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.
|Title of host publication||Proceedings of 37th International Conference on Machine Learning|
|Editors||Hal Daume, Aarti Singh|
|Publisher||International Machine Learning Society (IMLS)|
|Publication status||Published - 2020|
|Event||37th International Conference on Machine Learning - Virtual event, Virtual, Online|
Duration: 13 Jul 2020 → 18 Jul 2020
|Conference||37th International Conference on Machine Learning|
|Period||13/07/2020 → 18/07/2020|
Bibliographical noteFunding Information:
MJ was supported by a research grant (15334) from VIL-LUM FONDEN.
© 2020 by the Authors.