PAC-Bayesian Error Bound, via Rényi Divergence, for a Class of Linear Time-Invariant State-Space Models

Deividas Eringis, John Leth, Zheng-Hua Tan, Rafal Wisniewski, Mihaly Petreczky
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:12560-12587, 2024.

Abstract

In this paper we derive a PAC-Bayesian error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is widely used in control engineering and econometrics, in particular, they represent a special case of recurrent neural networks. In this paper we 1) formalize the learning problem for stochastic LTI systems with inputs, 2) derive a PAC-Bayesian error bound for such systems, and 3) discuss various consequences of this error bound.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-eringis24a, title = {{PAC}-{B}ayesian Error Bound, via Rényi Divergence, for a Class of Linear Time-Invariant State-Space Models}, author = {Eringis, Deividas and Leth, John and Tan, Zheng-Hua and Wisniewski, Rafal and Petreczky, Mihaly}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {12560--12587}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/eringis24a/eringis24a.pdf}, url = {https://proceedings.mlr.press/v235/eringis24a.html}, abstract = {In this paper we derive a PAC-Bayesian error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is widely used in control engineering and econometrics, in particular, they represent a special case of recurrent neural networks. In this paper we 1) formalize the learning problem for stochastic LTI systems with inputs, 2) derive a PAC-Bayesian error bound for such systems, and 3) discuss various consequences of this error bound.} }
Endnote
%0 Conference Paper %T PAC-Bayesian Error Bound, via Rényi Divergence, for a Class of Linear Time-Invariant State-Space Models %A Deividas Eringis %A John Leth %A Zheng-Hua Tan %A Rafal Wisniewski %A Mihaly Petreczky %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-eringis24a %I PMLR %P 12560--12587 %U https://proceedings.mlr.press/v235/eringis24a.html %V 235 %X In this paper we derive a PAC-Bayesian error bound for a class of stochastic dynamical systems with inputs, namely, for linear time-invariant stochastic state-space models (stochastic LTI systems for short). This class of systems is widely used in control engineering and econometrics, in particular, they represent a special case of recurrent neural networks. In this paper we 1) formalize the learning problem for stochastic LTI systems with inputs, 2) derive a PAC-Bayesian error bound for such systems, and 3) discuss various consequences of this error bound.
APA
Eringis, D., Leth, J., Tan, Z., Wisniewski, R. & Petreczky, M.. (2024). PAC-Bayesian Error Bound, via Rényi Divergence, for a Class of Linear Time-Invariant State-Space Models. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:12560-12587 Available from https://proceedings.mlr.press/v235/eringis24a.html.

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