A variational approach to sampling in diffusion processes

2024/04/30 by Maxim Raginsky, Raginsky, Maxim · 1 voice · 1 citation
#math.OC #math.PR

paper · pdf · doi:10.48550/arxiv.2405.00126

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 Schrödinger bridges.

Cited by

• Machine-Learned Sampling of Conditioned Path Measures

Discussions

• Gibbs free-energy minimization is everywhere. For example, time-reversal of a diffusion process is free-energy minimization in disguise. arxiv.org/abs/2405.00126 [bsky, 21 points, 0 comments]

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