Structured Variational Inference in Unstable Gaussian Process State Space Models
This work addresses a problem in machine learning for dynamical systems where previous algorithms fail, but it appears incremental as it builds on existing variational methods with modifications.
The authors tackled learning in unstable and partially observable Gaussian Process State-Space Models (GPSSMs) by proposing a new variational inference algorithm, which performs well in stable and unstable real systems with hidden states.
We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic contribution is a novel approximate posterior that can be calculated efficiently using a single forward and backward pass along the training trajectories. The forward-backward pass is inspired on Kalman smoothing for linear dynamical systems but generalizes to GPSSMs. Our second contribution is a modification of the conditioning step that effectively lowers the Kalman gain. This modification is crucial to attaining good test performance where no measurements are available. Finally, we show experimentally that our learning algorithm performs well in stable and unstable real systems with hidden states.