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

We study the multilayer random dot product graph (MRDPG) model, a generalization of the random dot product graph model 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, where, at each 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 that, under both fixed and random latent position scenarios, provably minimize the detection delay while controlling false alarms. In particular, in the random latent position case, we devise a novel nonparametric change point detection algorithm based on density kernel estimators that is applicable to a wide range of network settings, including stochastic block models as special cases. Our theoretical findings are supported by extensive numerical experiments, with the code available online.1