Stochastic Differential Equations with Variational Wishart Diffusions

TL;DR

This paper introduces a Bayesian non-parametric framework for inferring stochastic differential equations with Wishart process-based diffusion, enabling high-dimensional modeling of temporal systems with heteroskedastic noise and demonstrating improved performance and overfitting avoidance.

Contribution

It proposes a novel semi-parametric Bayesian approach for modeling diffusion in stochastic differential equations using Wishart processes, scalable to high dimensions.

Findings

Modeling diffusion enhances predictive performance.

The approach effectively captures heteroskedastic noise.

Stochastic modeling helps prevent overfitting.

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.