Nonparametric Modeling of Higher-Order Interactions via Hypergraphons
- URL: http://arxiv.org/abs/2105.08678v1
- Date: Tue, 18 May 2021 17:08:29 GMT
- Title: Nonparametric Modeling of Higher-Order Interactions via Hypergraphons
- Authors: Krishnakumar Balasubramanian
- Abstract summary: We study statistical and algorithmic aspects of using hypergraphons, that are limits of large hypergraphs, for modeling higher-order interactions.
We consider a restricted class of Simple Lipschitz Hypergraphons (SLH), that are amenable to practically efficient estimation.
- Score: 11.6503817521043
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- 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.
Related papers
- Degree Heterogeneity in Higher-Order Networks: Inference in the Hypergraph $\boldsymbolβ$-Model [4.540236408836132]
We study the hypergraph $boldsymbolbeta$-model with multiple layers, which allows for hyperedges of different sizes across the layers.
We derive the rates of convergence of maximum likelihood (ML) estimates and establish their minimax rate optimality.
We also consider the goodness-of-fit problem in the hypergraph $boldsymbolbeta$-model.
arXiv Detail & Related papers (2023-07-06T07:23:06Z) - From Hypergraph Energy Functions to Hypergraph Neural Networks [94.88564151540459]
We present an expressive family of parameterized, hypergraph-regularized energy functions.
We then demonstrate how minimizers of these energies effectively serve as node embeddings.
We draw parallels between the proposed bilevel hypergraph optimization, and existing GNN architectures in common use.
arXiv Detail & Related papers (2023-06-16T04:40:59Z) - Tensorized Hypergraph Neural Networks [69.65385474777031]
We propose a novel adjacency-tensor-based textbfTensorized textbfHypergraph textbfNeural textbfNetwork (THNN)
THNN is faithful hypergraph modeling framework through high-order outer product feature passing message.
Results from experiments on two widely used hypergraph datasets for 3-D visual object classification show the model's promising performance.
arXiv Detail & Related papers (2023-06-05T03:26:06Z) - Augmentations in Hypergraph Contrastive Learning: Fabricated and
Generative [126.0985540285981]
We apply the contrastive learning approach from images/graphs (we refer to it as HyperGCL) to improve generalizability of hypergraph neural networks.
We fabricate two schemes to augment hyperedges with higher-order relations encoded, and adopt three augmentation strategies from graph-structured data.
We propose a hypergraph generative model to generate augmented views, and then an end-to-end differentiable pipeline to jointly learn hypergraph augmentations and model parameters.
arXiv Detail & Related papers (2022-10-07T20:12:20Z) - Equivariant Hypergraph Diffusion Neural Operators [81.32770440890303]
Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data.
This work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators.
We evaluate ED-HNN for node classification on nine real-world hypergraph datasets.
arXiv Detail & Related papers (2022-07-14T06:17:00Z) - Core-periphery Models for Hypergraphs [0.0]
We introduce a random hypergraph model for core-periphery structure.
We develop a novel statistical inference algorithm that is able to scale to large hypergraphs with runtime that is practically linear wrt.
Our inference algorithm is capable of learning embeddings that correspond to the reputation (rank) of a node within the hypergraph.
arXiv Detail & Related papers (2022-06-01T22:11:44Z) - Hypergraph Convolutional Networks via Equivalency between Hypergraphs
and Undirected Graphs [59.71134113268709]
We present General Hypergraph Spectral Convolution(GHSC), a general learning framework that can handle EDVW and EIVW hypergraphs.
In this paper, we show that the proposed framework can achieve state-of-the-art performance.
Experiments from various domains including social network analysis, visual objective classification, protein learning demonstrate that the proposed framework can achieve state-of-the-art performance.
arXiv Detail & Related papers (2022-03-31T10:46:47Z) - The Performance of the MLE in the Bradley-Terry-Luce Model in
$\ell_{\infty}$-Loss and under General Graph Topologies [76.61051540383494]
We derive novel, general upper bounds on the $ell_infty$ estimation error of the Bradley-Terry-Luce model.
We demonstrate that the derived bounds perform well and in some cases are sharper compared to known results.
arXiv Detail & Related papers (2021-10-20T23:46:35Z) - HyperSF: Spectral Hypergraph Coarsening via Flow-based Local Clustering [9.438207505148947]
We propose an efficient spectral hypergraph coarsening scheme (HyperSF) for preserving the original spectral (structural) properties of hypergraphs.
Our results show that the proposed hypergraph coarsening algorithm can significantly improve the multi-way conductance of hypergraph clustering.
arXiv Detail & Related papers (2021-08-17T22:20:23Z) - Parameterized Hypercomplex Graph Neural Networks for Graph
Classification [1.1852406625172216]
We develop graph neural networks that leverage the properties of hypercomplex feature transformation.
In particular, in our proposed class of models, the multiplication rule specifying the algebra itself is inferred from the data during training.
We test our proposed hypercomplex GNN on several open graph benchmark datasets and show that our models reach state-of-the-art performance.
arXiv Detail & Related papers (2021-03-30T18:01:06Z) - Generative hypergraph clustering: from blockmodels to modularity [26.99290024958576]
We propose an expressive generative model of clustered hypergraphs with heterogeneous node degrees and edge sizes.
We show that hypergraph Louvain is highly scalable, including as an example an experiment on a synthetic hypergraph of one million nodes.
We use our model to analyze different patterns of higher-order structure in school contact networks, U.S. congressional bill cosponsorship, U.S. congressional committees, product categories in co-purchasing behavior, and hotel locations.
arXiv Detail & Related papers (2021-01-24T00:25:22Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.