# Structured Variational Inference in Unstable Gaussian Process State Space Models

arXiv: https://arxiv.org/abs/1907.07035 · HTML: https://mlsanity.com/paper/1907.07035/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jul 2019.

## Built on by (most cited first, 1 of 1)

- [Likelihood-Free Inference in State-Space Models with Unknown Dynamics](https://mlsanity.com/paper/2111.01555/) (2021)

## Abstract (arXiv)

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.