# Stochastic Differential Equations with Variational Wishart Diffusions

arXiv: https://arxiv.org/abs/2006.14895 · HTML: https://mlsanity.com/paper/2006.14895/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Variational multiple shooting for Bayesian ODEs with Gaussian processes](https://mlsanity.com/paper/2106.10905/) (2021)
- [A variational approximate posterior for the deep Wishart process](https://mlsanity.com/paper/2107.10125/) (2021)
- [E2V-SDE: From Asynchronous Events to Fast and Continuous Video Reconstruction via Neural Stochastic Differential Equations](https://mlsanity.com/paper/2206.07578/) (2022)
- [Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo](https://mlsanity.com/paper/2406.04796/) (2024)

## Abstract (arXiv)

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.