A GOODNESS-OF-FIT TEST FOR STOCHASTIC BLOCK MODELS
成果类型：
Article
署名作者：
Lei, Jing
署名单位：
Carnegie Mellon University
刊物名称：
ANNALS OF STATISTICS
ISSN/ISSBN：
0090-5364
DOI：
10.1214/15-AOS1370
发表日期：
2016
页码：
401-424
关键词：
摘要：
The stochastic block model is a popular tool for studying community structures in network data. We develop a goodness-of-fit test for the stochastic block model. The test statistic is based on the largest singular value of a residual matrix obtained by subtracting the estimated block mean effect from the adjacency matrix. Asymptotic null distribution is obtained using recent advances in random matrix theory. The test is proved to have full power against alternative models with finer structures. These results naturally lead to a consistent sequential testing estimate of the number of communities.