Maximum likelihood degree of the $\beta$-stochastic blockmodel
Statistics Theory
2025-03-12 v1 Statistics Theory
Abstract
Log-linear exponential random graph models are a specific class of statistical network models that have a log-linear representation. This class includes many stochastic blockmodel variants. In this paper, we focus on -stochastic blockmodels, which combine the -model with a stochastic blockmodel. Here, using recent results by Almendra-Hern\'{a}ndez, De Loera, and Petrovi\'{c}, which describe a Markov basis for -stochastic block model, we give a closed form formula for the maximum likelihood degree of a -stochastic blockmodel. The maximum likelihood degree is the number of complex solutions to the likelihood equations. In the case of the -stochastic blockmodel, the maximum likelihood degree factors into a product of Eulerian numbers.
Cite
@article{arxiv.2410.06223,
title = {Maximum likelihood degree of the $\beta$-stochastic blockmodel},
author = {Cashous Bortner and Jennifer Garbett and Elizabeth Gross and Christopher McClain and Naomi Krawzik and Derek Young},
journal= {arXiv preprint arXiv:2410.06223},
year = {2025}
}