Computational and Statistical Thresholds in Multi-layer Stochastic Block Models

Jing Lei; Anru R. Zhang; Zihan Zhu

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arXiv · 2311.07773

Computational and Statistical Thresholds in Multi-layer Stochastic Block Models

Jing Lei·Anru R. Zhang·Zihan Zhu

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Abstract

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 multi-layer 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 Lei and Lin (2022) regarding the optimality of the bias-adjusted spectral method.

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Jing Lei, Anru R. Zhang, Zihan Zhu. 2023-11-13. Computational and Statistical Thresholds in Multi-layer Stochastic Block Models. https://arxiv.org/abs/2311.07773

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