Gaussian process approximations of stochastic differential equations

Cédric Archambeau, Dan Cornford, Manfred Opper, John Shawe-Taylor

Research output: Contribution to journalArticlepeer-review


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

Bibliographical 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.


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


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