Classification and estimation in the Stochastic Block Model based on the empirical degrees

Details Classification and estimation in the Stochastic Block Model based on the empirical degrees Classification and estimation in the Stochastic Block Model based on the empirical degrees

2011-10-29

arxiv.org/abs/1110.6517v1

Mathematics

Statistics Theory

Scientific paper

The Stochastic Block Model (Holland et al., 1983) is a mixture model for heterogeneous network data. Unlike the usual statistical framework, new nodes give additional information about the previous ones in this model. Thereby the distribution of the degrees concentrates in points conditionally on the node class. We show under a mild assumption that classification, estimation and model selection can actually be achieved with no more than the empirical degree data. We provide an algorithm able to process very large networks and consistent estimators based on it. In particular, we prove a bound of the probability of misclassification of at least one node, including when the number of classes grows.

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