Entropic-Wasserstein Barycenters: PDE Characterization, Regularity, and CLT

DOI10.1137/20M1387262zbMath1476.49056arXiv2012.10701OpenAlexW3205899079MaRDI QIDQ5158392

Alexey Kroshnin, Guillaume Carlier, Katharina Eichinger

Publication date: 22 October 2021

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.10701

zbMATH Keywords

central limit theorem (CLT)entropic-Wasserstein barycentersMonge-Ampère equations and systems

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12) Monge-Ampère equations (35J96) Optimal transportation (49Q22)

Related Items (4)

Optimal transportation, modelling and numerical simulation ⋮ Quantitative Stability of Regularized Optimal Transport and Convergence of Sinkhorn's Algorithm ⋮ A GPM-based algorithm for solving regularized Wasserstein barycenter problems in some spaces of probability measures ⋮ Quantitative stability of barycenters in the Wasserstein space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convexity of the support of the displacement interpolation: counterexamples
• The Monge-Ampère equation and its applications
• Wasserstein barycenters over Riemannian manifolds
• Probability in Banach spaces. Isoperimetry and processes
• Global Hölder estimates for optimal transportation
• Boundary regularity of maps with convex potentials. II
• The Frechet distance between multivariate normal distributions
• Fréchet means and Procrustes analysis in Wasserstein space
• Optimal transportation with infinitely many marginals
• Towards a central limit theorem in the Wasserstein space?
• Convergence rates for empirical barycenters in metric spaces: curvature, convexity and extendable geodesics
• Statistical inference for Bures-Wasserstein barycenters
• Convergence of a Newton algorithm for semi-discrete optimal transport
• Regularity of monotone transport maps between unbounded domains
• Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
• Existence and consistency of Wasserstein barycenters
• The Monge–Ampère equation and its link to optimal transportation
• Barycenters in the Wasserstein Space
• Numerical methods for matching for teams and Wasserstein barycenters
• Polar factorization and monotone rearrangement of vector‐valued functions
• Boundary regularity of maps with convex potentials
• Elliptic Partial Differential Equations of Second Order
• The Variational Formulation of the Fokker--Planck Equation
• Fr\'echet barycenters in the Monge-Kantorovich spaces
• Characterization of barycenters in the Wasserstein space by averaging optimal transport maps
• Oblique Derivative Problems for Elliptic Equations
• Penalization of Barycenters in the Wasserstein Space
• Iterative Bregman Projections for Regularized Transportation Problems
• Convergence of Entropic Schemes for Optimal Transport and Gradient Flows
• Optimal Transport
• Monotonicity properties of optimal transportation and the FKG and related inequalities

This page was built for publication: Entropic-Wasserstein Barycenters: PDE Characterization, Regularity, and CLT