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COMPUTATIONAL AND STATISTICAL THRESHOLDS IN MULTI-LAYER STOCHASTIC BLOCK MODELS
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DOI：10.1214/24-AOS2441.png)
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We study the problem of community recovery and detection in multi- layer stochastic block models, focusing on the critical network density threshold for consistent community structure inference. Using a prototypical two- block model, we reveal a computational barrier for such multilayer stochastic block models that does not exist for its single-layer counterpart: When there are no computational constraints, the density threshold depends linearly on the number of layers. However, when restricted to polynomial-time algorithms, the density threshold scales with the square root of the number of layers, assuming correctness of a low-degree polynomial hardness conjecture. Our results provide a nearly complete picture of the optimal inference in multiple-layer stochastic block models and partially settle the open question in (J. Amer. Statist. Assoc. 118 (2023) 2433-2445) regarding the optimality of the bias-adjusted spectral method.
Keyword:
Community detection and recovery
computational barrier
low-degree polynomial hardness
multilayer network
期刊
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3.7
论文数:
2.8K
被引数:
2.9W
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