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

Zheng Zhao, Filip Tronarp, Roland Hostettler, Simo Särkkä

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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 Itô–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 logN), 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 realdata applications to sunspot activity and electromyography.
Original languageEnglish
Title of host publicationProceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020
PublisherIEEE
Number of pages5
DOIs
Publication statusAccepted/In press - 2020
MoE publication typeA4 Article in a conference publication
EventIEEE International Conference on Acoustics, Speech and Signal Processing - Barcelona, Spain
Duration: 4 May 20208 May 2020
Conference number: 45

Publication series

NameProceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
ISSN (Print)1520-6149
ISSN (Electronic)2379-190X

Conference

ConferenceIEEE International Conference on Acoustics, Speech and Signal Processing
Abbreviated titleICASSP
CountrySpain
CityBarcelona
Period04/05/202008/05/2020

Keywords

  • Gaussian process regression
  • Kalman filter and smoother
  • Stochastic differential equation
  • Drift estimation
  • Sunspot activity
  • Electromyography

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  • Projects

    ELEMON: Electrophysiological monitoring for digital healthcare

    Hostettler, R., Sarmavuori, J., Särkkä, S., Zhao, Z., Bahrami Rad, A., Suotsalo, K. & Palva, L.

    01/01/201730/06/2020

    Project: Business Finland: Other research funding

    Cite this

    Zhao, Z., Tronarp, F., Hostettler, R., & Särkkä, S. (Accepted/In press). State-space Gaussian Process for Drift Estimation in Stochastic Differential Equations. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2020 (Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing). IEEE. https://doi.org/10.1109/ICASSP40776.2020.9054472