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Full Bayesian identification of linear dynamic systems using stable kernels

System identification learns mathematical models of dynamic systems starting from input–output data. Despite its long history, such research area is still extremely active. New challenges are posed by identification of complex physical processes given by the interconnection of dynamic systems. Examp...

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Autores principales: Pillonetto, G., Ljung, L.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: National Academy of Sciences 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10161125/
https://www.ncbi.nlm.nih.gov/pubmed/37094150
http://dx.doi.org/10.1073/pnas.2218197120
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author Pillonetto, G.
Ljung, L.
author_facet Pillonetto, G.
Ljung, L.
author_sort Pillonetto, G.
collection PubMed
description System identification learns mathematical models of dynamic systems starting from input–output data. Despite its long history, such research area is still extremely active. New challenges are posed by identification of complex physical processes given by the interconnection of dynamic systems. Examples arise in biology and industry, e.g., in the study of brain dynamics or sensor networks. In the last years, regularized kernel-based identification, with inspiration from machine learning, has emerged as an interesting alternative to the classical approach commonly adopted in the literature. In the linear setting, it uses the class of stable kernels to include fundamental features of physical dynamical systems, e.g., smooth exponential decay of impulse responses. Such class includes also unknown continuous parameters, called hyperparameters, which play a similar role as the model discrete order in controlling complexity. In this paper, we develop a linear system identification procedure by casting stable kernels in a full Bayesian framework. Our models incorporate hyperparameters uncertainty and consist of a mixture of dynamic systems over a continuum spectrum of dimensions. They are obtained by overcoming drawbacks related to classical Markov chain Monte Carlo schemes that, when applied to stable kernels, are proved to become nearly reducible (i.e., unable to reconstruct posteriors of interest in reasonable time). Numerical experiments show that full Bayes frequently outperforms the state-of-the-art results on typical benchmark problems. Two real applications related to brain dynamics (neural activity) and sensor networks are also included.
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spelling pubmed-101611252023-10-24 Full Bayesian identification of linear dynamic systems using stable kernels Pillonetto, G. Ljung, L. Proc Natl Acad Sci U S A Physical Sciences System identification learns mathematical models of dynamic systems starting from input–output data. Despite its long history, such research area is still extremely active. New challenges are posed by identification of complex physical processes given by the interconnection of dynamic systems. Examples arise in biology and industry, e.g., in the study of brain dynamics or sensor networks. In the last years, regularized kernel-based identification, with inspiration from machine learning, has emerged as an interesting alternative to the classical approach commonly adopted in the literature. In the linear setting, it uses the class of stable kernels to include fundamental features of physical dynamical systems, e.g., smooth exponential decay of impulse responses. Such class includes also unknown continuous parameters, called hyperparameters, which play a similar role as the model discrete order in controlling complexity. In this paper, we develop a linear system identification procedure by casting stable kernels in a full Bayesian framework. Our models incorporate hyperparameters uncertainty and consist of a mixture of dynamic systems over a continuum spectrum of dimensions. They are obtained by overcoming drawbacks related to classical Markov chain Monte Carlo schemes that, when applied to stable kernels, are proved to become nearly reducible (i.e., unable to reconstruct posteriors of interest in reasonable time). Numerical experiments show that full Bayes frequently outperforms the state-of-the-art results on typical benchmark problems. Two real applications related to brain dynamics (neural activity) and sensor networks are also included. National Academy of Sciences 2023-04-24 2023-05-02 /pmc/articles/PMC10161125/ /pubmed/37094150 http://dx.doi.org/10.1073/pnas.2218197120 Text en Copyright © 2023 the Author(s). Published by PNAS. https://creativecommons.org/licenses/by-nc-nd/4.0/This article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND) (https://creativecommons.org/licenses/by-nc-nd/4.0/) .
spellingShingle Physical Sciences
Pillonetto, G.
Ljung, L.
Full Bayesian identification of linear dynamic systems using stable kernels
title Full Bayesian identification of linear dynamic systems using stable kernels
title_full Full Bayesian identification of linear dynamic systems using stable kernels
title_fullStr Full Bayesian identification of linear dynamic systems using stable kernels
title_full_unstemmed Full Bayesian identification of linear dynamic systems using stable kernels
title_short Full Bayesian identification of linear dynamic systems using stable kernels
title_sort full bayesian identification of linear dynamic systems using stable kernels
topic Physical Sciences
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10161125/
https://www.ncbi.nlm.nih.gov/pubmed/37094150
http://dx.doi.org/10.1073/pnas.2218197120
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