Information-Theoretic and Computational Limits of Correlation Detection under Graph Sampling
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914266275119104 |
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| author | Huang, Dong Yang, Pengkun |
| author_facet | Huang, Dong Yang, Pengkun |
| contents | Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are independent; under the alternative hypothesis, the two graphs are edge-correlated through a latent permutation. We focus on the scenario where only two induced subgraphs are sampled, and characterize the sample size threshold for detection. At the information-theoretic level, we establish the sample complexity rates that are optimal up to constant factors over most parameter regimes, and the remaining gap is bounded by a subpolynomial factor. On the algorithmic side, we propose polynomial-time tests based on counting trees and bounded degree motifs, and identify the regimes where they succeed. Moreover, leveraging the low-degree conjecture, we provide evidence of computational hardness that matches our achievable guarantees, showing that the proposed polynomial-time tests are rate-optimal. Together, these results reveal a statistical--computational gap in the sample size required for correlation detection. Finally, we validate the proposed algorithms on synthetic data and a real coauthor network, demonstrating strong empirical performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13966 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Information-Theoretic and Computational Limits of Correlation Detection under Graph Sampling Huang, Dong Yang, Pengkun Statistics Theory Correlation analysis is a fundamental problem in statistics. In this paper, we consider the correlation detection problem between a pair of Erdos-Renyi graphs. Specifically, the problem is formulated as a hypothesis testing problem: under the null hypothesis, the two graphs are independent; under the alternative hypothesis, the two graphs are edge-correlated through a latent permutation. We focus on the scenario where only two induced subgraphs are sampled, and characterize the sample size threshold for detection. At the information-theoretic level, we establish the sample complexity rates that are optimal up to constant factors over most parameter regimes, and the remaining gap is bounded by a subpolynomial factor. On the algorithmic side, we propose polynomial-time tests based on counting trees and bounded degree motifs, and identify the regimes where they succeed. Moreover, leveraging the low-degree conjecture, we provide evidence of computational hardness that matches our achievable guarantees, showing that the proposed polynomial-time tests are rate-optimal. Together, these results reveal a statistical--computational gap in the sample size required for correlation detection. Finally, we validate the proposed algorithms on synthetic data and a real coauthor network, demonstrating strong empirical performance. |
| title | Information-Theoretic and Computational Limits of Correlation Detection under Graph Sampling |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2601.13966 |