在对称性下，该研究为变分推断提供了更强的理论保证。
Even More Guarantees for Variational Inference in the Presence of Symmetries
- 基于前向KL散度和α散度，给出目标均值与相关矩阵精确恢复的条件
- 放宽了以往必须满足对数凹性的限制，适用于多峰分布等复杂目标
- 实验揭示优化失败原因，指导变分族与α值的选择
当通过变分推断（VI）近似不可计算密度时，变分族通常为简单参数族，很可能不包含真实目标。这引出一个问题：在模型误设情况下，能否仍恢复目标的某些特性？本文在已有工作基础上，针对具有对称性的目标，从两个方面扩展理论结果：(1) 将适用范围拓展至更广泛的散度，提供使用前向Kullback-Leibler散度和α-散度时目标均值与相关矩阵精确恢复的充分条件；(2) 放宽了此前需假设目标为对数凹性的严格限制，使理论适用于更广泛的目标，包括多峰分布。实验表明，这些保证可作为变分族与α值选择的指导，并在多种实例中揭示缺乏充分条件时优化失败的原因。
原文摘要 · Abstract (English)
When approximating an intractable density via variational inference (VI) the variational family is typically chosen as a simple parametric family that very likely does not contain the target. This raises the question: Under which conditions can we recover characteristics of the target despite misspecification? In this work, we extend previous theoretical results on robust VI with location-scale families under target symmetries in two substantial ways: (1) We open them up to a wider range of divergences by providing sufficient conditions for exact recovery of the target mean and correlation matrix when using the forward Kullback-Leibler divergence and $α$-divergences. (2) By doing so, we find that we can drop the restrictive assumption of a log-concave target made in previous work, allowing us to give guarantees for a wider range of targets, including multi-modal ones. In our experiments, we show how our guarantees can serve as guidelines for the choice of the variational family and $α$-value and we illustrate on a diverse set of examples how and why optimization can fail in the absence of our sufficient conditions.
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