Time Series Prediction with Variational Bayesian Nonlinear State-Space Models
Matti Tornio, Antti Honkela and Juha Karhunen
In: European Symposium on Time Series Prediction (ESTSP 2007), 7-9 Feb 2007, Espoo, Finland.
In this paper the variational Bayesian method for learning
nonlinear state-space models
introduced by Valpola and Karhunen in 2002 is applied to
prediction in the ESTSP'07 time series
prediction competition data set.
The data set is pre-processed by approximately removing the
periodic component of the data and the nonlinear state-space model
is only learned on the residuals.
The model uses multilayer perceptron (MLP)
networks to model the nonlinearities of the system which allows the
modelling of complex dynamical processes.
The variational Bayesian learning approach is resistant to
overfitting and allows comparison of
different model structures using the derived lower
bound on marginal log-likelihood.
The desired predictions are evaluated as the mean of a Monte Carlo
approximation of the predictive distribution.