Online Vector Autoregressive Models Over Expanding Graphs

Current spatiotemporal learning methods for complex data exploit the graph structure as an inductive bias to restrict the function space and improve data and computation efficiency. However, these methods work principally on graphs with a fixed size, whereas in several applications there are expanding graphs where new nodes join the network; e.g., new sensors joining a sensor network or new users joining a recommender system. This paper focuses on the non-trivial extension of spatiotemporal methods to this setting, where now it is key to jointly capture both the topological and signal dynamics. Specifically, it considers a graph vector autoregressive (GVAR) model for multivariate time series. The GVAR is a multivariate linear model that leverages a bank of graph filters allowing scalability and data efficiency. To account for the dynamic nature of the graphs, the filters’s parameters are learned on-the-fly via adaptive gradient descent with provable sub-linear regret. Numerical results on both synthetic and real data corroborate the proposed method.