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

In this paper we derive and present a new radial basis function framework that extends a recently proposed variational Bayesian algorithm for approximate inference in diffusion processes. Inference, for the state and in particular for the (hyper-) parameters, in such systems is a challenging and crucial task. We show that the new radial basis function approximation based algorithm not only converges to the original variational algorithm but also has beneficial characteristics when estimating (hyper-) parameters. We validate our new approach on three highly non-linear dynamical systems, namely the univariate stochastic double well, and the multivariate Lorenz 3D and Lorenz 40D systems. We show that we are able to recover good estimates of the system and noise parameters in the multivariate case, even for chaotic systems.