Estimating Structured Vector Autoregressive Models

Igor Melnyk, Arindam Banerjee
Proceedings of The 33rd International Conference on Machine Learning, PMLR 48:830-839, 2016.

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, 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v48-melnyk16, title = {Estimating Structured Vector Autoregressive Models}, author = {Melnyk, Igor and Banerjee, Arindam}, booktitle = {Proceedings of The 33rd International Conference on Machine Learning}, pages = {830--839}, year = {2016}, editor = {Balcan, Maria Florina and Weinberger, Kilian Q.}, volume = {48}, series = {Proceedings of Machine Learning Research}, address = {New York, New York, USA}, month = {20--22 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v48/melnyk16.pdf}, url = {https://proceedings.mlr.press/v48/melnyk16.html}, 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, 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.} }
Endnote
%0 Conference Paper %T Estimating Structured Vector Autoregressive Models %A Igor Melnyk %A Arindam Banerjee %B Proceedings of The 33rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2016 %E Maria Florina Balcan %E Kilian Q. Weinberger %F pmlr-v48-melnyk16 %I PMLR %P 830--839 %U https://proceedings.mlr.press/v48/melnyk16.html %V 48 %X 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.
RIS
TY - CPAPER TI - Estimating Structured Vector Autoregressive Models AU - Igor Melnyk AU - Arindam Banerjee BT - Proceedings of The 33rd International Conference on Machine Learning DA - 2016/06/11 ED - Maria Florina Balcan ED - Kilian Q. Weinberger ID - pmlr-v48-melnyk16 PB - PMLR DP - Proceedings of Machine Learning Research VL - 48 SP - 830 EP - 839 L1 - http://proceedings.mlr.press/v48/melnyk16.pdf UR - https://proceedings.mlr.press/v48/melnyk16.html AB - 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. ER -
APA
Melnyk, I. & Banerjee, A.. (2016). Estimating Structured Vector Autoregressive Models. Proceedings of The 33rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 48:830-839 Available from https://proceedings.mlr.press/v48/melnyk16.html.

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