提出新型采样算法NETS,提升复杂分布采样效率与精度。
NETS: A Non-Equilibrium Transport Sampler
- 基于非平衡输运原理,引入可学习漂移项降低偏差权重影响。
- 理论证明能控制目标分布的KL散度,且采样无偏,有效样本量可调。
- 适用于高维混合高斯和格点场论模型,性能优于现有方法。
我们提出一种名为非平衡输运采样器(NETS)的算法,用于从未归一化的概率分布中采样。NETS可视为基于Jarzynski等式的变体退火重要性采样(AIS),其随机微分方程通过加入一个可学习的漂移项,降低了AIS中使用的无偏权重的影响。我们证明该漂移项是最小化多种目标函数的解,这些目标函数均可在不反向传播求解随机微分方程的情况下无偏估计。此外,我们证明其中某些目标函数可控制估计分布与目标分布之间的Kullback-Leibler散度。NETS被证明是无偏的,并具有可调节的扩散系数,可在训练后调整以最大化有效样本量。我们在标准基准、高维高斯混合分布以及统计格点场论模型上验证了该方法的有效性,结果表明其性能超越相关工作与现有基线。
原文摘要 · Abstract (English)
We propose an algorithm, termed the Non-Equilibrium Transport Sampler (NETS), to sample from unnormalized probability distributions. NETS can be viewed as a variant of annealed importance sampling (AIS) based on Jarzynski's equality, in which the stochastic differential equation used to perform the non-equilibrium sampling is augmented with an additional learned drift term that lowers the impact of the unbiasing weights used in AIS. We show that this drift is the minimizer of a variety of objective functions, which can all be estimated in an unbiased fashion without backpropagating through solutions of the stochastic differential equations governing the sampling. We also prove that some these objectives control the Kullback-Leibler divergence of the estimated distribution from its target. NETS is shown to be unbiased and, in addition, has a tunable diffusion coefficient which can be adjusted post-training to maximize the effective sample size. We demonstrate the efficacy of the method on standard benchmarks, high-dimensional Gaussian mixture distributions, and a model from statistical lattice field theory, for which it surpasses the performances of related work and existing baselines.
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