Central limit theorems for entropy-regularized optimal transport on finite spaces and statistical applications

DOI10.1214/19-EJS1637zbMath1454.62136arXiv1711.08947OpenAlexW2913699596MaRDI QIDQ2283574

Nicolas Papadakis, Jérémie Bigot, Elsa Cazelles

Publication date: 3 January 2020

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.08947

zbMATH Keywords

bootstraphypothesis testingcentral limit theoremoptimal transportmultivariate probability distributionsSinkhorn divergence

Mathematics Subject Classification ID

Computational methods for problems pertaining to statistics (62-08) Nonparametric hypothesis testing (62G10) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Nonparametric statistical resampling methods (62G09)

Related Items (11)

Stochastic approximation versus sample average approximation for Wasserstein barycenters ⋮ The nested Sinkhorn divergence to learn the nested distance ⋮ Estimation of Wasserstein distances in the spiked transport model ⋮ Scaling positive random matrices: concentration and asymptotic convergence ⋮ Limit distributions and sensitivity analysis for empirical entropic optimal transport on countable spaces ⋮ An Improved Central Limit Theorem and Fast Convergence Rates for Entropic Transportation Costs ⋮ Uniform confidence band for optimal transport map on one-dimensional data ⋮ Limit theorems for entropic optimal transport maps and Sinkhorn divergence ⋮ Asymptotic distribution and convergence rates of stochastic algorithms for entropic optimal transportation between probability measures ⋮ Minimax estimation of smooth optimal transport maps ⋮ Empirical Regularized Optimal Transport: Statistical Theory and Applications

Uses Software

• bootstrap
• Wasserstein GAN

Cites Work

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• Limit laws of the empirical Wasserstein distance: Gaussian distributions
• Geodesic PCA in the Wasserstein space by convex PCA
• On Hadamard differentiability in \(k\)-sample semiparametric models -- with applications to the assessment of structural relationships
• Tests of goodness of fit based on the \(L_2\)-Wasserstein distance
• Inverses of \(2\times 2\) block matrices
• Asymptotics for \(L_2\) functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances
• Weak convergence and empirical processes. With applications to statistics
• Convergence of latent mixing measures in finite and infinite mixture models
• Inference on functionals under first order degeneracy
• Central limit theorems for empirical transportation cost in general dimension
• A Smoothed Dual Approach for Variational Wasserstein Problems
• Convolutional wasserstein distances
• Convex Color Image Segmentation with Optimal Transport Distances
• Inference for Empirical Wasserstein Distances on Finite Spaces
• Geodesic PCA versus Log-PCA of Histograms in the Wasserstein Space
• Fast Discrete Distribution Clustering Using Wasserstein Barycenter With Sparse Support
• Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised Nonlinear Dictionary Learning
• Data-driven regularization of Wasserstein barycenters with an application to multivariate density registration
• Empirical Regularized Optimal Transport: Statistical Theory and Applications

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