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

TL;DR

This paper demonstrates that in the Stochastic Block Model, classification and estimation can be effectively performed using only empirical degree data, even for large networks and multiple classes.

Contribution

It introduces a new algorithm and theoretical results showing that degree-based methods suffice for classification, estimation, and model selection in the SBM.

Findings

Consistent estimators based on empirical degrees.

Algorithm effective for very large networks.

Bound on misclassification probability even with many classes.

Abstract

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.