BLACK BOX VARIATIONAL INFERENCE FOR STATE SPACE MODELS
Authors: Evan Archer, Il Memming Park, Lars Buesing, John Cunningham, Liam Paninski

Abstract: 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.