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Scalable Inference in SDEs by Direct Matching of the Fokker–Planck–Kolmogorov Equation
Arno Solin · Ella Tamir · Prakhar Verma

Tue Dec 07 08:30 AM -- 10:00 AM (PST) @ None #None

Simulation-based techniques such as variants of stochastic Runge–Kutta 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 Runge–Kutta 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) Fokker–Planck–Kolmogorov 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.

Author Information

Arno Solin (Aalto University)
Ella Tamir (Aalto University)
Prakhar Verma (Aalto University)

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