Minimax Distribution Estimation in Wasserstein Distance

Abstract

The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on statistical minimax rates for the problem of estimating a probability distribution under Wasserstein loss, using only metric properties, such as covering and packing numbers, of the sample space, and weak moment assumptions on the probability distributions.

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• Distributionally Robust Optimization: A Review
• Convergence and Concentration of Empirical Measures under Wasserstein Distance in Unbounded Functional Spaces
• Faster Wasserstein Distance Estimation with the Sinkhorn Divergence
• Minimax Confidence Intervals for the Sliced Wasserstein Distance
• Sharp Convergence Rates for Empirical Optimal Transport with Smooth Costs
• Statistical guarantees for generative models without domination
• Asymptotic Guarantees for Generative Modeling Based on the Smooth Wasserstein Distance
• On Projection Robust Optimal Transport: Sample Complexity and Model Misspecification
• A short proof on the rate of convergence of the empirical measure for the Wasserstein distance
• Convergence of Gaussian-smoothed optimal transport distance with sub-gamma distributions and dependent samples
• A Mean-Field Theory for Kernel Alignment with Random Features in Generative and Discriminative Models
• High-Dimensional Non-Parametric Density Estimation in Mixed Smooth Sobolev Spaces
• Estimation and Quantization of Expected Persistence Diagrams