An exact test for the mixed membership stochastic block model
Methodology
2025-07-22 v1
Abstract
We present the first finite-sample goodness-of-fit test for the mixed membership stochastic block model (MMSBM). Using algebraic statistics theory, we derive a Markov basis that lets a Metropolis-Hastings sampler explore exactly the set of networks compatible with a fitted MMSBM. The resulting exact -value, based on a partial conjunction statistic, requires no asymptotic approximations. Simulations show nominal size and strong power against misspecified block numbers and connection patterns.
Cite
@article{arxiv.2507.14464,
title = {An exact test for the mixed membership stochastic block model},
author = {Sourav Majumdar},
journal= {arXiv preprint arXiv:2507.14464},
year = {2025}
}