Scalable inference in SDEs by direct matching of the Fokker–Planck–Kolmogorov equation

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Conference article in proceedings
Date
2021
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Language
en
Pages
13
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Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021), Advances in Neural Information Processing Systems
Abstract
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.
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Solin , A , Tamir , E & Verma , P 2021 , Scalable inference in SDEs by direct matching of the Fokker–Planck–Kolmogorov equation . in Advances in Neural Information Processing Systems 34 pre-proceedings (NeurIPS 2021) . Advances in Neural Information Processing Systems , Morgan Kaufmann Publishers , Conference on Neural Information Processing Systems , Virtual, Online , 06/12/2021 . < https://papers.nips.cc/paper/2021/hash/03e4d3f831100d4355663f3d425d716b-Abstract.html >