A1406
Title: Online graph topology learning from matrix-valued time series
Authors: Yiye Jiang - University of Grenoble Alpes (France) [presenting]
Abstract: The focus is on the statistical analysis of matrix-valued time series, where data is collected over a network of sensors, typically at spatial locations, over time. Each sensor records a vector of features per time instant. The goal is to identify the dependency structure among these sensors and represent it as a graph. When one feature per sensor is observed, vector auto-regressive (VAR) models are commonly used to infer Granger causality, forming a causal graph. The first contribution extends VAR models to matrix-variate models for graph learning. Two online procedures are proposed for low and high dimensions, enabling rapid updates of estimates as new samples arrive. In high dimensions, a novel Lasso-type is developed, and its homotopy algorithms are introduced for online learning. An adaptive tuning procedure for the regularization parameter is provided. Given that detrending is often required for applying auto-regressive models but infeasible in online settings, the proposed AR models are augmented by incorporating trend as an additional parameter, with a particular focus on periodic trends. The adapted algorithms can, therefore, simultaneously learn the graph and trend from streaming data. Numerical experiments with synthetic and real data demonstrate the effectiveness of these methods.
