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A Comparison of Variational and Markov Chain Monte Carlo Methods for Inference in Partially Observed Stochastic Dynamic Systems

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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.

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Authors and Affiliations

  1. Neural Computing Research Group, Aston University, Birmingham, UK

    Yuan Shen, Dan Cornford & Remi Barillec

  2. Department of Computer Science, University College London, London, UK

    Cedric Archambeau & John Shawe-Taylor

  3. Artificial Intelligence Group, Technical University Berlin, Berlin, Germany

    Manfred Opper

Authors
  1. Yuan Shen
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  2. Cedric Archambeau
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  3. Dan Cornford
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  4. Manfred Opper
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  5. John Shawe-Taylor
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  6. Remi Barillec
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Correspondence to Yuan Shen.

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Shen, Y., Archambeau, C., Cornford, D. et al. A Comparison of Variational and Markov Chain Monte Carlo Methods for Inference in Partially Observed Stochastic Dynamic Systems. J Sign Process Syst 61, 51–59 (2010). https://doi.org/10.1007/s11265-008-0299-y

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  • DOI: https://doi.org/10.1007/s11265-008-0299-y

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