Inference for Empirical Wasserstein Distances on Finite Spaces

DOI10.1111/rssb.12236zbMath1380.62121arXiv1610.03287OpenAlexW2530707152MaRDI QIDQ4603809

Axel Munk, Max Sommerfeld

Publication date: 19 February 2018

Published in: Journal of the Royal Statistical Society Series B: Statistical Methodology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.03287

zbMATH Keywords

bootstraphypothesis testingcentral limit theoremWasserstein distanceoptimal transportdirectional Hadamard derivative

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Nonparametric statistical resampling methods (62G09) Convergence of probability measures (60B10)

Related Items (44)

Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures ⋮ Minimax confidence intervals for the sliced Wasserstein distance ⋮ Stochastic approximation versus sample average approximation for Wasserstein barycenters ⋮ Randomized Wasserstein Barycenter Computation: Resampling with Statistical Guarantees ⋮ Unnamed Item ⋮ Kantorovich distance on finite metric spaces: Arens-Eells norm and CUT norms ⋮ Tropical optimal transport and Wasserstein distances ⋮ The Wasserstein impact measure (WIM): a practical tool for quantifying prior impact in Bayesian statistics ⋮ ON THE CONVERGENCE RATE OF POTENTIALS OF BRENIER MAPS ⋮ Limit laws for empirical optimal solutions in random linear programs ⋮ Some multivariate goodness of fit tests based on data depth ⋮ Directional differentiability for supremum-type functionals: statistical applications ⋮ A central limit theorem for Wasserstein type distances between two distinct univariate distributions ⋮ Optimal Estimation of Wasserstein Distance on a Tree With an Application to Microbiome Studies ⋮ Gaussian approximation for penalized Wasserstein barycenters ⋮ Measuring association with Wasserstein distances ⋮ Multisource Single-Cell Data Integration by MAW Barycenter for Gaussian Mixture Models ⋮ Density estimation of multivariate samples using Wasserstein distance ⋮ Uniform inference for value functions ⋮ Sharp convergence rates for empirical optimal transport with smooth costs ⋮ 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 ⋮ Distribution of Distances based Object Matching: Asymptotic Inference ⋮ Two-sample goodness-of-fit tests on the flat torus based on Wasserstein distance and their relevance to structural biology ⋮ Central limit theorems for semi-discrete Wasserstein distances ⋮ Asymptotics for Strassen's optimal transport problem ⋮ Uniform confidence band for optimal transport map on one-dimensional data ⋮ Semi-discrete optimal transport: a solution procedure for the unsquared Euclidean distance case ⋮ Fréchet means and Procrustes analysis in Wasserstein space ⋮ Stability of Gibbs Posteriors from the Wasserstein Loss for Bayesian Full Waveform Inversion ⋮ Central limit theorem and bootstrap procedure for Wasserstein's variations with an application to structural relationships between distributions ⋮ Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces ⋮ Hybrid Wasserstein distance and fast distribution clustering ⋮ Central limit theorems for entropy-regularized optimal transport on finite spaces and statistical applications ⋮ Empirical optimal transport on countable metric spaces: distributional limits and statistical applications ⋮ Asymptotic distribution and convergence rates of stochastic algorithms for entropic optimal transportation between probability measures ⋮ Multivariate goodness-of-fit tests based on Wasserstein distance ⋮ On the Computation of Kantorovich--Wasserstein Distances Between Two-Dimensional Histograms by Uncapacitated Minimum Cost Flows ⋮ Geometry-Sensitive Ensemble Mean Based on Wasserstein Barycenters: Proof-of-Concept on Cloud Simulations ⋮ Kantorovich-Rubinstein distance and barycenter for finitely supported measures: foundations and algorithms ⋮ Tackling algorithmic bias in neural-network classifiers using Wasserstein-2 regularization ⋮ Limitations of the Wasserstein MDE for univariate data ⋮ Likelihood estimation of sparse topic distributions in topic models and its applications to Wasserstein document distance calculations ⋮ Empirical Regularized Optimal Transport: Statistical Theory and Applications

Uses Software

• EMD
• mothur

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Limit laws of the empirical Wasserstein distance: Gaussian distributions
• Displacement convexity of entropy and related inequalities on graphs
• Geodesic PCA in the Wasserstein space by convex PCA
• Approximation by log-concave distributions, with applications to regression
• On Hadamard differentiability in \(k\)-sample semiparametric models -- with applications to the assessment of structural relationships
• Conditions for equivalence between Mallows distance and convergence to stable laws
• Central limit theorem and convergence to stable laws in Mallows distance
• A nonparametric test for similarity of marginals -- with applications to the assessment of population bioequivalence
• On optimal matchings
• Some asymptotic theory for the bootstrap
• Asymptotic analysis of stochastic programs
• Matching random samples in many dimensions
• On nondifferentiable functions and the bootstrap
• Two-sample test statistics for measuring discrepancies between two multivariate probability density functions using kernel-based density estimates
• The transportation cost from the uniform measure to the empirical measure in dimension \(\geq 3\)
• Mathematical aspects of evolving interfaces. Lectures given at the C. I. M. -C. I. M. E. joint Euro-summer school, Madeira, Funchal, Portugal, July 3--9, 2000
• Tests of goodness of fit based on the \(L_2\)-Wasserstein distance
• Ricci curvature of finite Markov chains via convexity of the entropy
• Asymptotics for \(L_2\) functionals of the empirical quantile process, with applications to tests of fit based on weighted Wasserstein distances
• On concepts of directional differentiability
• Pathologies of some minimum distance estimators
• The earth mover's distance as a metric for image retrieval
• Mean rates of convergence of empirical measures in the Wasserstein metric
• A parametric registration model for warped distributions with Wasserstein's distance
• Distribution's template estimate with Wasserstein metrics
• Sliced and Radon Wasserstein barycenters of measures
• On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• Barycenters in the Wasserstein Space
• On a Formula for the L2 Wasserstein Metric between Measures on Euclidean and Hilbert Spaces
• The Monge–Kantorovich Mass Transference Problem and Its Stochastic Applications
• Perturbation analysis of optimization problems in banach spaces
• Nonparametric Validation of Similar Distributions and Assessment of Goodness of Fit
• The Variational Formulation of the Fokker--Planck Equation
• Shape recognition via Wasserstein distance
• The Phylogenetic Kantorovich–Rubinstein Metric for Environmental Sequence Samples
• An Exact Distribution-Free Test Comparing Two Multivariate Distributions based on Adjacency
• A Note on Asymptotic Joint Normality
• Prescribing a System of Random Variables by Conditional Distributions

This page was built for publication: Inference for Empirical Wasserstein Distances on Finite Spaces