Finite Sample Analysis of Tensor Decomposition for Learning Mixtures of Linear Systems

Maryann Rui, Munther Dahleh
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:1313-1325, 2025.

Abstract

We study the problem of learning mixtures of linear dynamical systems (MLDS) from input-output data. The mixture setting allows us to leverage observations from related dynamical systems to improve the estimation of individual models. Building on spectral methods for mixtures of linear regressions, we propose a moment-based estimator that uses tensor decomposition to estimate the impulse response parameters of the mixture models. The estimator improves upon existing tensor decomposition approaches for MLDS by utilizing the entire length of the observed trajectories. We provide sample complexity bounds for estimating MLDS in the presence of noise, in terms of both the number of trajectories $N$ and the trajectory length $T$, and demonstrate the performance of the estimator through simulations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-rui25a, title = {Finite Sample Analysis of Tensor Decomposition for Learning Mixtures of Linear Systems}, author = {Rui, Maryann and Dahleh, Munther}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {1313--1325}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/rui25a/rui25a.pdf}, url = {https://proceedings.mlr.press/v283/rui25a.html}, abstract = {We study the problem of learning mixtures of linear dynamical systems (MLDS) from input-output data. The mixture setting allows us to leverage observations from related dynamical systems to improve the estimation of individual models. Building on spectral methods for mixtures of linear regressions, we propose a moment-based estimator that uses tensor decomposition to estimate the impulse response parameters of the mixture models. The estimator improves upon existing tensor decomposition approaches for MLDS by utilizing the entire length of the observed trajectories. We provide sample complexity bounds for estimating MLDS in the presence of noise, in terms of both the number of trajectories $N$ and the trajectory length $T$, and demonstrate the performance of the estimator through simulations.} }
Endnote
%0 Conference Paper %T Finite Sample Analysis of Tensor Decomposition for Learning Mixtures of Linear Systems %A Maryann Rui %A Munther Dahleh %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-rui25a %I PMLR %P 1313--1325 %U https://proceedings.mlr.press/v283/rui25a.html %V 283 %X We study the problem of learning mixtures of linear dynamical systems (MLDS) from input-output data. The mixture setting allows us to leverage observations from related dynamical systems to improve the estimation of individual models. Building on spectral methods for mixtures of linear regressions, we propose a moment-based estimator that uses tensor decomposition to estimate the impulse response parameters of the mixture models. The estimator improves upon existing tensor decomposition approaches for MLDS by utilizing the entire length of the observed trajectories. We provide sample complexity bounds for estimating MLDS in the presence of noise, in terms of both the number of trajectories $N$ and the trajectory length $T$, and demonstrate the performance of the estimator through simulations.
APA
Rui, M. & Dahleh, M.. (2025). Finite Sample Analysis of Tensor Decomposition for Learning Mixtures of Linear Systems. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:1313-1325 Available from https://proceedings.mlr.press/v283/rui25a.html.

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