Duncker, L; Bohner, G; Boussard, J; Sahani, M; (2019) Learning interpretable continuous-time models of latent stochastic dynamical systems. In: Salakhutdinov, Ruslan and Chaudhuri, Kamalika, (eds.) Proceedings of the 36th International Conference on Machine Learning (ICML 2019). PMLR (Proceedings of Machine Learning Research): Long Beach, CA, USA.

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Abstract

We develop an approach to learn an interpretable semi-parametric model of a latent continuoustime 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.

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