Learning interpretable continuous-time models of latent stochastic dynamical systems
Lea Duncker, Gergo Bohner, Julien Boussard, Maneesh Sahani
Abstract
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.
BibTeX
@InProceedings{pmlr-v97-duncker19a,
title = {Learning interpretable continuous-time models of latent stochastic dynamical systems},
author = {Duncker, Lea and Bohner, Gergo and Boussard, Julien and Sahani, Maneesh},
booktitle = {Proceedings of the 36th International Conference on Machine Learning},
pages = {1726--1734},
year = {2019},
editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
volume = {97},
series = {Proceedings of Machine Learning Research},
month = {09--15 Jun},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v97/duncker19a/duncker19a.pdf},
url = {https://proceedings.mlr.press/v97/duncker19a.html},
abstract = {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.}
}