Exact Recovery for a Family of Community-Detection Generative Models
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Generative models for networks with communities have been studied extensively for being a fertile ground to establish information-theoretic and computational thresholds. In this paper we propose a new simplistic model for planted generative models called planted Random Energy Model (REM), inspired by Derrida's REM. For this model we provide the asymptotic behaviour of the probability of error for the maximum likelihood estimator and hence the exact recovery threshold. As an application of it, we further consider the 2 non-equally sized community Weighted Stochastic Block Model (2-WSBM) on h-uniform hypergraphs, that is equivalent to the planted REM on both sides of the spectrum, for high and low edge cardinality h. We provide upper and lower bounds for the exact recoverability for any h, mapping these problems to the aforementioned planted-REM. To the best of our knowledge, these are the first consistency results for the 2-WSBM with non-equally sized community and for the 2-WSBM on hypergraphs.
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