Scalable Inference in SDEs by Direct Matching of the Fokker-Planck-Kolmogorov Equation

Simulation-based techniques such as variants of stochastic Runge-Kutta are\nthe de facto approach for inference with stochastic differential equations\n(SDEs) in machine learning. These methods are general-purpose and used with\nparametric and non-parametric models, and neural SDEs. Stochastic Runge-Kutta\nrelies on the use of sampling schemes that can be inefficient in high\ndimensions. We address this issue by revisiting the classical SDE literature\nand derive direct approximations to the (typically intractable)\nFokker-Planck-Kolmogorov equation by matching moments. We show how this\nworkflow is fast, scales to high-dimensional latent spaces, and is applicable\nto scarce-data applications, where a non-parametric SDE with a driving Gaussian\nprocess velocity field specifies the model.\n