Time Varying Regression with Hidden Linear Dynamics

Horia Mania, Ali Jadbabaie, Devavrat Shah, Suvrit Sra
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:858-869, 2022.

Abstract

We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates. We offer a finite sample guarantee on the estimation error of our method and discuss certain advantages it has over Expectation-Maximization (EM), which is the main approach proposed by prior work.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-mania22a, title = {Time Varying Regression with Hidden Linear Dynamics}, author = {Mania, Horia and Jadbabaie, Ali and Shah, Devavrat and Sra, Suvrit}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {858--869}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/mania22a/mania22a.pdf}, url = {https://proceedings.mlr.press/v168/mania22a.html}, abstract = {We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates. We offer a finite sample guarantee on the estimation error of our method and discuss certain advantages it has over Expectation-Maximization (EM), which is the main approach proposed by prior work.} }
Endnote
%0 Conference Paper %T Time Varying Regression with Hidden Linear Dynamics %A Horia Mania %A Ali Jadbabaie %A Devavrat Shah %A Suvrit Sra %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-mania22a %I PMLR %P 858--869 %U https://proceedings.mlr.press/v168/mania22a.html %V 168 %X We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates. We offer a finite sample guarantee on the estimation error of our method and discuss certain advantages it has over Expectation-Maximization (EM), which is the main approach proposed by prior work.
APA
Mania, H., Jadbabaie, A., Shah, D. & Sra, S.. (2022). Time Varying Regression with Hidden Linear Dynamics. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:858-869 Available from https://proceedings.mlr.press/v168/mania22a.html.

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