Estimating Structured Vector Autoregressive Model
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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 models), where the structure can be captured by any suitable norm, e.g., Lasso, group Lasso, order weighted Lasso, sparse group 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. Surprisingly, 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 data with a variety of structures as well as real aviation data are presented, validating theoretical results.
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