A Wasserstein-Type Distance in the Space of Gaussian Mixture Models

DOI10.1137/19M1301047MaRDI QIDQ3296474

Julie Delon, Agnès Desolneux

Publication date: 7 July 2020

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.05254

Has companion code repository: https://github.com/judelo/gmmot

zbMATH Keywords

barycenterWasserstein distanceoptimal transportGaussian mixture modelmultimarginal optimal transportimage processing applications

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Numerical mathematical programming methods (65K05) Numerical optimization and variational techniques (65K10) Computing methodologies for image processing (68U10) Linear programming (90C05) Graph theory (including graph drawing) in computer science (68R10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05)

Related Items (14)

GAT–GMM: Generative Adversarial Training for Gaussian Mixture Models ⋮ The geodesic distance on the generalized gamma manifold for texture image retrieval ⋮ Continualization of Probabilistic Programs With Correction ⋮ Stochastic approximation versus sample average approximation for Wasserstein barycenters ⋮ Stochastic saddle-point optimization for the Wasserstein barycenter problem ⋮ Multisource Single-Cell Data Integration by MAW Barycenter for Gaussian Mixture Models ⋮ An Integrated Transportation Distance between Kernels and Approximate Dynamic Risk Evaluation in Markov Systems ⋮ Generalized Wasserstein barycenters between probability measures living on different subspaces ⋮ Gradient projection methods for the $n$-coupling problem ⋮ A Wasserstein-type distance for Gaussian mixtures on vector bundles with applications to shape analysis ⋮ Empirical optimal transport under estimated costs: distributional limits and statistical applications ⋮ Learning from small data sets: patch-based regularizers in inverse problems for image reconstruction ⋮ Sparse mixture models inspired by ANOVA decompositions ⋮ Summary statistics and discrepancy measures for approximate Bayesian computation via surrogate posteriors

Uses Software

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• POT
• PRMLT

Cites Work

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