothing](https://mlsanity.com/paper/1509.08588/) (2015)
- [Community Detection for Hypergraph Networks via Regularized Tensor Power Iteration](https://mlsanity.com/paper/1909.06503/) (2019)
- [Concentration and regularization of random graphs](https://mlsanity.com/paper/1506.00669/) (2015)
- [Consistency of Spectral Hypergraph Partitioning under Planted Partition Model](https://mlsanity.com/paper/1505.01582/) (2015)
- [Coauthorship and Citation Networks for Statisticians](https://mlsanity.com/paper/1410.2840/) (2014)
- [Stochastic Block Model for Hypergraphs: Statistical limits and a semidefinite programming approach](https://mlsanity.com/paper/1807.02884/) (2018)
- [Sparse graphs using exchangeable random measures](https://mlsanity.com/paper/1401.1137/) (2014)
- [Hypergraph Spectral Clustering in the Weighted Stochastic Block Model](https://mlsanity.com/paper/1805.08956/) (2018)
- [Private Graphon Estimation for Sparse Graphs](https://mlsanity.com/paper/1506.06162/) (2015)
- [Spectral Detection on Sparse Hypergraphs](https://mlsanity.com/paper/1507.04113/) (2015)
- [Uniform Hypergraph Partitioning: Provable Tensor Methods and Sampling Techniques](https://mlsanity.com/paper/1602.06516/) (2016)
- [Community Recovery in Hypergraphs](https://mlsanity.com/paper/1709.03670/) (2017)
- [Community detection in the sparse hypergraph stochastic block model](https://mlsanity.com/paper/1904.05981/) (2019)
- [Graphons, mergeons, and so on!](https://mlsanity.com/paper/1607.01718/) (2016)
- [Spectral Thresholds in the Bipartite Stochastic Block Model](https://mlsanity.com/paper/1506.06737/) (2015)
- [β models for random hypergraphs with a given degree sequence](https://mlsanity.com/paper/1407.1004/) (2014)
- [Sampling and Estimation for (Sparse) Exchangeable Graphs](https://mlsanity.com/paper/1611.00843/) (2016)
- [Model-based clustering for random hypergraphs](https://mlsanity.com/paper/1808.05185/) (2018)
- [Hierarchical network models for structured exchangeable interaction processes](https://mlsanity.com/paper/1901.09982/) (2019)

## Built on by (most cited first, 4 of 4)

- [Latent Space Model for Higher-order Networks and Generalized Tensor Decomposition](https://mlsanity.com/paper/2106.16042/) (2021)
- [Statistical and Computational Efficiency for Smooth Tensor Estimation with Unknown Permutations](https://mlsanity.com/paper/2111.04681/) (2021)
- [Degree Heterogeneity in Higher-Order Networks: Inference in the Hypergraph boldsymbolβ-Model](https://mlsanity.com/paper/2307.02818/) (2023)
- [Statistical and computational rates in high rank tensor estimation](https://mlsanity.com/paper/2304.04043/) (2023)

## Abstract (arXiv)

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.