标题： 加权随机块模型中社区估计的最优速率 显示英文标题

标题： Optimal Rates for Community Estimation in the Weighted Stochastic Block Model

摘要： 网络中的社区识别是社会学、神经科学和遗传学等领域的重要问题。在过去十年中，随机块模型（SBM）已成为解决该问题的一种流行统计框架。然而，SBM有一个重要的局限性，即它仅适用于无权边的网络；在各种科学应用中，忽略边的权重可能会导致有价值信息的丢失。我们研究了SBM的一个加权广义版本，在这个版本中，观测值以加权邻接矩阵的形式收集，并且每条边的权重独立地由其端点的社区成员关系所确定的未知概率密度生成。我们通过社区内边与跨社区边的权重分布之间的1/2阶Renyi散度来刻画加权SBM的误聚类误差的最优速率，这大大推广了现有针对无权SBM的结果。此外，我们提出了一种基于离散化的原则性、计算上可行的算法，该算法能够在不假设已知权重密度的情况下达到最优的误分类率。 显示英文摘要

摘要： Community identification in a network is an important problem in fields such as social science, neuroscience, and genetics. Over the past decade, stochastic block models (SBMs) have emerged as a popular statistical framework for this problem. However, SBMs have an important limitation in that they are suited only for networks with unweighted edges; in various scientific applications, disregarding the edge weights may result in a loss of valuable information. We study a weighted generalization of the SBM, in which observations are collected in the form of a weighted adjacency matrix and the weight of each edge is generated independently from an unknown probability density determined by the community membership of its endpoints. We characterize the optimal rate of misclustering error of the weighted SBM in terms of the Renyi divergence of order 1/2 between the weight distributions of within-community and between-community edges, substantially generalizing existing results for unweighted SBMs. Furthermore, we present a principled, computationally tractable algorithm based on discretization that achieves the optimal error rate without assuming knowledge of the weight densities.