Consistent model selection in a collection of stochastic block models

TL;DR

This paper presents a consistent penalized KT estimator for accurately determining the number of clusters in multi-layer and dynamic stochastic block models, applicable to both dense and sparse networks.

Contribution

It introduces a new penalized KT estimator that is proven to be consistent without requiring an upper bound on the number of clusters.

Findings

Estimator converges to the true number of clusters as network size increases

Works in both dense and sparse network regimes

Demonstrated effectiveness on synthetic datasets

Abstract

We introduce the penalized Krichevsky-Trofimov (KT) estimator as a convergent method for estimating the number of nodes clusters when observing multiple networks within both multi-layer and dynamic Stochastic Block Models. We establish the consistency of the KT estimator, showing that it converges to the correct number of clusters in both types of models when the number of nodes in the networks increases. Our estimator does not require a known upper bound on this number to be consistent. Furthermore, we show that these consistency results hold in both dense and sparse regimes, making the penalized KT estimator robust across various network configurations. We illustrate its performance on synthetic datasets.