Scalable Inference in SDEs by Direct Matching of the Fokkeru2013Plancku2013Kolmogorov Equation
Arno Solin,Ella Tamir,Prakhar Verma
Simulation-based techniques such as variants of stochastic Rungeu2013Kutta are the de facto approach for inference with stochastic differential equations (SDEs) in machine learning. These methods are general-purpose and used with parametric and non-parametric models, and neural SDEs. Stochastic Rungeu2013Kutta relies on the use of sampling schemes that can be inefficient in high dimensions. We address this issue by revisiting the classical SDE literature and derive direct approximations to the (typically intractable) Fokkeru2013Plancku2013Kolmogorov equation by matching moments. We show how this workflow is fast, scales to high-dimensional latent spaces, and is applicable to scarce-data applications, where a non-parametric SDE with a driving Gaussian process velocity field specifies the model.
