Title: Robust Forecasting of Network Systems Subject to Topology Perturbation
Primary area: learning on time series and dynamical systems
Keywords: Robust Learning, Network Forecasting, Bayesian Coresets, Model Reduction

Abstract: Many real-world dynamical systems, such as epidemic, traffic, and logistics networks, consist of sparsely interacting components and thus naturally exhibit an underlying graph structure. Forecasting their evolution is computationally challenging due to high dimensionality and is further complicated by measurement noise and uncertainty in the network topology. We address this problem by studying the predictability of graph time series under random topology perturbations, a problem with major implications that has remained largely unexplored. In the limit of large networks, we uncover distinct noise regimes: systems that are predictable with arbitrary accuracy, systems predictable only up to limited accuracy, and systems that become entirely unpredictable. Motivated by this characterization, we propose a time series forecasting framework based on a probabilistic representation of network dynamics, which leverages Bayesian coreset approximations for scalable and robust dimentionality reduction. Numerical experiments on both synthetic and real-world networks demonstrate that our approach achieves competitive accuracy and robustness under topology uncertainty, while significantly reducing computational costs.

TL;DR: We propose a forecasting scheme for network time series that is robust to topology perturbation.