Learning interpretable continuous-time models of latent stochastic dynamical systems

Lea Duncker, Gergo Bohner, Julien Boussard, Maneesh Sahani
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:1726-1734, 2019.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T Learning interpretable continuous-time models of latent stochastic dynamical systems %A Lea Duncker %A Gergo Bohner %A Julien Boussard %A Maneesh Sahani %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-duncker19a %I PMLR %P 1726--1734 %U https://proceedings.mlr.press/v97/duncker19a.html %V 97 %X 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.
APA
Duncker, L., Bohner, G., Boussard, J. & Sahani, M.. (2019). Learning interpretable continuous-time models of latent stochastic dynamical systems. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:1726-1734 Available from https://proceedings.mlr.press/v97/duncker19a.html.

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