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

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › 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.

Originalsprog	Engelsk
Titel	Proceedings of the 41st International Conference on Machine Learning
Antal sider	28
Forlag	ML Research Press
Publikationsdato	2024
Status	Udgivet - 2024
Begivenhed	41st International Conference on Machine Learning - Vienna, Østrig Varighed: 21 jul. 2024 → 27 jul. 2024 Konferencens nummer: 41 https://icml.cc/Conferences/2024

Konference

Konference	41st International Conference on Machine Learning
Nummer	41
Land/Område	Østrig
By	Vienna
Periode	21/07/2024 → 27/07/2024
Internetadresse	https://icml.cc/Conferences/2024

Navn	The Proceedings of Machine Learning Research
Vol/bind	235
ISSN	2640-3498

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https://proceedings.mlr.press/v235/eringis24a.html

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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. i Proceedings of the 41st International Conference on Machine Learning. ML Research Press, The Proceedings of Machine Learning Research, bind 235, 41st International Conference on Machine Learning, Vienna, Østrig, 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, Bind 235).

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning › 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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