Learning interpretable continuous-time models of latent stochastic dynamical systems
This work addresses the challenge of modeling complex, latent stochastic dynamics for researchers in fields like systems biology or physics, though it appears incremental as it builds on existing methods like Gaussian processes and sparse variational inference.
The authors tackled the problem of learning interpretable continuous-time models of latent stochastic dynamical systems from noisy, unevenly sampled high-dimensional data, and demonstrated their approach on simulated nonlinear dynamical systems.
We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear stochastic differential equation (SDE) driven by a Wiener process, with a drift evolution function drawn from a Gaussian process (GP) conditioned on a set of learnt fixed points and corresponding local Jacobian matrices. This form yields a flexible nonparametric model of the dynamics, with a representation corresponding directly to the interpretable portraits routinely employed in the study of nonlinear dynamical systems. The learning algorithm combines inference of continuous latent paths underlying observed data with a sparse variational description of the dynamical process. We demonstrate our approach on simulated data from different nonlinear dynamical systems.