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This research establishes rigorous local convergence guarantees for coordinate ascent variational inference by leveraging transport-information inequalities and functional smoothness conditions. The findings extend applicability to general smooth and non-smooth manifolds, offering theoretical sharpness for Bayesian inference tasks like Gaussian Mixture Models and high-dimensional Probit regression. These results provide a solid mathematical foundation for optimizing variational algorithms in complex, high-dimensional statistical learning scenarios.

Sursă care acoperăarXiv

Wasserstein Contraction of Coordinate Ascent Variational Inference

arXiv3 iunie 20261 min de cititArticolul și perspectiva sunt în engleză.

arXiv:2605.30253v2 Announce Type: replace-cross 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).

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

17 pages + 3 pages appendix, 3 figures. V2 fixes some citations not displaying properly in the appendix. No content change compared to prior version

Machine Learning (stat.ML); Machine Learning (cs.LG); Functional Analysis (math.FA); Optimization and Control (math.OC); Probability (math.PR); Computation (stat.CO)

arXiv:2605.30253 [stat.ML]

(or arXiv:2605.30253v2 [stat.ML] for this version)

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