A new variational radial basis function approximation for inference in multivariate diffusions

Michail D. Vrettas; Dan Cornford; Manfred Opper; Yuan Shen

doi:10.1016/j.neucom.2009.11.026

A new variational radial basis function approximation for inference in multivariate diffusions

Michail D. Vrettas, Dan Cornford, Manfred Opper, Yuan Shen

Computer Science Research Group

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we present a radial basis function based extension to a recently proposed variational algorithm for approximate inference for diffusion processes. Inference, for state and in particular (hyper-) parameters, in diffusion processes is a challenging and crucial task. We show that the new radial basis function approximation based algorithm converges to the original algorithm and has beneficial characteristics when estimating (hyper-)parameters. We validate our new approach on a nonlinear double well potential dynamical system.

Original language	English
Pages (from-to)	1186-1198
Number of pages	13
Journal	Neurocomputing
Volume	73
Issue number	7-9
DOIs	https://doi.org/10.1016/j.neucom.2009.11.026
Publication status	Published - Mar 2010
Event	17th European Symposium on Artificial Neural Networks: Advances in Computational Intelligence and Learning - Bruges, Belgium Duration: 22 Apr 2009 → 24 Apr 2009

Bibliographical note

NOTICE: this is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Vrettas, Michail D.; Cornford, Dan; Opper, Manfred and Shen, Yuan (2010). A variational basis function approximation for diffusion processes. Neurocomputing, 73 (7-9), pp. 1186-1198. DOI 10.1016/j.neucom.2009.11.026

Keywords

radial basis functions
dynamical systems
stochastic differential equations
parameter estimation
Bayesian inference

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10.1016/j.neucom.2009.11.026

Vrettas2009ESANN.pdf
Advances in Computational Intelligence and Learning - 17th European Symposium on Artificial Neural Networks 2009, Bruges (BE), 22-24 April 2009. NOTICE: this is the author’s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Vrettas, Michail D.; Cornford, Dan; Opper, Manfred and Shen, Yuan (2010). A variational basis function approximation for diffusion processes. Neurocomputing, 73 (7-9), pp. 1186-1198. DOI 10.1016/j.neucom.2009.11.026
Accepted author manuscript, 183 KB

http://dx.doi.org/10.1016/j.neucom.2009.11.026

Cite this

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title = "A new variational radial basis function approximation for inference in multivariate diffusions",

abstract = "In this paper we present a radial basis function based extension to a recently proposed variational algorithm for approximate inference for diffusion processes. Inference, for state and in particular (hyper-) parameters, in diffusion processes is a challenging and crucial task. We show that the new radial basis function approximation based algorithm converges to the original algorithm and has beneficial characteristics when estimating (hyper-)parameters. We validate our new approach on a nonlinear double well potential dynamical system.",

keywords = "radial basis functions, dynamical systems, stochastic differential equations, parameter estimation, Bayesian inference",

author = "Vrettas, {Michail D.} and Dan Cornford and Manfred Opper and Yuan Shen",

note = "NOTICE: this is the author{\textquoteright}s version of a work that was accepted for publication in Neurocomputing. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Vrettas, Michail D.; Cornford, Dan; Opper, Manfred and Shen, Yuan (2010). A variational basis function approximation for diffusion processes. Neurocomputing, 73 (7-9), pp. 1186-1198. DOI 10.1016/j.neucom.2009.11.026; 17th European Symposium on Artificial Neural Networks : Advances in Computational Intelligence and Learning, ESANN 2009 ; Conference date: 22-04-2009 Through 24-04-2009",

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AU - Vrettas, Michail D.

AU - Cornford, Dan

AU - Opper, Manfred

AU - Shen, Yuan

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AB - In this paper we present a radial basis function based extension to a recently proposed variational algorithm for approximate inference for diffusion processes. Inference, for state and in particular (hyper-) parameters, in diffusion processes is a challenging and crucial task. We show that the new radial basis function approximation based algorithm converges to the original algorithm and has beneficial characteristics when estimating (hyper-)parameters. We validate our new approach on a nonlinear double well potential dynamical system.

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KW - dynamical systems

KW - stochastic differential equations

KW - parameter estimation

KW - Bayesian inference

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JF - Neurocomputing

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T2 - 17th European Symposium on Artificial Neural Networks

Y2 - 22 April 2009 through 24 April 2009

ER -

A new variational radial basis function approximation for inference in multivariate diffusions

Abstract

Bibliographical note

Keywords

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