Poster
in
Workshop: Geometry-grounded Representation Learning and Generative Modeling
Gaussian Process-Based Representation Learning via Timeseries Symmetries
Petar Bevanda · Max Beier · Armin Lederer · Alexandre Capone · Stefan Sosnowski · Sandra Hirche
Keywords: [ Representation Learning ] [ Equivariance ] [ Dynamical Systems ] [ Gaussian Processes ] [ Koopman Operator ]
Credible forecasting and representation learningof dynamical systems are of ever-increasing importance for reliable decision-making. To thatend, we propose a family of Gaussian processes for dynamical systems with linear time-invariantresponses, which are nonlinear only in initial conditions. This linearity allows us to tractably quantify both forecasting and representational uncertainty simultaneously — alleviating the traditionalchallenge 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 theneed for multiple models or approximate uncertainty propagation.