随机区块模型中存在坏的局部极小值

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Statistical Physics Pub Date : 2024-11-11 DOI:10.1007/s10955-024-03366-w

Amin Coja-Oghlan, Lena Krieg, Johannes Christian Lawnik, Olga Scheftelowitsch

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引用次数: 0

摘要

我们研究了具有三个群落的非畸变随机块模型，这是一个经过充分研究的图分割和贝叶斯推断模型，基于空穴法对其进行了详细预测（Decelle 等人，发表于《物理评论 E》84:066106，2011 年）。我们提供的有力证据表明，对于存在近似重建群落的高效算法的部分阶段，基于最大后验（MAP）的推断是失败的。换句话说，我们证明了后验分布中存在与地面实况一致性消失的模式。该证明基于对 Achlioptas 和 Moore 的图着色算法的分析（J Comput Syst Sci 67:441-471, 2003）。

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Bad Local Minima Exist in the Stochastic Block Model

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. in Phys Rev E 84:066106, 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 (J Comput Syst Sci 67:441–471, 2003).

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来源期刊

Journal of Statistical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

12.50%

发文量

152

审稿时长

3-6 weeks

期刊介绍： The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.