Predicting Latent States of Dynamical Systems With State-Space Reconstruction and Gaussian Processes

Predicting future observations of a system is a classical task in signal processing. However the effects of nonlinear dynamics, unobserved variables and observation noise make this task difficult in practice. We propose a data-driven non-parametric approach to model systems with latent dynamics using state-space reconstruction and Gaussian processes. With this approach, both latent states and future observations can be predicted together. When applicable, this method is efficient even with short time series. We demonstrate the method on synthetic data and then showcase its efficacy and accuracy in predicting brain dynamics on a data set obtained from traumatic brain injury patients.