Variational inference for diffusion processes

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 multimodal. 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.
Original languageEnglish
Title of host publicationAnnual Conference on Neural Information Processing Systems 2007
EditorsJ.C. Platt, D. Koller, Y. Singer, S. Roweis
Place of PublicationCambridge, MA (US)
PublisherMIT
Pages17-24
Number of pages8
ISBN (Print)978-1-60560352-0
Publication statusPublished - 2008
Event21st Annual Conference on Neural Information Processing Systems, NIPS 2007 - Vancouver, BC, Canada
Duration: 3 Dec 20076 Dec 2007

Publication series

NameAdvances In Neural Information Processing Systems
PublisherMassachusetts Institute of Technology Press
Volume20

Conference

Conference21st Annual Conference on Neural Information Processing Systems, NIPS 2007
CountryCanada
CityVancouver, BC
Period3/12/076/12/07

Fingerprint

Diffusion Process
Markov Chain Monte Carlo
Maximum Likelihood Estimate
Volatility
Forcing
Continuous Time
Stochastic Processes
Free Energy
Dynamical system
Gradient
Estimate
Family

Bibliographical note

Copyright of the Massachusetts Institute of Technology Press (MIT Press)

Keywords

  • diffusion processes
  • continuous-time continuous-state stochastic processes
  • system noise
  • volatility
  • variational free energy

Cite this

Archambeau, C., Opper, M., Shen, Y., Cornford, D., & Shawe-Taylor, J. (2008). Variational inference for diffusion processes. In J. C. Platt, D. Koller, Y. Singer, & S. Roweis (Eds.), Annual Conference on Neural Information Processing Systems 2007 (pp. 17-24). (Advances In Neural Information Processing Systems; Vol. 20). Cambridge, MA (US): MIT.
Archambeau, Cédric ; Opper, Manfred ; Shen, Yuan ; Cornford, Dan ; Shawe-Taylor, John. / Variational inference for diffusion processes. Annual Conference on Neural Information Processing Systems 2007. editor / J.C. Platt ; D. Koller ; Y. Singer ; S. Roweis. Cambridge, MA (US) : MIT, 2008. pp. 17-24 (Advances In Neural Information Processing Systems).
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Archambeau, C, Opper, M, Shen, Y, Cornford, D & Shawe-Taylor, J 2008, Variational inference for diffusion processes. in JC Platt, D Koller, Y Singer & S Roweis (eds), Annual Conference on Neural Information Processing Systems 2007. Advances In Neural Information Processing Systems, vol. 20, MIT, Cambridge, MA (US), pp. 17-24, 21st Annual Conference on Neural Information Processing Systems, NIPS 2007, Vancouver, BC, Canada, 3/12/07.

Variational inference for diffusion processes. / Archambeau, Cédric; Opper, Manfred; Shen, Yuan; Cornford, Dan; Shawe-Taylor, John.

Annual Conference on Neural Information Processing Systems 2007. ed. / J.C. Platt; D. Koller; Y. Singer; S. Roweis. Cambridge, MA (US) : MIT, 2008. p. 17-24 (Advances In Neural Information Processing Systems; Vol. 20).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Archambeau C, Opper M, Shen Y, Cornford D, Shawe-Taylor J. Variational inference for diffusion processes. In Platt JC, Koller D, Singer Y, Roweis S, editors, Annual Conference on Neural Information Processing Systems 2007. Cambridge, MA (US): MIT. 2008. p. 17-24. (Advances In Neural Information Processing Systems).