Expectation Propagation in Gaussian Process Dynamical Systems: Extended Version

TL;DR

This paper introduces an expectation propagation-based message passing algorithm for Gaussian process dynamical systems, enhancing inference accuracy and predictive performance on complex time-series data compared to existing methods.

Contribution

It presents a unified message passing framework for GPDS inference using expectation propagation, improving upon previous smoothers with more accurate posterior estimates.

Findings

Enhanced posterior distributions over latent variables.

Improved predictive accuracy over state-of-the-art GPDS smoothers.

Unified message passing approach for Gaussian process dynamical systems.

Abstract

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.