Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels

• 成果类型: Article
• 署名作者: Karwa, Vishesh; Pati, Debdeep; Petrovic, Sonja; Solus, Liam; Alexeev, Nikita; Raic, Mateja; Wilburne, Dane; Williams, Robert; Yan, Bowei
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; Texas A&M University System; Texas A&M University College Station; Illinois Institute of Technology; Royal Institute of Technology; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; MITRE Corporation; Rose Hulman Institute Technology; Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkad084
• 发表日期: 2024
• 页码: 90-121
• 关键词: Community Detection; MODEL; likelihood; statistics; networks

摘要

We construct Bayesian and frequentist finite-sample goodness-of-fit tests for three different variants of the stochastic blockmodel for network data. Since all of the stochastic blockmodel variants are log-linear in form when block assignments are known, the tests for the latent block model versions combine a block membership estimator with the algebraic statistics machinery for testing goodness-of-fit in log-linear models. We describe Markov bases and marginal polytopes of the variants of the stochastic blockmodel and discuss how both facilitate the development of goodness-of-fit tests and understanding of model behaviour. The general testing methodology developed here extends to any finite mixture of log-linear models on discrete data, and as such is the first application of the algebraic statistics machinery for latent-variable models.