Wasserstein Contraction of Coordinate Ascent Variational Inference

• URL: http://arxiv.org/abs/2605.30253v2
• Date: Tue, 02 Jun 2026 09:51:10 GMT
• Title: Wasserstein Contraction of Coordinate Ascent Variational Inference
• Abstract summary: We study the contraction in Wasserstein distance of the coordinate ascent variational inference algorithm.<n>This is shown to hold under a transport-information inequality at the fixed points and a functional smoothness condition.
• Score: 2.8211276672560452
• License: http://creativecommons.org/licenses/by/4.0/
• 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).

Related papers

• Relative Wasserstein Angle and the Problem of the $W_2$-Nearest Gaussian Distribution [4.042425236692822]
  We study the problem of quantifying how far an empirical distribution deviates from Gaussianity under the framework of optimal transport.<n>By exploiting the cone geometry of the relative translation invariant quadratic Wasserstein space, we introduce two novel geometric quantities.<n>We prove that the filling cone generated by any two rays in this space is flat, ensuring angles, projections, and inner products are rigorously well-defined.
  arXiv  Detail & Related papers  (2026-01-29T22:03:10Z)
• Efficient Covariance Estimation for Sparsified Functional Data [51.69796254617083]
  proposed Random-knots (Random-knots-Spatial) and B-spline (Bspline-Spatial) estimators of the covariance function are computationally efficient.<n>Asymptotic pointwise of the covariance are obtained for sparsified individual trajectories under some regularity conditions.
  arXiv  Detail & Related papers  (2025-11-23T00:50:33Z)
• Variational Inference with Mixtures of Isotropic Gaussians [8.365869192421865]
  Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family.<n>We develop a variational framework and provide efficient algorithms suited for this family.
  arXiv  Detail & Related papers  (2025-06-16T15:42:15Z)
• Evolution of Gaussians in the Hellinger-Kantorovich-Boltzmann gradient flow [44.500314182711236]
  We derive explicit ordinary equations govern the evolution of mean, covariance, and mass under HK-Boltzmann flow.<n>We demonstrate exponential convergence to equilibrium through constructing a gradient structure associated with a Polyak-Lojasiewicz-type inequalities.<n>We extend our analysis to non-Gaussian targets exhibiting strong log-lambda-concavity.
  arXiv  Detail & Related papers  (2025-04-29T03:54:56Z)
• Stable Derivative Free Gaussian Mixture Variational Inference for Bayesian Inverse Problems [4.842853252452336]
  Key challenges include costly repeated evaluations of forward models, multimodality, and inaccessible gradients for the forward model.<n>We develop a variational inference framework that combines Fisher-Rao natural gradient with specialized quadrature rules to enable derivative free updates of Gaussian mixture variational families.<n>The resulting method, termed Derivative Free Gaussian Mixture Variational Inference (DF-GMVI), guarantees covariance positivity and affine invariance, offering a stable and efficient framework for approximating complex posterior distributions.
  arXiv  Detail & Related papers  (2025-01-08T03:50:15Z)
• Convergence rate of random scan Coordinate Ascent Variational Inference under log-concavity [0.18416014644193066]
  The Coordinate Ascent Variational Inference scheme is a popular algorithm used to compute the mean-field approximation of a probability distribution of interest. We analyze its random scan version, under log-concavity assumptions on the target density.
  arXiv  Detail & Related papers  (2024-06-11T14:23:01Z)
• Generalized Variational Inference in Function Spaces: Gaussian Measures meet Bayesian Deep Learning [9.106412307976067]
  We develop a framework for generalized variational inference in infinite-dimensional function spaces. We use it to construct a method termed Gaussian Wasserstein inference (GWI) An exciting application of GWI is the ability to use deep neural networks in the variational parametrisation of GWI.
  arXiv  Detail & Related papers  (2022-05-12T20:10:31Z)
• Minibatch vs Local SGD with Shuffling: Tight Convergence Bounds and Beyond [63.59034509960994]
  We study shuffling-based variants: minibatch and local Random Reshuffling, which draw gradients without replacement. For smooth functions satisfying the Polyak-Lojasiewicz condition, we obtain convergence bounds which show that these shuffling-based variants converge faster than their with-replacement counterparts. We propose an algorithmic modification called synchronized shuffling that leads to convergence rates faster than our lower bounds in near-homogeneous settings.
  arXiv  Detail & Related papers  (2021-10-20T02:25:25Z)
• Spectral clustering under degree heterogeneity: a case for the random walk Laplacian [83.79286663107845]
  This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. In the special case of a degree-corrected block model, the embedding concentrates about K distinct points, representing communities.
  arXiv  Detail & Related papers  (2021-05-03T16:36:27Z)
• Optimal oracle inequalities for solving projected fixed-point equations [53.31620399640334]
  We study methods that use a collection of random observations to compute approximate solutions by searching over a known low-dimensional subspace of the Hilbert space. We show how our results precisely characterize the error of a class of temporal difference learning methods for the policy evaluation problem with linear function approximation.
  arXiv  Detail & Related papers  (2020-12-09T20:19:32Z)
• Local optimization on pure Gaussian state manifolds [63.76263875368856]
  We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm. The method is based on notions of descent gradient attuned to the local geometry. We use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.
  arXiv  Detail & Related papers  (2020-09-24T18:00:36Z)
• Stochastic Saddle-Point Optimization for Wasserstein Barycenters [69.68068088508505]
  We consider the populationimation barycenter problem for random probability measures supported on a finite set of points and generated by an online stream of data. We employ the structure of the problem and obtain a convex-concave saddle-point reformulation of this problem. In the setting when the distribution of random probability measures is discrete, we propose an optimization algorithm and estimate its complexity.
  arXiv  Detail & Related papers  (2020-06-11T19:40:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.