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

Deividas Eringis; John-Josef Leth; Zheng-Hua Tan; Rafal Wisniewski; Mihaly Petreczky

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

Deividas Eringis, John-Josef Leth, Zheng-Hua Tan, Rafal Wisniewski, Mihaly Petreczky

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

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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.

Original language	English
Title of host publication	Proceedings of the 41st International Conference on Machine Learning
Number of pages	28
Publisher	ML Research Press
Publication date	2024
Publication status	Published - 2024
Event	41st International Conference on Machine Learning - Vienna, Austria Duration: 21 Jul 2024 → 27 Jul 2024 Conference number: 41 https://icml.cc/Conferences/2024

Conference

Conference	41st International Conference on Machine Learning
Number	41
Country/Territory	Austria
City	Vienna
Period	21/07/2024 → 27/07/2024
Internet address	https://icml.cc/Conferences/2024

Series	The Proceedings of Machine Learning Research
Volume	235
ISSN	2640-3498

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@inproceedings{cc629334e8ea48ea88959e00af9a9566,

title = "PAC-Bayesian Error Bound, via R{\'e}nyi Divergence, for a Class of Linear Time-Invariant State-Space Models",

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.",

author = "Deividas Eringis and John-Josef Leth and Zheng-Hua Tan and Rafal Wisniewski and Mihaly Petreczky",

year = "2024",

language = "English",

series = "The Proceedings of Machine Learning Research",

booktitle = "Proceedings of the 41st International Conference on Machine Learning",

publisher = "ML Research Press",

note = "41st International Conference on Machine Learning, ICML ; Conference date: 21-07-2024 Through 27-07-2024",

url = "https://icml.cc/Conferences/2024",

}

Eringis, D, Leth, J-J , Tan, Z-H , Wisniewski, R & Petreczky, M 2024, PAC-Bayesian Error Bound, via Rényi Divergence, for a Class of Linear Time-Invariant State-Space Models. in Proceedings of the 41st International Conference on Machine Learning. ML Research Press, The Proceedings of Machine Learning Research, vol. 235, 41st International Conference on Machine Learning, Vienna, Austria, 21/07/2024. <https://proceedings.mlr.press/v235/eringis24a.html>

PAC-Bayesian Error Bound, via Rényi Divergence, for a Class of Linear Time-Invariant State-Space Models. / Eringis, Deividas; Leth, John-Josef ; Tan, Zheng-Hua et al.
Proceedings of the 41st International Conference on Machine Learning. ML Research Press, 2024. (The Proceedings of Machine Learning Research, Vol. 235).

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

TY - GEN

T1 - PAC-Bayesian Error Bound, via Rényi Divergence, for a Class of Linear Time-Invariant State-Space Models

AU - Eringis, Deividas

AU - Leth, John-Josef

AU - Tan, Zheng-Hua

AU - Wisniewski, Rafal

AU - Petreczky, Mihaly

N1 - Conference code: 41

PY - 2024

Y1 - 2024

N2 - 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.

AB - 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.

M3 - Article in proceeding

T3 - The Proceedings of Machine Learning Research

BT - Proceedings of the 41st International Conference on Machine Learning

PB - ML Research Press

T2 - 41st International Conference on Machine Learning

Y2 - 21 July 2024 through 27 July 2024

ER -

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

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