On Representations of Mean-Field Variational Inference. (arXiv:2210.11385v1 [stat.ML])

The mean field variational inference (MFVI) formulation restricts the general
Bayesian inference problem to the subspace of product measures. We present a
framework to analyze MFVI algorithms, which is inspired by a similar
development for general variational Bayesian formulations. Our approach enables
the MFVI problem to be represented in three different manners: a gradient flow
on Wasserstein space, a system of Fokker-Planck-like equations and a diffusion
process. Rigorous guarantees are established to show that a time-discretized
implementation of the coordinate …

arxiv inference mean