论文标题
具有变化的欲望扩散的随机微分方程
Stochastic Differential Equations with Variational Wishart Diffusions
论文作者
论文摘要
我们提出了一种用于回归任务和连续时间动态建模的随机微分方程的贝叶斯非参数方式。这项工作高度强调了微分方程的随机部分，也称为扩散，并通过WishArt过程对其进行建模。此外，我们提出了一种半参数方法，该方法使框架可以扩展到高维度。这成功地使我们进入了如何使用条件异质噪声对潜在和自动回归时间系统进行建模。我们提供了实验证据，表明建模扩散通常会改善性能，并且微分方程中的这种随机性对于避免过度拟合至关重要。
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.
