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).

翻译：我们研究了坐标上升变分推断算法在Wasserstein距离下的收缩性质。该性质在不动点处满足传输-信息不等式以及函数光滑性条件的前提下成立。所得结果具有一般性和精确性，能够提供局部收敛保证，适用于一般光滑流形，并在某些非光滑空间中也成立。我们将该方法应用于贝叶斯高斯混合模型、高维贝叶斯概率回归，以及基于Pólya-Gamma随机变量的逻辑回归（即Jaakkola-Jordan算法）。