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Optimal transport for Gaussian mixture models

arXiv 1710.07876 ↗First posted 22 Oct 2017math.PR cs.SY eess.SYcited by 45

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Abstract (arXiv)

We present an optimal mass transport framework on the space of Gaussian mixture models, which are widely used in statistical inference. Our method leads to a natural way to compare, interpolate and average Gaussian mixture models. Basically, we study such models on a certain submanifold of probability densities with certain structure. Different aspects of this framework are discussed and several examples are presented to illustrate the results. This method represents our first attempt to study optimal transport problems for more general probability densities with structures.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Oct 2017.

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Citing papers per year: 2021: 5; 2022: 6; 2023: 13; 2024: 5; 2025: 10; 2026: 6.

45 papers.

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  1. 2022Variational inference via Wasserstein gradient flowscited by 84
  2. 2023Analysis of learning a flow-based generative model from limited sample complexitycited by 38
  3. 2022Calibration tests beyond classificationcited by 20
  4. 2023Algorithms for mean-field variational inference via polyhedral optimization in the Wasserstein spacecited by 20
  5. 2022Robust Bayesian Recoursecited by 18
  6. 2022Rethinking Initialization of the Sinkhorn Algorithmcited by 14
  7. 2021Evaluating generative networks using Gaussian mixtures of image featurescited by 11
  8. 2021Dynamical Wasserstein Barycenters for Time-series Modelingcited by 10
  9. 2023Coin Sampling: Gradient-Based Bayesian Inference without Learning Ratescited by 8
  10. 2023Wasserstein Gradient Flows for Optimizing Gaussian Mixture Policiescited by 8
  11. 2025Hierarchical Refinement: Optimal Transport to Infinity and Beyondcited by 8
  12. 2025Slicing the Gaussian Mixture Wasserstein Distancecited by 7
33 more
  1. 2025Gaussian Herding across Pens: An Optimal Transport Perspective on Global Gaussian Reduction for 3DGScited by 7
  2. 2023Bures-Wasserstein Means of Graphscited by 6
  3. 2025Variational Inference with Mixtures of Isotropic Gaussianscited by 6
  4. 2023Personalised Federated Learning On Heterogeneous Feature Spacescited by 5
  5. 2023Wasserstein Gradient Flow over Variational Parameter Space for Variational Inferencecited by 5
  6. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  7. 2023Gromov-Wasserstein-like Distances in the Gaussian Mixture Models Spacecited by 4
  8. 2023Mitigating Source Bias for Fairer Weak Supervisioncited by 3
  9. 2024Optimal Transport for Domain Adaptation through Gaussian Mixture Modelscited by 3
  10. 2024Pixel Is Not a Barrier: An Effective Evasion Attack for Pixel-Domain Diffusion Modelscited by 3
  11. 2025SwarmDiff: Swarm Robotic Trajectory Planning in Cluttered Environments via Diffusion Transformercited by 3
  12. 2021Consistency issues in Gaussian Mixture Models reduction algorithmscited by 2
  13. 2022An Optimal Transport-driven Approach for Cultivating Latent Space in Online Incremental Learningcited by 2
  14. 2023Perceptual Scales Predicted by Fisher Information Metricscited by 2
  15. 2025Variational Online Mirror Descent for Robust Learning in Schr"odinger Bridgecited by 2
  16. 2021Shape-Preserving Dimensionality Reduction : An Algorithm and Measures of Topological Equivalencecited by 1
  17. 2021Expectation Distance-based Distributional Clustering for Noise-Robustnesscited by 1
  18. 2022Fixed-point iterations for several dissimilarity measure barycenters in the Gaussian casecited by 1
  19. 2024Byzantine-tolerant distributed learning of finite mixture modelscited by 1
  20. 2024Optimal Transport for Probabilistic Circuitscited by 1
  21. 2024ELBOing Stein: Variational Bayes with Stein Mixture Inferencecited by 1
  22. 2025Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicingcited by 1
  23. 2026Sliced Wasserstein Steering between Gaussian Measurescited by 1
  24. 2023Scaling Limits of the Wasserstein information matrix on Gaussian Mixture Modelscited by 0
  25. 2023Robust Graph Matching Using An Unbalanced Hierarchical Optimal Transport Frameworkcited by 0
  26. 2023Optimal Transport for Kernel Gaussian Mixture Modelscited by 0
  27. 2025Subgraph Gaussian Embedding Contrast for Self-Supervised Graph Representation Learningcited by 0
  28. 2025Gaussian mixture layers for neural networkscited by 0
  29. 2026A Mean Field Games Perspective on Evolutionary Clusteringcited by 0
  30. 2026Lifted Schr"odinger Bridges for Gaussian Mixture Endpoints: Projection Gaps and Path-Space Obstructionscited by 0
  31. 2026Entropic Partial Optimal Transport and Partial Gromov--Wasserstein Distance between Gaussian Mixturescited by 0
  32. 2026Distribution Steering via Sliced Optimal Transport Controlcited by 0
  33. 2026Coupled Usage-Sense Processes: Temporal and Attributable Lexical Semantic Changecited by 0