Gaussian Process-Based Representation Learning via Timeseries Symmetries

Petar Bevanda, Max Beier, Armin Lederer, Alexandre Capone, Stefan Georg Sosnowski, Sandra Hirche

Track: Extended abstract

Keywords: Representation Learning, Dynamical Systems, Gaussian Processes, Koopman Operator, Equivariance

TL;DR: We introduce a new family of Gaussian processes for dynamical systems with linear time-invariant responses, exploiting a timeseries symmetry to facilitate efficient representation learning.

Abstract:

Credible forecasting and representation learning
of dynamical systems are of ever-increasing importance for reliable decision-making. To that
end, we propose a family of Gaussian processes for dynamical systems with linear time-invariant
responses, which are nonlinear only in initial conditions. This linearity allows us to tractably quantify both forecasting and representational uncertainty simultaneously — alleviating the traditional
challenge of multistep uncertainty propagation in GP models and enabling a new probabilistic treatment of learning representations. Using a novel data-based symmetrization, we improve the generalization ability of Gaussian processes and obtain tractable, continuous-time posteriors without the
need for multiple models or approximate uncertainty propagation.

Submission Number: 28