English

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 pp-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.

Keywords

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}
}
R2 v1 2026-07-01T04:08:57.616Z