Work

Stochastic Block Model for Hypergraphs: Statistical limits and a semidefinite programming approach

Year: 2018

Type: preprint

Abstract: We study the problem of community detection in a random hypergraph model which we call the stochastic block model for $k$-uniform hypergraphs ($k$-SBM). We investigate the exact recovery problem in $k$-SBM and show that a sharp phase transition occurs around a threshold: below the threshold it is impossible to recover the communities with non-vanishing probability, yet above the threshold there is an estimator which recovers the communities almost asymptotically surely. We also consider a simple, efficient algorithm for the exact recovery problem which is based on a semidefinite relaxation technique.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1807.02884

Authors: Kim, Chiheon, Bandeira, Afonso S., Goemans, Michel X.

Institutions: Massachusetts Institute of Technology, New York University

Language: English

Topic: Complex Network Analysis Techniques

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Office of Naval Research

Awards: Collaborative Research: Statistical Estimation with Algebraic Structure, Collaborative Research: Tractable Non-Convex Optimization, Statistical and Computational Tradeoffs in High Dimensional Learning, G4504108201, G5737228787, G8876996369, G8929337198

OpenAlex ID: W2844556331

Cites: 27

Cited by: 28

Related to: 10