Stochastic Differential Equations with Variational Wishart Diffusions

• URL: http://arxiv.org/abs/2006.14895v1
• Date: Fri, 26 Jun 2020 10:21:35 GMT
• Title: Stochastic Differential Equations with Variational Wishart Diffusions
• Authors: Martin J{\o}rgensen, Marc Peter Deisenroth, Hugh Salimbeni
• Abstract summary: We present a non-parametric way of inferring differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the part of the differential equation, also known as the diffusion, and modelling it by means of Wishart processes.
• Score: 18.590352916158093
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 semi-parametric approach that allows the framework to scale to high dimensions. This successfully lead us onto how to model both latent and auto-regressive 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.

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