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arXiv · 2407.17851

Bad local minima exist in the stochastic block model

Amin Coja-Oghlan·Lena Krieg·Johannes Christian Lawnik·Olga Scheftelowitsch
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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)].

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Amin Coja-Oghlan, Lena Krieg, Johannes Christian Lawnik, Olga Scheftelowitsch. 2024-07-25. Bad local minima exist in the stochastic block model. https://arxiv.org/abs/2407.17851

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