Variational Inference for Diffusion Processes
Cedric Archambeau, Manfred Opper, Yuan Shen, Dan Cornford and John Shawe-Taylor
In: NIPS 21, 3-8 Dec 2007, Vancouver, Canada.

There is a more recent version of this eprint available. Click here to view it.

Abstract

Diffusion processes are a family of continuous-time continuous-state stochastic processes that are in general only partially observed. The joint estimation of the forcing parameters and the system noise (volatility) in these dynamical systems is a crucial, but non-trivial task, especially when the system is nonlinear and multi-modal. We propose a variational treatment of diffusion processes, which allows us to compute type II maximum likelihood estimates of the parameters by simple gradient techniques and which is computationally less demanding than most MCMC approaches. We also show how a cheap estimate of the posterior over the parameters can be constructed based on the variational free energy.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.

PDF - Requires Adobe Acrobat Reader or other PDF viewer.

Available Versions of this Item

• Gaussian Process Approximations of Stochastic Differential Equations (deposited 22 November 2006)
  • Gaussian Process Approximations of Stochastic Differential Equations (deposited 21 December 2007)
  • Variational Inference for Diffusion Processes (deposited 21 December 2007) [Currently Displayed]
    • Stochastic Memoizer for Sequence Data (deposited 08 March 2010)
  • Evaluation of Variational and Markov Chain Monte Carlo Methods for Inference in Partially Observed Stochastic Dynamic Systems (deposited 21 December 2007)
    • Evaluation of Variational and Markov Chain Monte Carlo Methods for Inference in Partially Observed Stochastic Dynamic Systems (deposited 24 March 2009)

[Edit]