Semidefinite Programming for the Asymmetric Stochastic Block Model
Year: 2025
Type: preprint
Abstract: We consider semidefinite programming (SDP) for the binary stochastic block model with equal-sized communities. Prior work of Hajek, Wu, and Xu proposed an SDP (sym-SDP) for the symmetric case where the intra-community edge probabilities are equal, and showed that the SDP achieves the information-theoretic threshold for exact recovery under the symmetry assumption. A key open question is whether SDPs can be used to achieve exact recovery for non-symmetric block models. In order to inform the design of a new SDP for the non-symmetric setting, we investigate the failure of sym-SDP when it is applied to non-symmetric settings. We formally show that sym-SDP fails to return the correct labeling of the vertices in some information-theoretically feasible, asymmetric cases. In addition, we give an intuitive geometric interpretation of the failure of sym-SDP in asymmetric settings, which in turn suggests an SDP formulation to handle the asymmetric setting. Still, this new SDP cannot be readily analyzed by existing techniques, suggesting a fundamental limitation in the design of SDPs for community detection.
Source: arXiv (Cornell University)
Authors: Gaudio, Julia, Prongpaophan, Phawin
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6891920628
Cites:
Cited by:
Related to: