mlsanityData to 7 Oct 2026

Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein space

arXiv 2312.02849 ↗First posted 5 Dec 2023math.ST cs.LG math.OCcited by 20

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Abstract (arXiv)

We develop a theory of finite-dimensional polyhedral subsets over the Wasserstein space and optimization of functionals over them via first-order methods. Our main application is to the problem of mean-field variational inference, which seeks to approximate a distribution π over ℝd by a product measure π^star. When π is strongly log-concave and log-smooth, we provide (1) approximation rates certifying that π^star is close to the minimizer π^star_diamond of the KL divergence over a polyhedral set P_diamond, and (2) an algorithm for minimizing KL(·|π) over P_diamond based on accelerated gradient descent over Rd. As a byproduct of our analysis, we obtain the first end-to-end analysis for gradient-based algorithms for MFVI.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). Builds on 43 of its 92 references that are in the map. First posted on arXiv 5 Dec 2023.

Builds on

43 of 92 references.

References · 43

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31 more
  1. 2022Variational inference via Wasserstein gradient flowscited by 84
  2. 2019A Wasserstein-type distance in the space of Gaussian Mixture Modelscited by 75
  3. 2021Plugin Estimation of Smooth Optimal Transport Mapscited by 67
  4. 2021Rates of Estimation of Optimal Transport Maps using Plug-in Estimators via Barycentric Projectionscited by 52
  5. 2017Optimal transport for Gaussian mixture modelscited by 45
  6. 2019Accelerating Langevin Sampling with Birth-deathcited by 45
  7. 2023Forward-backward Gaussian variational inference via JKO in the Bures-Wasserstein Spacecited by 36
  8. 2021Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descentcited by 32
  9. 2019Provable Smoothness Guarantees for Black-Box Variational Inferencecited by 29
  10. 2023Provable convergence guarantees for black-box variational inferencecited by 29
  11. 2020On Linear Optimization over Wasserstein Ballscited by 23
  12. 2023On the Convergence of Black-Box Variational Inferencecited by 22
  13. 2020Fast and Smooth Interpolation on Wasserstein Spacecited by 21
  14. 2022Optimal transport map estimation in general function spacescited by 20
  15. 2017Theoretical and Computational Guarantees of Mean Field Variational Inference for Community Detectioncited by 19
  16. 2022Mean-field Variational Inference via Wasserstein Gradient Flowcited by 19
  17. 2017Fr'echet Means and Procrustes Analysis in Wasserstein Spacecited by 18
  18. 2020Learning normalizing flows from Entropy-Kantorovich potentialscited by 18
  19. 2023On the Convergence of Coordinate Ascent Variational Inferencecited by 18
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  21. 2019Bounding the error of discretized Langevin algorithms for non-strongly log-concave targetscited by 16
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  25. 2023Independent projections of diffusions: Gradient flows for variational inference and optimal mean field approximationscited by 12
  26. 2022Measure Estimation in the Barycentric Coding Modelcited by 9
  27. 2023Bridging the Gap Between Variational Inference and Wasserstein Gradient Flowscited by 8
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 10; 2025: 6; 2026: 4.

20 papers.

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  1. 2024Measure-to-measure interpolation using Transformerscited by 28
  2. 2024Convergence of coordinate ascent variational inference for log-concave measures via optimal transportcited by 13
  3. 2024Theoretical Guarantees for Variational Inference with Fixed-Variance Mixture of Gaussianscited by 11
  4. 2024Mirror and Preconditioned Gradient Descent in Wasserstein Spacecited by 11
  5. 2024Convergence rate of random scan Coordinate Ascent Variational Inference under log-concavitycited by 9
  6. 2024Variational Inference in Location-Scale Families: Exact Recovery of the Mean and Correlation Matrixcited by 9
  7. 2024Sampling from the Mean-Field Stationary Distributioncited by 7
  8. 2025Variational Inference with Mixtures of Isotropic Gaussianscited by 6
  9. 2024Constructive approximate transport maps with normalizing flowscited by 4
  10. 2024A Particle Algorithm for Mean-Field Variational Inferencecited by 3
  11. 2025Stability of Mean-Field Variational Inferencecited by 3
  12. 2024Linearized Wasserstein Barycenters: Synthesis, Analysis, Representational Capacity, and Applicationscited by 1
8 more
  1. 2025Nearly Dimension-Independent Convergence of Mean-Field Black-Box Variational Inferencecited by 1
  2. 2025Rotated Mean-Field Variational Inference and Iterative Gaussianizationcited by 1
  3. 2026Radon--Wasserstein Gradient Flows for Interacting-Particle Sampling in High Dimensionscited by 1
  4. 2026Wasserstein Contraction of Coordinate Ascent Variational Inferencecited by 1
  5. 2025Gaussian mixture layers for neural networkscited by 0
  6. 2025Mode Collapse of Mean-Field Variational Inferencecited by 0
  7. 2026Static and Dynamic Approaches to Computing Barycenters of Probability Measures on Graphscited by 0
  8. 2026Stability of Finite-Batch Particle Mean-Field Variational Inference Beyond Strong Convexitycited by 0