In this article we introduce an estimator for the number of communities in the Stochastic Block Model (SBM), based on the maximization of a penalized version of the so-called Krichevsky-Trofimov mixture distribution. We prove its eventual almost sure convergence to the underlying number of communities, without assuming a known upper bound on that quantity. Our results apply to both the dense and the sparse regimes. To our knowledge this is the first consistency result for the estimation of the number of communities in the SBM in the unbounded case, that is when the number of communities is allowed to grow with the same size.

中文翻译：

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随机块模型中社区数量的估计

在本文中，我们基于所谓的 Krichevsky-Trofimov 混合分布的惩罚版本的最大化，介绍了随机块模型 (SBM) 中社区数量的估计器。我们证明了它最终几乎可以肯定地收敛到潜在的社区数量，而无需假设该数量的已知上限。我们的结果适用于密集和稀疏制度。据我们所知，这是在无界情况下估计 SBM 中社区数量的第一个一致性结果，即当允许社区数量以相同大小增长时。