Stability Enhanced Gaussian Process Variational Autoencoders

TL;DR

The paper introduces SEGP-VAE, a stability-enhanced Gaussian process variational autoencoder that models low-dimensional LTI systems from high-dimensional video data, ensuring stability and interpretability.

Contribution

It develops a novel SEGP prior derived from LTI system definitions, enabling stable, unconstrained training of the model with improved physical interpretability.

Findings

Successfully applied to videos of spiralling particles with accurate latent state predictions.

The parametrisation prevents numerical issues related to non-Hurwitz matrices.

Enables training using unconstrained optimisation algorithms.

Abstract

A novel stability-enhanced Gaussian process variational autoencoder (SEGP-VAE) is proposed for indirectly training a low-dimensional linear time invariant (LTI) system, using high-dimensional video data. The mean and covariance function of the novel SEGP prior are derived from the definition of an LTI system, enabling the SEGP to capture the indirectly observed latent process using a combined probabilistic and interpretable physical model. The search space of LTI parameters is restricted to the set of semi-contracting systems via a complete and unconstrained parametrisation. As a result, the SEGP-VAE can be trained using unconstrained optimisation algorithms. Furthermore, this parametrisation prevents numerical issues caused by the presence of a non-Hurwitz state matrix. A case study applies SEGP-VAE to a dataset containing videos of spiralling particles. This highlights the benefits of the approach and the application-specific design choices that enabled accurate latent state predictions.