Online Learning for Autoregressive Multilayer Stochastic Block Models under Stationarity and Non-Stationarity

Abstract

Dynamic multilayer networks arise in many applications where multiple types of relations among a common set of nodes evolve over time. We introduce a first-order autoregressive multilayer stochastic block model (AR(1)-MSBM), in which edge formation and dissolution probabilities are determined by latent community memberships. Under stationarity, we develop an online estimation procedure based on recursive updates and tensor-based spectral refinement, and establish minimax-optimal estimation rates and guarantees for community recovery. We further consider a non-stationary setting that allows both abrupt changes and gradual shifts. An adaptive windowed algorithm automatically adjusts to unknown structural changes and, under a quasi-stationary segmentation framework, achieves segmentwise estimation and community recovery guarantees matching those in the stationary setting. Numerical experiments support our theoretical results. This is joint work with Haotian Xu and Yi Yu.

Bio

Fan Wang is a Lecturer in Data Science at the School of Mathematics and Statistics, University of Melbourne. She received her PhD in Statistics from the University of Warwick in 2024 and subsequently worked there as a Research Fellow. Her research interests include change-point analysis, statistical network analysis, online learning, transfer learning and differential privacy.