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)].

翻译：我们研究具有三个社区的反相随机块模型，这是一个在图划分和贝叶斯推断领域被深入研究的模型，基于腔方法已存在详细的理论预测[Decelle等人(2011)]。我们提供了有力证据表明，在相图的某个区域——虽然存在能近似重建社区的高效算法——基于最大后验概率的推断方法会失效。换言之，我们证明了后验分布的某些模态与真实社区结构的吻合度趋近于零。该证明基于对[Achlioptas与Moore(2003)]提出的图着色算法的分析。