Learning interpretable continuoustime models of latent stochastic dynamical systems
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:17261734, 2019.
Abstract
We develop an approach to learn an interpretable semiparametric model of a latent continuoustime stochastic dynamical system, assuming noisy highdimensional 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.
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