提出加速版Stein采样，提升高维采样速度与稳定性。
Accelerated Stein Variational Gradient Flow
- 基于Nesterov加速梯度流设计新采样算法
- 在多种目标分布下收敛更快，优于传统SVGD
- 适合需要高效采样的生成模型与贝叶斯推断
Stein变分梯度下降（SVGD）是一种基于核函数的粒子方法，用于从目标分布中采样，广泛应用于生成建模和贝叶斯推断。与依赖对数密度梯度估计（即得分估计）的方法不同，SVGD无需进行得分估计，但在实际应用中可能比基于得分估计的算法慢。为设计快速高效的高维采样算法，本文提出ASVGD，一种基于度量空间中概率分布的Nesterov加速梯度流的加速SVGD。我们推导出一种基于动量的离散时间采样算法，可确定性地演化一组粒子。为稳定粒子的动量更新，还研究了Wasserstein度量正则化。针对广义双线性核和高斯核，在多种目标分布下的小型数值实验表明，ASVGD在收敛速度和稳定性上均优于SVGD及其他主流采样方法。
原文摘要 · Abstract (English)
Stein variational gradient descent (SVGD) is a kernel-based particle method for sampling from a target distribution, e.g., in generative modeling and Bayesian inference. SVGD does not require estimating the gradient of the log-density, which is called score estimation. In practice, SVGD can be slow compared to score-estimation based sampling algorithms. To design fast and efficient high-dimensional sampling algorithms, we introduce ASVGD, an accelerated SVGD, based on an accelerated gradient flow in a metric space of probability densities following Nesterov's method. We then derive a momentum-based discrete-time sampling algorithm, which evolves a set of particles deterministically. To stabilize the particles' momentum update, we also study a Wasserstein metric regularization. For the generalized bilinear kernel and the Gaussian kernel, toy numerical examples with varied target distributions demonstrate the effectiveness of ASVGD compared to SVGD and other popular sampling methods.
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