Gaussian process approximations of stochastic differential equations

Archambeau, Cédric, Cornford, Dan, Opper, Manfred and Shawe-Taylor, John (2007). Gaussian process approximations of stochastic differential equations. Journal of Machine Learning Research, 1 , pp. 1-16.

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.

Divisions: Engineering & Applied Sciences > Computer science
Engineering & Applied Sciences > Computer science research group
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: 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.
Uncontrolled Keywords: dynamical systems,stochastic processes,Bayesian inference,Gaussian processes
Full Text Link: http://jmlr.csa ... ings/papers/v1/
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Published Date: 2007-03-11
Authors: Archambeau, Cédric
Cornford, Dan ( 0000-0001-8787-6758)
Opper, Manfred
Shawe-Taylor, John

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