Gaussian Process Approximations of Stochastic Differential Equations
Cedric Archambeau, Dan Cornford, Manfred Opper and John Shawe-Taylor
In: Gaussian Process In Practice, 12-13 June 2006, Bletchley Park, UK.

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Abstract

Stochastic differential equations arise naturally in a range of contexts, from financial to environmental modelling. Current solution methods are based on a range of strong and weak approximation techniques, however these 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 approximation outperforms standard Gaussian process regression for non-Gaussian Markov processes.

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Available Versions of this Item

• Gaussian Process Approximations of Stochastic Differential Equations (deposited 22 November 2006) [Currently Displayed]
  • Gaussian Process Approximations of Stochastic Differential Equations (deposited 21 December 2007)
  • Variational Inference for Diffusion Processes (deposited 21 December 2007)
  • Evaluation of Variational and Markov Chain Monte Carlo Methods for Inference in Partially Observed Stochastic Dynamic Systems (deposited 21 December 2007)

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