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

arXiv: https://arxiv.org/abs/1612.06040 · HTML: https://mlsanity.com/paper/1612.06040/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2016.

## Built on by (most cited first, 2 of 2)

- [A Pure Hypothesis Test for Inhomogeneous Random Graph Models Based on a Kernelised Stein Discrepancy](https://mlsanity.com/paper/2505.21580/) (2025)
- [Spectral goodness-of-fit tests for complete and partial network data](https://mlsanity.com/paper/2106.09702/) (2021)

## Abstract (arXiv)

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 behavior. 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.