标题： 多层随机块模型中的计算和统计阈值 显示英文标题

标题： Computational and Statistical Thresholds in Multi-layer Stochastic Block Models

摘要： 我们研究多层随机块模型中的社区恢复和检测问题，重点关注一致社区结构推断的关键网络密度阈值。 使用一个典型的两块模型，我们揭示了这种多层随机块模型中存在的计算障碍，而这种障碍在单层模型中并不存在：当没有计算约束时，密度阈值与层数成线性关系。 然而，当限制在多项式时间算法时，密度阈值随着层数的平方根变化，假设低次数多项式难度猜想是正确的。 我们的结果提供了多层随机块模型中最佳推断的几乎完整的图景，并部分解决了Lei和Lin（2022）关于偏差调整谱方法最优性的开放问题。 显示英文摘要

摘要： 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.