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Causality graphs are routinely estimated in social sciences, naturalsciences, and engineering due to their capacity to efficiently represent thespatiotemporal structure of multivariate data sets in a format amenable forhuman interpretation, forecasting, and anomaly detection. A popular approach tomathematically formalize causality is based on vector autoregressive (VAR)models and constitutes an alternative to the well-known, yet usuallyintractable, Granger causality. Relying on such a VAR causality notion, thispaper develops two algorithms with complementary benefits to track time-varyingcausality graphs in an online fashion. Their constant complexity per updatealso renders these algorithms appealing for big-data scenarios. Despite usingdata sequentially, both algorithms are shown to asymptotically attain the sameaverage performance as a batch estimator which uses the entire data set atonce. To this end, sublinear (static) regret bounds are established.Performance is also characterized in time-varying setups by means of dynamicregret analysis. Numerical results with real and synthetic data further supportthe merits of the proposed algorithms in static and dynamic scenarios.

Online Topology Identification from Vector Autoregressive Time Series