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State-Space Gaussian Process for Drift Estimation in Stochastic Differential Equations

Zhao, Zheng ; Tronarp, Filip LU ; Särkkä, Simo and Hostettler, Roland (2020) IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2020
Abstract
This paper is concerned with the estimation of unknown drift functions of stochastic differential equations (SDEs) from observations of their sample paths. We propose to formulate this as a non-parametric Gaussian process regression problem and use an Ito-Taylor expansion for approximating the SDE. To address the computational complexity problem of Gaussian process regression, we cast the model in an equivalent state-space representation, such that (non-linear) Kalman filters and smoothers can be used. The benefit of these methods is that computational complexity scales linearly with respect to the number of measurements and hence the method remains tractable also with large amounts of data. The overall complexity of the proposed method is... (More)
This paper is concerned with the estimation of unknown drift functions of stochastic differential equations (SDEs) from observations of their sample paths. We propose to formulate this as a non-parametric Gaussian process regression problem and use an Ito-Taylor expansion for approximating the SDE. To address the computational complexity problem of Gaussian process regression, we cast the model in an equivalent state-space representation, such that (non-linear) Kalman filters and smoothers can be used. The benefit of these methods is that computational complexity scales linearly with respect to the number of measurements and hence the method remains tractable also with large amounts of data. The overall complexity of the proposed method is O(N log N), where N is the number of measurements, due to the requirement of sorting the input data. We evaluate the performance of the proposed method using simulated data as well as with real-data applications to sunspot activity and electromyography. (Less)
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author
; ; and
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
conference name
IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2020
conference location
Barcelona, Spain
conference dates
2020-05-04 - 2020-05-08
external identifiers
  • scopus:85091179111
ISBN
978-1-5090-6631-5
978-1-5090-6632-2
DOI
10.1109/ICASSP40776.2020.9054472
language
English
LU publication?
no
id
178f072e-99a3-4704-bb9b-6009bf73ac4c
date added to LUP
2023-08-20 22:58:04
date last changed
2025-04-04 14:42:31
@inproceedings{178f072e-99a3-4704-bb9b-6009bf73ac4c,
  abstract     = {{This paper is concerned with the estimation of unknown drift functions of stochastic differential equations (SDEs) from observations of their sample paths. We propose to formulate this as a non-parametric Gaussian process regression problem and use an Ito-Taylor expansion for approximating the SDE. To address the computational complexity problem of Gaussian process regression, we cast the model in an equivalent state-space representation, such that (non-linear) Kalman filters and smoothers can be used. The benefit of these methods is that computational complexity scales linearly with respect to the number of measurements and hence the method remains tractable also with large amounts of data. The overall complexity of the proposed method is O(N log N), where N is the number of measurements, due to the requirement of sorting the input data. We evaluate the performance of the proposed method using simulated data as well as with real-data applications to sunspot activity and electromyography.}},
  author       = {{Zhao, Zheng and Tronarp, Filip and Särkkä, Simo and Hostettler, Roland}},
  booktitle    = {{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}},
  isbn         = {{978-1-5090-6631-5}},
  language     = {{eng}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{State-Space Gaussian Process for Drift Estimation in Stochastic Differential Equations}},
  url          = {{http://dx.doi.org/10.1109/ICASSP40776.2020.9054472}},
  doi          = {{10.1109/ICASSP40776.2020.9054472}},
  year         = {{2020}},
}