Wasserstein Contraction of Coordinate Ascent Variational Inference
Abstract
We study the contraction in Wasserstein distance of the coordinate ascent variational inference algorithm. This is shown to hold under a transport-information inequality at the fixed points and a functional smoothness condition. The results are general and sharp, allow for local convergence guarantees, hold for general smooth manifolds, and also in some non-smooth spaces. We consider applications to Bayesian Gaussian Mixture Models, and high-dimensional Bayesian Probit Regression, and Logistic Regression with P\'olya-Gamma random variables (i.e. Jaakkola-Jordan's algorithm).
Comments: 17 pages + 3 pages appendix, 3 figures
Cite
@article{arxiv.2605.30253,
title = {Wasserstein Contraction of Coordinate Ascent Variational Inference},
author = {Rocco Caprio and Adrien Corenflos and Sam Power},
journal= {arXiv preprint arXiv:2605.30253},
year = {2026}
}