  Latent variable time-series models are among the most heavily used tools from
machine learning and applied statistics. These models have the advantage of
learning latent structure both from noisy observations and from the temporal
ordering in the data, where it is assumed that meaningful correlation structure
exists across time. A few highly-structured models, such as the linear
dynamical system with linear-Gaussian observations, have closed-form inference
procedures (e.g. the Kalman Filter), but this case is an exception to the
general rule that exact posterior inference in more complex generative models
is intractable. Consequently, much work in time-series modeling focuses on
approximate inference procedures for one particular class of models. Here, we
extend recent developments in stochastic variational inference to develop a
`black-box' approximate inference technique for latent variable models with
latent dynamical structure. We propose a structured Gaussian variational
approximate posterior that carries the same intuition as the standard Kalman
filter-smoother but, importantly, permits us to use the same inference approach
to approximate the posterior of much more general, nonlinear latent variable
generative models. We show that our approach recovers accurate estimates in the
case of basic models with closed-form posteriors, and more interestingly
performs well in comparison to variational approaches that were designed in a
bespoke fashion for specific non-conjugate models.
