Corrected Bayesian Information Criterion for Stochastic Block Models

• 成果类型: Article
• 署名作者: Hu, Jianwei; Qin, Hong; Yan, Ting; Zhao, Yunpeng
• 署名单位: Central China Normal University; Zhongnan University of Economics & Law; Arizona State University; Arizona State University-Tempe
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2019.1637744
• 发表日期: 2020
• 页码: 1771-1783
• 关键词: Community Detection; maximum-likelihood; blockmodels; Consistency; prediction

摘要

Estimating the number of communities is one of the fundamental problems in community detection. We re-examine the Bayesian paradigm for stochastic block models (SBMs) and propose a corrected Bayesian information criterion (CBIC), to determine the number of communities and show that the proposed criterion is consistent under mild conditions as the size of the network and the number of communities go to infinity. The CBIC outperforms those used in Wang and Bickel and Saldana, Yu, and Feng which tend to underestimate and overestimate the number of communities, respectively. The results are further extended to degree corrected SBMs. Numerical studies demonstrate our theoretical results.