Stochastic Differential Equations with Variational Wishart Diffusions

Martin Jørgensen; Marc Peter Deisenroth; Hugh Salimbeni

Stochastic Differential Equations with Variational Wishart Diffusions

Martin Jørgensen^*
, Marc Peter Deisenroth
, Hugh Salimbeni

^*Corresponding author for this work

University College London
G-Research

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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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 lead 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.

Original language	English
Title of host publication	Proceedings of 37^th International Conference on Machine Learning
Editors	Hal Daume, Aarti Singh
Volume	119
Publisher	International Machine Learning Society (IMLS)
Publication date	2020
Pages	4941-4950
ISBN (Electronic)	9781713821120
Publication status	Published - 2020
Event	37^th International Conference on Machine Learning - Virtual event, Virtual, Online Duration: 13 Jul 2020 → 18 Jul 2020 https://icml.cc/Conferences/2020

Conference

Conference	37^th International Conference on Machine Learning
Location	Virtual event
City	Virtual, Online
Period	13/07/2020 → 18/07/2020
Internet address	https://icml.cc/Conferences/2020

Bibliographical note

Funding Information:
MJ was supported by a research grant (15334) from VIL-LUM FONDEN.

Publisher Copyright:
© 2020 by the Authors.

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title = "Stochastic Differential Equations with Variational Wishart Diffusions",

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 lead 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.",

author = "Martin J{\o}rgensen and Deisenroth, \{Marc Peter\} and Hugh Salimbeni",

note = "Funding Information: MJ was supported by a research grant (15334) from VIL-LUM FONDEN. Publisher Copyright: {\textcopyright} 2020 by the Authors.; 37<sup>th</sup> International Conference on Machine Learning, ICML 2020 ; Conference date: 13-07-2020 Through 18-07-2020",

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language = "English",

volume = "119",

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Stochastic Differential Equations with Variational Wishart Diffusions. / Jørgensen, Martin; Deisenroth, Marc Peter; Salimbeni, Hugh.
Proceedings of 37^th International Conference on Machine Learning. ed. / Hal Daume; Aarti Singh. Vol. 119 International Machine Learning Society (IMLS), 2020. p. 4941-4950.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Stochastic Differential Equations with Variational Wishart Diffusions

AU - Jørgensen, Martin

AU - Deisenroth, Marc Peter

AU - Salimbeni, Hugh

PY - 2020

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N2 - 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 lead 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.

AB - 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 lead 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.

M3 - Article in proceedings

AN - SCOPUS:85103748177

VL - 119

SP - 4941

EP - 4950

BT - Proceedings of 37th International Conference on Machine Learning

A2 - Daume, Hal

A2 - Singh, Aarti

PB - International Machine Learning Society (IMLS)

T2 - 37<sup>th</sup> International Conference on Machine Learning

Y2 - 13 July 2020 through 18 July 2020

ER -

Stochastic Differential Equations with Variational Wishart Diffusions

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