Bad local minima exist in the stochastic block model
Statistics Theory
2024-07-26 v1 Discrete Mathematics
Information Theory
Mathematical Physics
math.IT
math.MP
Probability
Statistics Theory
Abstract
We study the disassortative stochastic block model with three communities, a well-studied model of graph partitioning and Bayesian inference for which detailed predictions based on the cavity method exist [Decelle et al. (2011)]. We provide strong evidence that for a part of the phase where efficient algorithms exist that approximately reconstruct the communities, inference based on maximum a posteriori (MAP) fails. In other words, we show that there exist modes of the posterior distribution that have a vanishing agreement with the ground truth. The proof is based on the analysis of a graph colouring algorithm from [Achlioptas and Moore (2003)].
Keywords
Cite
@article{arxiv.2407.17851,
title = {Bad local minima exist in the stochastic block model},
author = {Amin Coja-Oghlan and Lena Krieg and Johannes Christian Lawnik and Olga Scheftelowitsch},
journal= {arXiv preprint arXiv:2407.17851},
year = {2024}
}