Embedding Birth-Death Processes within a Dynamic Stochastic Block Model

TL;DR

This paper introduces a new dynamic stochastic block model incorporating birth-death processes to handle networks with changing populations, providing a framework for community detection and efficient inference.

Contribution

It extends existing dynamic SBMs by modeling node entry and exit, and develops a variational EM algorithm for inference in this novel setting.

Findings

Successfully models networks with variable populations.

Provides an inference framework for community detection.

Demonstrates effectiveness on simulated data.

Abstract

Statistical clustering in dynamic networks aims to identify groups of nodes with similar or distinct internal connectivity patterns as the network evolves over time. While early research primarily focused on static Stochastic Block Models (SBMs), recent advancements have extended these models to handle dynamic and weighted networks, allowing for a more accurate representation of temporal variations in structure. Additional developments have introduced methods for detecting structural changes, such as shifts in community membership. However, limited attention has been paid to dynamic networks with variable population sizes, where nodes may enter or exit the network. To address this gap, we propose an extension of dynamic SBMs (dSBMs) that incorporates a birth-death process, enabling the statistical clustering of nodes in dynamic networks with evolving population sizes. This work makes three main contributions: (1) the introduction of a novel model for dSBMs with birth-death processes, (2) a framework for parameter inference and prediction of latent communities in this model, and (3) the development of an adapted Variational Expectation-Maximization (VEM) algorithm for efficient inference within this extended framework.