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.
Lea Duncker (Gatsby Unit, UCL)
Gergo Bohner (Gatsby Unit, UCL)
Julien Boussard (Stanford university)
Maneesh Sahani (Gatsby Unit, UCL)
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2019 Poster: Learning interpretable continuous-time models of latent stochastic dynamical systems »
Wed Jun 12th 06:30 -- 09:00 PM Room Pacific Ballroom