Dynamical Computation of the Density of States and Bayes Factors Using Nonequilibrium Importance Sampling.
Dynamical Computation of the Density of States and Bayes Factors Using Nonequilibrium Importance Sampling.
复制标题
使用非平衡重要性采样动态计算状态密度和贝叶斯因子。
DOI：
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发表时间：
2018
影响因子：
8.6
通讯作者：
E. Vanden
中科院分区：
文献类型：
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作者：
Grant M. Rotskoff;E. Vanden
非平衡采样可能比平衡采样更通用，但它也带来了挑战，因为当动态打破详细平衡时，通常不知道不变分布。在这里，我们得到一个通用的重要性抽样技术，利用非平衡轨迹传输的配置的统计功率，并可用于计算平均值相对于任意目标分布。作为一个耗散的重新加权计划，该方法可以被视为退火重要性抽样（AIS）方法和相关的Jarzynski等式。与AIS不同，我们的方法提供了一个无偏估计器，其方差可证明低于直接估计可观察值的平均值。我们还建立了动力学量，耗散和相空间的体积之间的直接关系，从中我们可以计算诸如态密度和贝叶斯因子之类的量。我们说明的估计依赖于这种采样技术的状态密度计算的背景下，显示它的规模有利的维度，特别是，我们表明，它可以用来计算的平均场伊辛模型从一个单一的非平衡轨迹的相图的属性。我们还展示了该方法的鲁棒性和效率，并将其应用于天体物理学和机器学习中遇到的贝叶斯模型比较问题。
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.
影响因子：
44.1
作者：
Bechinger, Clemens;Di Leonardo, Roberto;Volpe, Giovanni
通讯作者：
Volpe, Giovanni