Modeling the Drift Function in Stochastic Differential Equations using Reduced Rank Gaussian Processes

Roland Hostettler; Filip Tronarp; Simo Särkkä

doi:10.1016/j.ifacol.2018.09.137

Modeling the Drift Function in Stochastic Differential Equations using Reduced Rank Gaussian Processes

Roland Hostettler, Filip Tronarp, Simo Särkkä

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

2 Citations (Scopus)

255 Downloads (Pure)

Abstract

In this paper, we propose a Gaussian process-based nonlinear, time-varying drift model for stochastic differential equations. In particular, we combine eigenfunction expansion of the Gaussian process’ covariance kernel in the spatial input variables with spectral decomposition in the time domain to obtain a reduced rank state space representation of the drift model, which avoids the growing complexity (with respect to time) of the full Gaussian process solution. The proposed approach is evaluated on two nonlinear benchmark problems, the Bouc Wen and the cascaded tanks systems.

Original language	English
Title of host publication	18th IFAC Symposium on System Identification, SYSID 2018
Publisher	Elsevier
Pages	778-783
Number of pages	6
Volume	51
Edition	15
DOIs	https://doi.org/10.1016/j.ifacol.2018.09.137
Publication status	Published - 1 Jan 2018
MoE publication type	A4 Article in a conference publication
Event	IFAC Symposium on System Identification - Stockholm, Sweden Duration: 9 Jul 2018 → 11 Jul 2018 Conference number: 18

Publication series

Name	IFAC-PapersOnLine
Publisher	Elsevier Science Ltd (Pergamon)
ISSN (Print)	2405-8963

Conference

Conference	IFAC Symposium on System Identification
Abbreviated title	SYSID
Country/Territory	Sweden
City	Stockholm
Period	09/07/2018 → 11/07/2018

Keywords

Bayesian methods
estimation
filtering
Gaussian processes
Nonlinear system identification
nonparametric methods
smoothing

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10.1016/j.ifacol.2018.09.137

ELEC_Hostettler_etal_Modeling-the-Drift_IFACPapersOnline_51_15_2018Final published version, 557 KB

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title = "Modeling the Drift Function in Stochastic Differential Equations using Reduced Rank Gaussian Processes",

abstract = "In this paper, we propose a Gaussian process-based nonlinear, time-varying drift model for stochastic differential equations. In particular, we combine eigenfunction expansion of the Gaussian process{\textquoteright} covariance kernel in the spatial input variables with spectral decomposition in the time domain to obtain a reduced rank state space representation of the drift model, which avoids the growing complexity (with respect to time) of the full Gaussian process solution. The proposed approach is evaluated on two nonlinear benchmark problems, the Bouc Wen and the cascaded tanks systems.",

keywords = "Bayesian methods, estimation, filtering, Gaussian processes, Nonlinear system identification, nonparametric methods, smoothing",

author = "Roland Hostettler and Filip Tronarp and Simo S{\"a}rkk{\"a}",

year = "2018",

month = jan,

day = "1",

doi = "10.1016/j.ifacol.2018.09.137",

language = "English",

volume = "51",

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pages = "778--783",

booktitle = "18th IFAC Symposium on System Identification, SYSID 2018",

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edition = "15",

note = "IFAC Symposium on System Identification, SYSID ; Conference date: 09-07-2018 Through 11-07-2018",

}

Hostettler, R, Tronarp, F & Särkkä, S 2018, Modeling the Drift Function in Stochastic Differential Equations using Reduced Rank Gaussian Processes. in 18th IFAC Symposium on System Identification, SYSID 2018. 15 edn, vol. 51, IFAC-PapersOnLine, Elsevier, pp. 778-783, IFAC Symposium on System Identification, Stockholm, Sweden, 09/07/2018. https://doi.org/10.1016/j.ifacol.2018.09.137

Modeling the Drift Function in Stochastic Differential Equations using Reduced Rank Gaussian Processes. / Hostettler, Roland; Tronarp, Filip; Särkkä, Simo.
18th IFAC Symposium on System Identification, SYSID 2018. Vol. 51 15. ed. Elsevier, 2018. p. 778-783 (IFAC-PapersOnLine).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

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N2 - In this paper, we propose a Gaussian process-based nonlinear, time-varying drift model for stochastic differential equations. In particular, we combine eigenfunction expansion of the Gaussian process’ covariance kernel in the spatial input variables with spectral decomposition in the time domain to obtain a reduced rank state space representation of the drift model, which avoids the growing complexity (with respect to time) of the full Gaussian process solution. The proposed approach is evaluated on two nonlinear benchmark problems, the Bouc Wen and the cascaded tanks systems.

AB - In this paper, we propose a Gaussian process-based nonlinear, time-varying drift model for stochastic differential equations. In particular, we combine eigenfunction expansion of the Gaussian process’ covariance kernel in the spatial input variables with spectral decomposition in the time domain to obtain a reduced rank state space representation of the drift model, which avoids the growing complexity (with respect to time) of the full Gaussian process solution. The proposed approach is evaluated on two nonlinear benchmark problems, the Bouc Wen and the cascaded tanks systems.

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KW - estimation

KW - filtering

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KW - Nonlinear system identification

KW - nonparametric methods

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Modeling the Drift Function in Stochastic Differential Equations using Reduced Rank Gaussian Processes

Abstract

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Crowdsourced mapping of the environment- multimodal real-time SLAM via combinedinertial, optical, and magnetic sensoring

Sequential Monte Carlo Methods for State and Parameter Estimation in Stochastic Dynamic Systems

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Modeling the Drift Function in Stochastic Differential Equations using Reduced Rank Gaussian Processes

Abstract

Publication series

Conference

Keywords

Access to Document

OpenUrl availability

Other files and links

Fingerprint

Projects

Crowdsourced mapping of the environment- multimodal real-time SLAM via combinedinertial, optical, and magnetic sensoring

Sequential Monte Carlo Methods for State and Parameter Estimation in Stochastic Dynamic Systems

Cite this