Poster
Stochastic Differential Equations with Variational Wishart Diffusions
Martin Jørgensen · Marc Deisenroth · Hugh Salimbeni
Keywords: [ Probabilistic Inference - Models and Probabilistic Programming ] [ Time Series and Sequence Models ] [ Gaussian Processes ] [ Bayesian Nonparametrics ] [ Approximate Inference ]
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.