Year: 2023
Type: article
Abstract: 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.
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1523888516, Mathematics Research Communities, PostDoctoral Research Fellowship, TRIPODS+X:RES: Collaborative Research:Privacy-Preserving Genomic Data Analysis, G391554652, G4068192495, G5513889982, G5975578989, G6098521345, G707281404, Collaborative Research: Scalable Bayesian Methods for Complex Data with Optimality Guarantees, G7425413337, G8467107387
OpenAlex ID: W4386758592