Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputs

Harish Doddi, Deepjyoti Deka, Saurav Talukdar, Murti Salapaka
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:9982-9997, 2022.

Abstract

We consider a networked linear dynamical system with p agents/nodes. We study the problem of learning the underlying graph of interactions/dependencies from observations of the nodal trajectories over a time-interval T. We present a regularized non-casual consistent estimator for this problem and analyze its sample complexity over two regimes: (a) where the interval T consists of n i.i.d. observation windows of length T/n (restart and record), and (b) where T is one continuous observation window (consecutive). Using the theory of M-estimators, we show that the estimator recovers the underlying interactions, in either regime, in a time-interval that is logarithmic in the system size p. To the best of our knowledge, this is the first work to analyze the sample complexity of learning linear dynamical systems driven by unobserved not-white wide-sense stationary (WSS) inputs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-doddi22a, title = { Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputs }, author = {Doddi, Harish and Deka, Deepjyoti and Talukdar, Saurav and Salapaka, Murti}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {9982--9997}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/doddi22a/doddi22a.pdf}, url = {https://proceedings.mlr.press/v151/doddi22a.html}, abstract = { We consider a networked linear dynamical system with p agents/nodes. We study the problem of learning the underlying graph of interactions/dependencies from observations of the nodal trajectories over a time-interval T. We present a regularized non-casual consistent estimator for this problem and analyze its sample complexity over two regimes: (a) where the interval T consists of n i.i.d. observation windows of length T/n (restart and record), and (b) where T is one continuous observation window (consecutive). Using the theory of M-estimators, we show that the estimator recovers the underlying interactions, in either regime, in a time-interval that is logarithmic in the system size p. To the best of our knowledge, this is the first work to analyze the sample complexity of learning linear dynamical systems driven by unobserved not-white wide-sense stationary (WSS) inputs. } }
Endnote
%0 Conference Paper %T Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputs %A Harish Doddi %A Deepjyoti Deka %A Saurav Talukdar %A Murti Salapaka %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-doddi22a %I PMLR %P 9982--9997 %U https://proceedings.mlr.press/v151/doddi22a.html %V 151 %X We consider a networked linear dynamical system with p agents/nodes. We study the problem of learning the underlying graph of interactions/dependencies from observations of the nodal trajectories over a time-interval T. We present a regularized non-casual consistent estimator for this problem and analyze its sample complexity over two regimes: (a) where the interval T consists of n i.i.d. observation windows of length T/n (restart and record), and (b) where T is one continuous observation window (consecutive). Using the theory of M-estimators, we show that the estimator recovers the underlying interactions, in either regime, in a time-interval that is logarithmic in the system size p. To the best of our knowledge, this is the first work to analyze the sample complexity of learning linear dynamical systems driven by unobserved not-white wide-sense stationary (WSS) inputs.
APA
Doddi, H., Deka, D., Talukdar, S. & Salapaka, M.. (2022). Efficient and passive learning of networked dynamical systems driven by non-white exogenous inputs . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:9982-9997 Available from https://proceedings.mlr.press/v151/doddi22a.html.

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