Semidefinite Programming for the Asymmetric Stochastic Block Model
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911019502141440 |
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| author | Gaudio, Julia Prongpaophan, Phawin |
| author_facet | Gaudio, Julia Prongpaophan, Phawin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_18754 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semidefinite Programming for the Asymmetric Stochastic Block Model Gaudio, Julia Prongpaophan, Phawin Information Theory Data Structures and Algorithms 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. |
| title | Semidefinite Programming for the Asymmetric Stochastic Block Model |
| topic | Information Theory Data Structures and Algorithms |
| url | https://arxiv.org/abs/2506.18754 |