Gaussian Process-Based Representation Learning via Timeseries Symmetries

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.