一般稀疏随机块模型的最优重构
Optimal reconstruction of general sparse stochastic block models
AI总结：
本文将对称双社区稀疏随机块模型的重构结果推广至任意数量非对称社区的一般情形，证明与Belief Propagation密切相关的算法可恢复最优比例社区标签。
摘要：
本文的研究动机源于稀疏随机块模型上的重构问题。Mossel等人证明了在对称双社区情形下，存在一种重构算法可恢复最优比例的社区划分。其证明的核心贡献在于表明，当信噪比足够大（具体为$\lambda^2d > C$）时，带叶节点噪声与不带叶节点噪声的树上广播过程的重构精度渐近一致。本文将他们的结果（包括核心步骤）推广至一类具有任意数量社区且社区不一定对称的一般稀疏随机块模型，证明了一种与Belief Propagation（置信传播）密切相关的算法可恢复最优比例的社区标签。
英文摘要：
This paper is motivated by the reconstruction problem on the sparse stochastic block model. Mossel, et. al. proved that a reconstruction algorithm that recovers an optimal fraction of the communities in the symmetric, 2-community case. The main contribution of their proof is to show that when the signal to noise ratio is sufficiently large, in particular $λ^2d > C$, the reconstruction accuracy for a broadcast process on a tree with or without noise on the leaves is asymptotically the same. This paper will generalize their results, including the main step, to a general class of the sparse stochastic block model with any number of communities that are not necessarily symmetric, proving that an algorithm closely related to Belief Propagation recovers an optimal fraction of community labels.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
