Wasserstein Contraction of Coordinate Ascent Variational Inference

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 Pólya-Gamma random variables (i.e. Jaakkola-Jordan's algorithm).

Source: arXiv:2605.30253v1 - http://arxiv.org/abs/2605.30253v1 PDF: https://arxiv.org/pdf/2605.30253v1 Original Link: http://arxiv.org/abs/2605.30253v1