Even More Guarantees for Variational Inference in the Presence of Symmetries
Provides theoretical guidelines for practitioners choosing variational families and α-values in misspecified VI settings.
The paper extends theoretical guarantees for variational inference under target symmetries, deriving sufficient conditions for exact mean recovery using forward KL and α-divergences, and explains optimization failures when conditions are unmet.
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 $α$-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 $α$-value.