Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations
A. Besginow, M. Lange-Hegermann, Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations, Curran Associates, Inc., Red Hook, NY , 2022.
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Konferenzband - Beitrag
| Veröffentlicht
| Englisch
Herausgeber*in
Koyejo, S.;
Mohamed, S.;
Agarwal, A.;
Belgrave, D.;
Cho, K.;
Oh, A.
Körperschaftlicher Herausgeber
Neural Information Processing Systems Foundation
Abstract
Data in many applications follows systems of Ordinary Differential Equations (ODEs). This paper presents a novel algorithmic and symbolic construction for covariance functions of Gaussian Processes (GPs) with realizations strictly following a system of linear homogeneous ODEs with constant coefficients, which we call LODE-GPs. Introducing this strong inductive bias into a GP improves modelling of such data. Using smith normal form algorithms, a symbolic technique, we overcome two current restrictions in the state of the art: (1) the need for certain uniqueness conditions in the set of solutions, typically assumed in classical ODE solvers and their probabilistic counterparts, and (2) the restriction to controllable systems, typically assumed when encoding differential equations in covariance functions. We show the effectiveness of LODE-GPs in a number of experiments, for example learning physically interpretable parameters by maximizing the likelihood.
Stichworte
Erscheinungsjahr
Titel Konferenzband
36th Conference on Neural Information Processing Systems (NeurIPS 2022)
Band
35
Seite
29386 - 29399
Konferenz
36th Conference on Neural Information Processing Systems (NeurIPS)
Konferenzort
New Orleans, La.; Online
Konferenzdatum
2022-11-28 – 2022-12-09
ISBN
eISBN
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ELSA-ID
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Besginow A, Lange-Hegermann M. Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations. Vol 35. (Koyejo S, Mohamed S, Agarwal A, et al., eds.). Curran Associates, Inc.; 2022:29386-29399.
Besginow, A., & Lange-Hegermann, M. (2022). Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh, & Neural Information Processing Systems Foundation (Eds.), 36th Conference on Neural Information Processing Systems (NeurIPS 2022) (Vol. 35, pp. 29386–29399). Curran Associates, Inc.
Besginow A and Lange-Hegermann M (2022) Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations, Koyejo S et al. (eds). Red Hook, NY : Curran Associates, Inc.
Besginow, Andreas, and Markus Lange-Hegermann. Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations. Edited by S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh, and Neural Information Processing Systems Foundation . 36th Conference on Neural Information Processing Systems (NeurIPS 2022) . Vol. 35. Advances in Neural Information Processing Systems. Red Hook, NY : Curran Associates, Inc., 2022.
Besginow, Andreas und Markus Lange-Hegermann. 2022. Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations. Hg. von S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh, und Neural Information Processing Systems Foundation . 36th Conference on Neural Information Processing Systems (NeurIPS 2022) . Bd. 35. Advances in Neural Information Processing Systems. Red Hook, NY : Curran Associates, Inc.
Besginow, Andreas ; Lange-Hegermann, Markus ; Koyejo, S. ; Mohamed, S. ; Agarwal, A. ; Belgrave, D. ; Cho, K. ; Oh, A. ; Neural Information Processing Systems Foundation (Hrsg.): Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations, Advances in Neural Information Processing Systems. Bd. 35. Red Hook, NY : Curran Associates, Inc., 2022
A. Besginow, M. Lange-Hegermann, Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations, Curran Associates, Inc., Red Hook, NY , 2022.
A. Besginow and M. Lange-Hegermann, Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations, vol. 35. Red Hook, NY : Curran Associates, Inc., 2022, pp. 29386–29399.
Besginow, Andreas, and Markus Lange-Hegermann. “Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations.” 36th Conference on Neural Information Processing Systems (NeurIPS 2022) , edited by S. Koyejo et al., vol. 35, Curran Associates, Inc., 2022, pp. 29386–99.
Besginow, Andreas/Lange-Hegermann, Markus: Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations, Bd. 35, hg. von Koyejo, S. u. a., Red Hook, NY 2022 (Advances in Neural Information Processing Systems).
Besginow A, Lange-Hegermann M. Constraining Gaussian Processes to Systems of Linear Ordinary Differential Equations. Koyejo S, Mohamed S, Agarwal A, Belgrave D, Cho K, Oh A, et al., editors. 36th Conference on Neural Information Processing Systems (NeurIPS 2022) . Red Hook, NY : Curran Associates, Inc.; 2022. (Advances in Neural Information Processing Systems; vol. 35).
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