Estimating Structured Vector Autoregressive Models

While considerable advances have been made in estimating high-dimensional structured models from independent data using Lasso-type models, limited progress has been made for settings when the samples are dependent. We consider estimating structured VAR (vector auto-regressive model), where the structure can be captured by any suitable norm, e.g., Lasso, group Lasso, order weighted Lasso, etc. In VAR setting with correlated noise, although there is strong dependence over time and covariates, we establish bounds on the non-asymptotic estimation error of structured VAR parameters. The estimation error is of the same order as that of the corresponding Lasso-type estimator with independent samples, and the analysis holds for any norm. Our analysis relies on results in generic chaining, subexponential martingales, and spectral representation of VAR models. Experimental results on synthetic and real data with a variety of structures are presented, validating theoretical results.