改进变分推断的径向分布建模，提升高维分布逼近精度。
Variational inference via radial transport
- 通过优化径向分布结构改进变分推断，无需改变原有框架。
- 在多个真实数据集上显著提升后验分布覆盖能力，收敛性有理论保证。
- 适合需要更精确后验估计的机器学习研究者使用。
在变分推断（VI）中，通常用简单的近似分布（如高斯分布）来逼近高维分布 π。然而，在许多实际场景中，高斯分布无法准确捕捉 π 的径向特征，导致覆盖率不足。本文从优化径向分布的角度出发，提出 radVI 算法，作为现有变分推断方法（如均值场高斯变分推断、拉普拉斯近似）的低成本有效增强模块。该算法基于对沃尔什空间（Wasserstein space）优化的最新进展，以及卡法雷利（Caffarelli, 2000）风格的径向传输映射新正则性性质，提供了理论收敛保证。
原文摘要 · Abstract (English)
In variational inference (VI), the practitioner approximates a high-dimensional distribution $π$ with a simple surrogate one, often a (product) Gaussian distribution. However, in many cases of practical interest, Gaussian distributions might not capture the correct radial profile of $π$, resulting in poor coverage. In this work, we approach the VI problem from the perspective of optimizing over these radial profiles. Our algorithm radVI is a cheap, effective add-on to many existing VI schemes, such as Gaussian (mean-field) VI and Laplace approximation. We provide theoretical convergence guarantees for our algorithm, owing to recent developments in optimization over the Wasserstein space--the space of probability distributions endowed with the Wasserstein distance--and new regularity properties of radial transport maps in the style of Caffarelli (2000).
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