Optimal rates for community estimation in the weighted stochastic block model
Optimal rates for community estimation in the weighted stochastic block model
复制标题
加权随机区组模型中群落估计的最优率
DOI：
10.1214/18-aos1797
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Po
中科院分区：
文献类型：
--
作者：
Min Xu;Varun Jog;Po
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 computationally tractable algorithm based on discretization that achieves the optimal error rate. Our method is adaptive in the sense that the algorithm, without assuming knowledge of the weight densities, performs as well as the best algorithm that knows the weight densities.
通过消息传递进行子矩阵定位
影响因子：
6
作者：
Hajek, Bruce;Wu, Yihong;Xu, Jiaming
通讯作者：
Xu, Jiaming