𝒲_∞-transport with discrete target as a combinatorial matching problem

by   Mohit Bansil, et al.

In this short note, we show that given a cost function c, any coupling Ο€ of two probability measures where the second is a discrete measure can be associated to a certain bipartite graph containing a perfect matching, based on the value of the infinity transport cost c_L^∞(Ο€). This correspondence between couplings and bipartite graphs is explicitly constructed. We give two applications of this result to the 𝒲_∞ optimal transport problem when the target measure is discrete, the first is a condition to ensure existence of an optimal plan induced by a mapping, and the second is a numerical approach to approximating optimal plans.



There are no comments yet.


page 1

page 2

page 3

page 4

βˆ™ 08/04/2019

Pairwise Multi-marginal Optimal Transport via Universal Poisson Coupling

We investigate the problem of pairwise multi-marginal optimal transport,...
βˆ™ 04/11/2020

Quantitative Stability and Error Estimates for Optimal Transport Plans

Optimal transport maps and plans between two absolutely continuous measu...
βˆ™ 10/19/2020

Bayesian Inference for Optimal Transport with Stochastic Cost

In machine learning and computer vision, optimal transport has had signi...
βˆ™ 11/17/2020

Asymptotics of Entropy-Regularized Optimal Transport via Chaos Decomposition

Consider the problem of estimating the optimal coupling (i.e., matching)...
βˆ™ 09/29/2019

Learning transport cost from subset correspondence

Learning to align multiple datasets is an important problem with many ap...
βˆ™ 10/16/2019

On the Computational Complexity of Finding a Sparse Wasserstein Barycenter

The discrete Wasserstein barycenter problem is a minimum-cost mass trans...
βˆ™ 09/28/2018

Γ‰tude pour l'analyse et l'optimisation du transport des personnes en situation de handicap

From 2010, the medical transport has become one of the top ten prioritie...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.