Gaussian process approximations of stochastic differential equations

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Abstract

Stochastic differential equations arise naturally in a range of contexts, from financial to environmental modeling. Current solution methods are limited in their representation of the posterior process in the presence of data. In this work, we present a novel Gaussian process approximation to the posterior measure over paths for a general class of stochastic differential equations in the presence of observations. The method is applied to two simple problems: the Ornstein-Uhlenbeck process, of which the exact solution is known and can be compared to, and the double-well system, for which standard approaches such as the ensemble Kalman smoother fail to provide a satisfactory result. Experiments show that our variational approximation is viable and that the results are very promising as the variational approximate solution outperforms standard Gaussian process regression for non-Gaussian Markov processes.

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  • archambeau07a.pdf

    Rights statement: JMLR Workshop and Conference Proceedings Volume 1: GPIP, 12-13 June 2006, Bletchley (UK). © 2007 C. Archambeau, D. Cornford, M. Opper and J. Shawe-Taylor.

    302 KB, PDF-document

Details

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalJournal of Machine Learning Research
Volume1
StatePublished - 11 Mar 2007

Bibliographic note

JMLR Workshop and Conference Proceedings Volume 1: GPIP, 12-13 June 2006, Bletchley (UK). © 2007 C. Archambeau, D. Cornford, M. Opper and J. Shawe-Taylor.

    Keywords

  • dynamical systems, stochastic processes, Bayesian inference, Gaussian processes

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