A variational approach to sampling in diffusion processes

Maxim Raginsky

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arXiv · 2405.00126

A variational approach to sampling in diffusion processes

Maxim Raginsky

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Abstract

We revisit the work of Mitter and Newton on an information-theoretic interpretation of Bayes' formula through the Gibbs variational principle. This formulation allowed them to pose nonlinear estimation for diffusion processes as a problem in stochastic optimal control, so that the posterior density of the signal given the observation path could be sampled by adding a drift to the signal process. We show that this control-theoretic approach to sampling provides a common mechanism underlying several distinct problems involving diffusion processes, specifically importance sampling using Feynman-Kac averages, time reversal, and Schr\"odinger bridges.

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Maxim Raginsky. 2024-04-30. A variational approach to sampling in diffusion processes. https://arxiv.org/abs/2405.00126

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