论文标题
上下文随机块模型：尖锐的阈值和连续性
Contextual Stochastic Block Model: Sharp Thresholds and Contiguity
论文作者
论文摘要
我们在上下文随机块模型ARXIV中研究社区检测：1807.09596 [CS.SI]，ARXIV：1607.02675 [Stat.me]。在ARXIV：1807.09596 [CS.SI]中，第二作者在具有高维节点果膜的稀疏图中研究了这个问题。他们使用统计物理学的非核心腔法，猜想在这种情况下，急剧的社区检测限制。此外，假设观察到的图的平均程度很大，则验证了信息理论阈值。预计猜想在平均程度超过一个时立即保持，因此图具有巨大的组件。我们建立了这种猜想，并表征了检测和恢复较弱的尖锐阈值。
We study community detection in the contextual stochastic block model arXiv:1807.09596 [cs.SI], arXiv:1607.02675 [stat.ME]. In arXiv:1807.09596 [cs.SI], the second author studied this problem in the setting of sparse graphs with high-dimensional node-covariates. Using the non-rigorous cavity method from statistical physics, they conjectured the sharp limits for community detection in this setting. Further, the information theoretic threshold was verified, assuming that the average degree of the observed graph is large. It is expected that the conjecture holds as soon as the average degree exceeds one, so that the graph has a giant component. We establish this conjecture, and characterize the sharp threshold for detection and weak recovery.
