论文标题
基于粒子的能量变异推断
Particle-based Energetic Variational Inference
论文作者
论文摘要
我们引入了一种新的变分推断（VI）框架，称为“能量变异推理”（EVI）。它基于规定的能量隔离法最小化VI目标函数。使用EVI框架，我们可以得出许多现有的基于粒子的变异推理（PARVI）方法，包括流行的Stein变分梯度下降（SVGD）方法。更重要的是，可以在此框架下创建许多新的PARVI计划。为了进行说明，我们提出了一种新的基于粒子的EVI方案，该方案首先执行基于粒子的近似值，然后在变化过程中使用近似密度，或简称“近似-then-variation”。由于这种近似和变化的顺序，新方案可以将变异结构保持在粒子水平上，并且可以显着降低每种迭代中的KL差异。数值实验表明，根据对目标分布的保真度，所提出的方法优于某些现有的PARVI方法。
We introduce a new variational inference (VI) framework, called energetic variational inference (EVI). It minimizes the VI objective function based on a prescribed energy-dissipation law. Using the EVI framework, we can derive many existing Particle-based Variational Inference (ParVI) methods, including the popular Stein Variational Gradient Descent (SVGD) approach. More importantly, many new ParVI schemes can be created under this framework. For illustration, we propose a new particle-based EVI scheme, which performs the particle-based approximation of the density first and then uses the approximated density in the variational procedure, or "Approximation-then-Variation" for short. Thanks to this order of approximation and variation, the new scheme can maintain the variational structure at the particle level, and can significantly decrease the KL-divergence in each iteration. Numerical experiments show the proposed method outperforms some existing ParVI methods in terms of fidelity to the target distribution.
