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.
|Number of pages||16|
|Journal||Journal of Machine Learning Research|
|Publication status||Published - 11 Mar 2007|
Bibliographical noteJMLR 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