Instrumental variables system identification with $L^p$ consistency

Simon Kuang, Xinfan Lin
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:1713-1740, 2026.

Abstract

Instrumental variables (IV) eliminate the bias that afflicts least-squares identification of dynamical systems through noisy data, yet traditionally relies on external instruments that are seldom available for nonlinear time series data. We propose an IV estimator that synthesizes instruments from the data. We establish finite-sample $L^{p}$ consistency for _all_ $p \ge $ in both discrete- and continuous-time models, recovering a nonparametric $\sqrt{n}$-convergence rate. On a forced Lorenz system our estimator reduces parameter bias by 200x (continuous-time) and 500x (discrete-time) relative to least squares and reduces RMSE by up to tenfold. Because the method only assumes that the model is linear in the unknown parameters, it is broadly applicable to modern sparsity-promoting dynamics learning models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-kuang26a, title = {Instrumental variables system identification with $L^p$ consistency}, author = {Kuang, Simon and Lin, Xinfan}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {1713--1740}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/kuang26a/kuang26a.pdf}, url = {https://proceedings.mlr.press/v331/kuang26a.html}, abstract = {Instrumental variables (IV) eliminate the bias that afflicts least-squares identification of dynamical systems through noisy data, yet traditionally relies on external instruments that are seldom available for nonlinear time series data. We propose an IV estimator that synthesizes instruments from the data. We establish finite-sample $L^{p}$ consistency for _all_ $p \ge $ in both discrete- and continuous-time models, recovering a nonparametric $\sqrt{n}$-convergence rate. On a forced Lorenz system our estimator reduces parameter bias by 200x (continuous-time) and 500x (discrete-time) relative to least squares and reduces RMSE by up to tenfold. Because the method only assumes that the model is linear in the unknown parameters, it is broadly applicable to modern sparsity-promoting dynamics learning models.} }
Endnote
%0 Conference Paper %T Instrumental variables system identification with $L^p$ consistency %A Simon Kuang %A Xinfan Lin %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-kuang26a %I PMLR %P 1713--1740 %U https://proceedings.mlr.press/v331/kuang26a.html %V 331 %X Instrumental variables (IV) eliminate the bias that afflicts least-squares identification of dynamical systems through noisy data, yet traditionally relies on external instruments that are seldom available for nonlinear time series data. We propose an IV estimator that synthesizes instruments from the data. We establish finite-sample $L^{p}$ consistency for _all_ $p \ge $ in both discrete- and continuous-time models, recovering a nonparametric $\sqrt{n}$-convergence rate. On a forced Lorenz system our estimator reduces parameter bias by 200x (continuous-time) and 500x (discrete-time) relative to least squares and reduces RMSE by up to tenfold. Because the method only assumes that the model is linear in the unknown parameters, it is broadly applicable to modern sparsity-promoting dynamics learning models.
APA
Kuang, S. & Lin, X.. (2026). Instrumental variables system identification with $L^p$ consistency. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:1713-1740 Available from https://proceedings.mlr.press/v331/kuang26a.html.

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