Stochastic Differential Equations with Variational Wishart Diffusions

Martin Jørgensen, Marc Deisenroth, Hugh Salimbeni
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:4974-4983, 2020.

Abstract

We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also known as the diffusion, and modelling it by means of Wishart processes. Further, we present a semiparametric approach that allows the framework to scale to high dimensions. This successfully leads us onto how to model both latent and autoregressive temporal systems with conditional heteroskedastic noise. We provide experimental evidence that modelling diffusion often improves performance and that this randomness in the differential equation can be essential to avoid overfitting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-jorgensen20a, title = {Stochastic Differential Equations with Variational Wishart Diffusions}, author = {J{\o}rgensen, Martin and Deisenroth, Marc and Salimbeni, Hugh}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {4974--4983}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/jorgensen20a/jorgensen20a.pdf}, url = {https://proceedings.mlr.press/v119/jorgensen20a.html}, abstract = {We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also known as the diffusion, and modelling it by means of Wishart processes. Further, we present a semiparametric approach that allows the framework to scale to high dimensions. This successfully leads us onto how to model both latent and autoregressive temporal systems with conditional heteroskedastic noise. We provide experimental evidence that modelling diffusion often improves performance and that this randomness in the differential equation can be essential to avoid overfitting.} }
Endnote
%0 Conference Paper %T Stochastic Differential Equations with Variational Wishart Diffusions %A Martin Jørgensen %A Marc Deisenroth %A Hugh Salimbeni %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-jorgensen20a %I PMLR %P 4974--4983 %U https://proceedings.mlr.press/v119/jorgensen20a.html %V 119 %X We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also known as the diffusion, and modelling it by means of Wishart processes. Further, we present a semiparametric approach that allows the framework to scale to high dimensions. This successfully leads us onto how to model both latent and autoregressive temporal systems with conditional heteroskedastic noise. We provide experimental evidence that modelling diffusion often improves performance and that this randomness in the differential equation can be essential to avoid overfitting.
APA
Jørgensen, M., Deisenroth, M. & Salimbeni, H.. (2020). Stochastic Differential Equations with Variational Wishart Diffusions. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:4974-4983 Available from https://proceedings.mlr.press/v119/jorgensen20a.html.

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