Title: Online Learning of Nonlinear Autoregressive Processes over Cellular Complexes
Primary area: learning on graphs and other geometries & topologies
Keywords: cellular complex, time series, kernel methods, online learning

Abstract: Real-world time-series are often high-dimensional, structured with higher-order dependencies, and exhibit time-varying dynamics, making them challenging to model effectively. Abstract Cellular Complexes (ACCs) provide a principled way to capture such higher-order topological structure, serving as a powerful inductive bias for multivariate time-series modeling. While recent methods based on message-passing neural networks and Hodge Laplacians exploit higher-order relationships, they are primarily designed for offline settings and lack adaptability to streaming and non-stationary environments. In this work, we introduce a framework for nonlinear autoregressive modeling over ACCs, where predictive functions are defined in a reproducing kernel Hilbert space (RKHS) induced by shift-invariant kernels. We further propose an efficient online learning algorithm to estimate these functions. Experimental results on synthetic and real-world datasets demonstrate that our method shows competitive or improved performance in prediction accuracy and adaptability under streaming conditions.