Multilayer random dot product graphs: Estimation and online change point detection

TL;DR

This paper introduces the multilayer random dot product graph model, proposes tensor-based estimation methods, and develops online change point detection algorithms, including a novel nonparametric approach, with theoretical analysis and numerical validation.

Contribution

It extends the random dot product graph to multilayer networks, proposes superior tensor-based estimation, and develops efficient online change point detection methods, including a new nonparametric algorithm.

Findings

Tensor-based estimation outperforms existing methods.

Effective online change point detection with minimized delay.

Nonparametric detection applicable to diverse models.

Abstract

We study the multilayer random dot product graph (MRDPG) model, an extension of the random dot product graph to multilayer networks. To estimate the edge probabilities, we deploy a tensor-based methodology and demonstrate its superiority over existing approaches. Moving to dynamic MRDPGs, we formulate and analyse an online change point detection framework. At every time point, we observe a realization from an MRDPG. Across layers, we assume fixed shared common node sets and latent positions but allow for different connectivity matrices. We propose efficient tensor algorithms under both fixed and random latent position cases to minimize the detection delay while controlling false alarms. Notably, in the random latent position case, we devise a novel nonparametric change point detection algorithm based on density kernel estimation that is applicable to a wide range of scenarios, including stochastic block models as special cases. Our theoretical findings are supported by extensive numerical experiments, with the code available online https://github.com/MountLee/MRDPG.