Year: 2024
Type: article
Abstract: The stochastic block model is a canonical random graph model for clustering and community detection on network-structured data. Decades of extensive study on the problem have established many profound results, among which the phase transition at the Kesten-Stigum threshold is particularly interesting both from a mathematical and an applied standpoint. It states that no estimator based on the network topology can perform substantially better than chance on sparse graphs if the model parameter is below a certain threshold. Nevertheless, if we slightly extend the horizon to the ubiquitous semi-supervised setting, such a fundamental limitation will disappear completely. We prove that with an arbitrary fraction of the labels revealed, the detection problem is feasible throughout the parameter domain. Moreover, we introduce two efficient algorithms, one combinatorial and one based on optimization, to integrate label information with graph structures. Our work brings a new perspective to the stochastic model of networks and semidefinite program research.
Source: Journal of Machine Learning
DOI: 10.4208/jml.230624
Authors: Junda Sheng, Thomas Strohmer
Institution: University of California, Davis
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: ATD: A Mathematical Framework for Generating Synthetic Data, G1573444065, G2273714462, HDR TRIPODS: UC Davis TETRAPODS Institute of Data Science, G3504598162, G6679937290, The National Center for Interventional Biophotonic Technologies (NCIBT), SCH: Heterogenous, dynamic synthetic data: From algorithms to clinical applications
OpenAlex ID: W4393052256