A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems

Yuan Shen*, Cédric Archambeau, Dan Cornford, Manfred Opper, John Shawe-Taylor, Remi Barillec

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

In recent work we have developed a novel variational inference method for partially observed systems governed by stochastic differential equations. In this paper we provide a comparison of the Variational Gaussian Process Smoother with an exact solution computed using a Hybrid Monte Carlo approach to path sampling, applied to a stochastic double well potential model. It is demonstrated that the variational smoother provides us a very accurate estimate of mean path while conditional variance is slightly underestimated. We conclude with some remarks as to the advantages and disadvantages of the variational smoother. © 2008 Springer Science + Business Media LLC.

Original languageEnglish
Pages (from-to)51-59
Number of pages9
JournalJournal of Signal Processing Systems
Volume61
Issue number1
Early online date11 Nov 2008
DOIs
Publication statusPublished - Oct 2010
EventIEEE International Workshop on Machine Learning for Signal Processing - Thessaloniki, Greece
Duration: 27 Aug 200729 Aug 2007

Fingerprint

Markov Chain Monte Carlo Methods
Stochastic Dynamics
Stochastic Systems
Markov processes
Dynamic Systems
Dynamical systems
Differential equations
Monte Carlo methods
Sampling
Industry
Path Sampling
Hybrid Monte Carlo
Conditional Variance
Double-well Potential
Gaussian Process
Stochastic Equations
Exact Solution
Differential equation
Path
Estimate

Bibliographical note

The original publication is available at www.springerlink.com

Keywords

  • Bayesian computation
  • data assimilation
  • nonlinear smoothing
  • signal processing
  • variational approximation

Cite this

Shen, Yuan ; Archambeau, Cédric ; Cornford, Dan ; Opper, Manfred ; Shawe-Taylor, John ; Barillec, Remi. / A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems. In: Journal of Signal Processing Systems. 2010 ; Vol. 61, No. 1. pp. 51-59.
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A comparison of variational and Markov chain Monte Carlo methods for inference in partially observed stochastic dynamic systems. / Shen, Yuan; Archambeau, Cédric; Cornford, Dan; Opper, Manfred; Shawe-Taylor, John; Barillec, Remi.

In: Journal of Signal Processing Systems, Vol. 61, No. 1, 10.2010, p. 51-59.

Research output: Contribution to journalArticle

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