Rich and complex time-series data, such as those generated from engineering
systems, financial markets, videos or neural recordings, are now a common
feature of modern data analysis. Explaining the phenomena underlying these
diverse data sets requires flexible and accurate models. In this paper, we
promote Gaussian process dynamical systems (GPDS) as a rich model class that is
appropriate for such analysis. In particular, we present a message passing
algorithm for approximate inference in GPDSs based on expectation propagation.
By posing inference as a general message passing problem, we iterate
forward-backward smoothing. Thus, we obtain more accurate posterior
distributions over latent structures, resulting in improved predictive
performance compared to state-of-the-art GPDS smoothers, which are special
cases of our general message passing algorithm. Hence, we provide a unifying
approach within which to contextualize message passing in GPDSs.