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, sub-exponential martingales, and spectral representation of VAR models. Experimental results on synthetic and real data with a variety of structures are presented, validating theoretical results.

Authors

• Igor Melnyk
• Arindam Banerjee 0001

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