Bayesian Delay Embeddings for Dynamical Systems

Selecting a suitable embedding space is a key issue in modelling nonlinear dynamics. In classical phase-space reconstruction, which relies on time-delay vectors, the embedding space is highly dependent on two discrete parameters (for the univariate case), the values of which greatly affect model performance. They also determine the complexity of the dynamics topology. In consequence, the parameters and dynamics are intimately linked. Thus we propose a modelling framework that jointly models the embedding dynamics and parameters, in a Bayesian fashion by framing the learning problem in terms of variational inference over model parameters. We compare our methods to other models on noisy synthetic observations.