PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

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.

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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.

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EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:3134
Deposited By:Cedric Archambeau
Deposited On:21 December 2007

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