Dynamical Computation of the Density of States and Bayes Factors Using Nonequilibrium Importance Sampling

Grant M. Rotskoff, Eric Vanden Eijnden

Research output: Contribution to journalArticle

Abstract

Nonequilibrium sampling is potentially much more versatile than its equilibrium counterpart, but it comes with challenges because the invariant distribution is not typically known when the dynamics breaks detailed balance. Here, we derive a generic importance sampling technique that leverages the statistical power of configurations transported by nonequilibrium trajectories and can be used to compute averages with respect to arbitrary target distributions. As a dissipative reweighting scheme, the method can be viewed in relation to the annealed importance sampling (AIS) method and the related Jarzynski equality. Unlike AIS, our approach gives an unbiased estimator, with a provably lower variance than directly estimating the average of an observable. We also establish a direct relation between a dynamical quantity, the dissipation, and the volume of phase space, from which we can compute quantities such as the density of states and Bayes factors. 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 - in particular, we show that it can be used to compute the phase diagram of the mean-field Ising model from a single nonequilibrium trajectory. 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.

Original languageEnglish (US)
Article number150602
JournalPhysical Review Letters
Volume122
Issue number15
DOIs
StatePublished - Apr 16 2019

Fingerprint

sampling
estimators
trajectories
machine learning
learning
Ising model
astrophysics
estimating
dissipation
phase diagrams
configurations

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Dynamical Computation of the Density of States and Bayes Factors Using Nonequilibrium Importance Sampling. / Rotskoff, Grant M.; Vanden Eijnden, Eric.

In: Physical Review Letters, Vol. 122, No. 15, 150602, 16.04.2019.

Research output: Contribution to journalArticle

@article{5ea35ce54d854410bc8a61c76eecb5ed,
title = "Dynamical Computation of the Density of States and Bayes Factors Using Nonequilibrium Importance Sampling",
abstract = "Nonequilibrium sampling is potentially much more versatile than its equilibrium counterpart, but it comes with challenges because the invariant distribution is not typically known when the dynamics breaks detailed balance. Here, we derive a generic importance sampling technique that leverages the statistical power of configurations transported by nonequilibrium trajectories and can be used to compute averages with respect to arbitrary target distributions. As a dissipative reweighting scheme, the method can be viewed in relation to the annealed importance sampling (AIS) method and the related Jarzynski equality. Unlike AIS, our approach gives an unbiased estimator, with a provably lower variance than directly estimating the average of an observable. We also establish a direct relation between a dynamical quantity, the dissipation, and the volume of phase space, from which we can compute quantities such as the density of states and Bayes factors. 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 - in particular, we show that it can be used to compute the phase diagram of the mean-field Ising model from a single nonequilibrium trajectory. 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.",
author = "Rotskoff, {Grant M.} and {Vanden Eijnden}, Eric",
year = "2019",
month = "4",
day = "16",
doi = "10.1103/PhysRevLett.122.150602",
language = "English (US)",
volume = "122",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "15",

}

TY - JOUR

T1 - Dynamical Computation of the Density of States and Bayes Factors Using Nonequilibrium Importance Sampling

AU - Rotskoff, Grant M.

AU - Vanden Eijnden, Eric

PY - 2019/4/16

Y1 - 2019/4/16

N2 - Nonequilibrium sampling is potentially much more versatile than its equilibrium counterpart, but it comes with challenges because the invariant distribution is not typically known when the dynamics breaks detailed balance. Here, we derive a generic importance sampling technique that leverages the statistical power of configurations transported by nonequilibrium trajectories and can be used to compute averages with respect to arbitrary target distributions. As a dissipative reweighting scheme, the method can be viewed in relation to the annealed importance sampling (AIS) method and the related Jarzynski equality. Unlike AIS, our approach gives an unbiased estimator, with a provably lower variance than directly estimating the average of an observable. We also establish a direct relation between a dynamical quantity, the dissipation, and the volume of phase space, from which we can compute quantities such as the density of states and Bayes factors. 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 - in particular, we show that it can be used to compute the phase diagram of the mean-field Ising model from a single nonequilibrium trajectory. 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.

AB - Nonequilibrium sampling is potentially much more versatile than its equilibrium counterpart, but it comes with challenges because the invariant distribution is not typically known when the dynamics breaks detailed balance. Here, we derive a generic importance sampling technique that leverages the statistical power of configurations transported by nonequilibrium trajectories and can be used to compute averages with respect to arbitrary target distributions. As a dissipative reweighting scheme, the method can be viewed in relation to the annealed importance sampling (AIS) method and the related Jarzynski equality. Unlike AIS, our approach gives an unbiased estimator, with a provably lower variance than directly estimating the average of an observable. We also establish a direct relation between a dynamical quantity, the dissipation, and the volume of phase space, from which we can compute quantities such as the density of states and Bayes factors. 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 - in particular, we show that it can be used to compute the phase diagram of the mean-field Ising model from a single nonequilibrium trajectory. 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.

UR - http://www.scopus.com/inward/record.url?scp=85064844240&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064844240&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.122.150602

DO - 10.1103/PhysRevLett.122.150602

M3 - Article

C2 - 31050526

AN - SCOPUS:85064844240

VL - 122

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 15

M1 - 150602

ER -