Stochastic Differential Equations with Variational Wishart Diffusions
This work addresses modeling uncertainty in continuous-time systems for applications like regression and dynamics, but it appears incremental as it builds on existing Bayesian non-parametric and Wishart process methods.
The authors tackled the problem of inferring stochastic differential equations for regression and dynamical modeling by focusing on modeling the diffusion (stochastic part) using Wishart processes, with a semi-parametric approach for scalability. They found that modeling diffusion improves performance and is essential to avoid overfitting, though no concrete numbers are provided.
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.