Community recovery in hypergraphs

Ahn, Kyu-Joong; Lee, Kangwook; Suh, Changho

doi:10.1109/allerton.2016.7852294

Cited by 28 publications

(50 citation statements)

References 37 publications

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“…Theorem 2 says that the conditions (3) and ( 10) are nearly sharp for exact recovery. Again, these conditions are fundamentally different from those derived in the literature of stochastic block models (Ahn et al, 2018;Liang et al, 2021) or generalized censored block models (Ahn et al, 2019). In particular, exact recovery in Liang et al (2021) only requires a condition similar to (3) up to some constant.…”

Section: Resultsmentioning

confidence: 85%

Information limits for detecting a subhypergraph

Yuan

Shang

2021

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We consider the problem of recovering a subhypergraph based on an observed adjacency tensor corresponding to a uniform hypergraph. The uniform hypergraph is assumed to contain a subset of vertices called as subhypergraph. The edges restricted to the subhypergraph are assumed to follow a different probability distribution than other edges. We consider both weak recovery and exact recovery of the subhypergraph, and establish information‐theoretic limits in each case. Specifically, we establish sharp conditions for the possibility of weakly or exactly recovering the subhypergraph from an information‐theoretic point of view. These conditions are fundamentally different from their counterparts derived in the hypothesis testing literature.

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Section: Resultsmentioning

confidence: 85%

Information limits for detecting a subhypergraph

Yuan

Shang

2021

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“…See for example Ghoshdastidar and Dukkipati (2017a); Ke et al (2019); Ahn et al (2018); Pal and Zhu (2019) for statistical and computational results in this setting. Furthermore, fundamental limits, in both estimation and hypothesis testing context was studied in Angelini et al; Chien et al (2018); Kim et al (2018); Ahn et al (2019). Below, we describe the stochastic hypergraph block models, of which the standard stochastic block models are a special case.…”

Section: Stochastic Block Modelsmentioning

confidence: 99%

Nonparametric Modeling of Higher-Order Interactions via Hypergraphons

Balasubramanian¹

2021

Preprint

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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.

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“…One data example is from multi-tissue multi-individual gene expression study Hore et al, 2016), where the data tensor consists of expression measurements indexed by (gene, individual, tissue) triplets. Another example is hypergraph network (Ghoshdastidar and Dukkipati, 2017;Ghoshdastidar et al, 2017;Ahn et al, 2019;Ke et al, 2019) in social science. A K-uniform hypergraph can be naturally represented as an order-K tensor, where each entry indicates the presence of K-way hyperedge among nodes (a.k.a.…”

Section: Introductionmentioning

confidence: 99%

Multiway Spherical Clustering via Degree-Corrected Tensor Block Models

Hu¹,

Wang²

2022

Preprint

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We consider the problem of multiway clustering in the presence of unknown degree heterogeneity. Such data problems arise commonly in applications such as recommendation system, neuroimaging, community detection, and hypergraph partitions in social networks. The allowance of degree heterogeneity provides great flexibility in clustering models, but the extra complexity poses significant challenges in both statistics and computation. Here, we develop a degree-corrected tensor block model with estimation accuracy guarantees. We present the phase transition of clustering performance based on the notion of angle separability, and we characterize three signal-to-noise regimes corresponding to different statistical-computational behaviors. In particular, we demonstrate that an intrinsic statistical-to-computational gap emerges only for tensors of order three or greater. Further, we develop an efficient polynomial-time algorithm that provably achieves exact clustering under mild signal conditions. The efficacy of our procedure is demonstrated through two data applications, one on human brain connectome project, and another on Peru Legislation network dataset.

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Community recovery in hypergraphs

Cited by 28 publications

References 37 publications

Information limits for detecting a subhypergraph

Information limits for detecting a subhypergraph

Nonparametric Modeling of Higher-Order Interactions via Hypergraphons

Multiway Spherical Clustering via Degree-Corrected Tensor Block Models

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