Title: Convergence Properties of Coordinate Ascent Variational Inference via Wasserstein Distance

Abstract: This paper investigates the contraction behavior of the Coordinate Ascent Variational Inference (CAVI) algorithm within the Wasserstein metric. We demonstrate that this contraction occurs when the fixed points satisfy a transport-information inequality alongside a functional smoothness requirement. Our findings are both general and precise, providing local convergence assurances. These guarantees extend to arbitrary smooth manifolds and apply to certain non-smooth spaces as well. We illustrate the utility of these results through applications to Bayesian Gaussian Mixture Models, high-dimensional Bayesian Probit Regression, and Logistic Regression incorporating P\'olya-Gamma random variables, specifically referencing Jaakkola-Jordan’s algorithm.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC