Even More Guarantees for Variational Inference in the Presence of Symmetries

TL;DR

This paper investigates conditions under which variational inference can accurately recover target characteristics despite model misspecification, especially in the presence of symmetries, and provides guidelines for better inference.

Contribution

It extends previous results on robust variational inference with symmetry considerations, deriving conditions for exact mean recovery and analyzing failure modes.

Findings

Sufficient conditions for exact mean recovery with KL and α-divergences.

Analysis of optimization failures without these conditions.

Guidelines for choosing variational families and divergence parameters.

Abstract

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 results on robust VI with location-scale families under target symmetries. We derive sufficient conditions guaranteeing exact recovery of the mean when using the forward Kullback-Leibler divergence and $\alpha$-divergences. We further show how and why optimization can fail to recover the target mean in the absence of our sufficient conditions, providing initial guidelines on the choice of the variational family and $\alpha$-value.