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Importance sampling with nonequilibrium trajectories

Banff International Research Station for Mathematical Innovation and Discovery

Sampling with a dynamics that breaks detailed balance poses a challenge because the steady state probability is not typically known. In some cases, most notably in uses of the Jarzynski estimator in statistical physics, astrophysics, and machine learning, it is possible to estimate an equilibrium average using nonequilibrium dynamics. Here, we derive a generic importance sampling technique that leverages the statistical power of configurations that have been transported by nonequilibrium trajectories. Our approach can be viewed as a continuous generalization of the Jarzynski equality that can be used to compute averages with respect to arbitrary target distributions. We illustrate the properties of estimators relying on this sampling technique in the context of density of state calculations, showing that it scales favorable with dimensionality. We also demonstrate the robustness and efficiency of the approach with an application to a Bayesian model comparison problem of the type encountered in astrophysics and machine learning. This is joint work with Grant Rotskoff (https://arxiv.org/abs/1809.11132)

Mathematics; Statistics; Statistical mechanics, structure of matter; Statistical mechanics

video/mp4

Author affiliation: Courant Institute

2019-05-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/70185

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/