Estimating structured vector autoregressive models

Igor Melnyk, Arindam Banerjee

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publication33rd International Conference on Machine Learning, ICML 2016
EditorsMaria Florina Balcan, Kilian Q. Weinberger
PublisherInternational Machine Learning Society (IMLS)
Pages1297-1330
Number of pages34
ISBN (Electronic)9781510829008
StatePublished - Jan 1 2016
Event33rd International Conference on Machine Learning, ICML 2016 - New York City, United States
Duration: Jun 19 2016Jun 24 2016

Publication series

Name33rd International Conference on Machine Learning, ICML 2016
Volume2

Other

Other33rd International Conference on Machine Learning, ICML 2016
CountryUnited States
CityNew York City
Period6/19/166/24/16

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