PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Gaussian Process Approximations of Stochastic Differential Equation
Cedric Archambeau, Dan Cornford, Manfred Opper and John Shawe-Taylor
Journal of Machine Learning Research: Workshop and Conference Volume 11, pp. 1-16, 2007.


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 \emph{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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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3705
Deposited By:Manfred Opper
Deposited On:14 February 2008