Constructing a variational family for nonlinear state-space models

We consider the problem of maximum likelihood parameter estimation for nonlinear state-space models. This is an important, but challenging problem. This challenge stems from the intractable multidimensional integrals that must be solved in order to compute, and maximise, the likelihood. Here we present a new variational family where variational inference is used in combination with tractable approximations of these integrals resulting in a deterministic optimisation problem. Our developments also include a novel means for approximating the smoothed state distributions. We demonstrate our construction on several examples and show that they perform well compared to state of the art methods on real data-sets.