Identification of Gaussian Process State Space Models
This addresses the system identification problem for researchers and practitioners in non-linear dynamical systems, representing an incremental improvement over prior work focused on state estimation.
The paper tackles the challenge of system identification in Gaussian process state space models (GPSSMs) by introducing a structured Gaussian variational posterior parameterized by a bi-directional recurrent neural network, enabling efficient learning and generation of plausible future trajectories after observing only a few episodes.
The Gaussian process state space model (GPSSM) is a non-linear dynamical system, where unknown transition and/or measurement mappings are described by GPs. Most research in GPSSMs has focussed on the state estimation problem, i.e., computing a posterior of the latent state given the model. However, the key challenge in GPSSMs has not been satisfactorily addressed yet: system identification, i.e., learning the model. To address this challenge, we impose a structured Gaussian variational posterior distribution over the latent states, which is parameterised by a recognition model in the form of a bi-directional recurrent neural network. Inference with this structure allows us to recover a posterior smoothed over sequences of data. We provide a practical algorithm for efficiently computing a lower bound on the marginal likelihood using the reparameterisation trick. This further allows for the use of arbitrary kernels within the GPSSM. We demonstrate that the learnt GPSSM can efficiently generate plausible future trajectories of the identified system after only observing a small number of episodes from the true system.