Variational Bayes for Continuous-Time Nonlinear State-Space Models
Antti Honkela, Matti Tornio and Tapani Raiko
In: NIPS*2006 Workshop on Dynamical Systems, Stochastic Processes and Bayesian Inference, 2006, Whistler, B.C., Canada.
We present an extension of the variational Bayesian nonlinear state-space model introduced by Valpola and Karhunen in 2002  for continuous-time models. The model is based on using multilayer perceptron (MLP) networks to model the nonlinearities. Moving to continuous-time requires solving a stochastic differential equation (SDE) to evaluate the predictive distribution of the states, but otherwise all computation happens as in the discrete-time case. The close connection between the methods allows utilising our new improved state inference method for both discrete-time and continuous-time modelling.