MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV ( that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint

Optimal Transport to a Variety

Türkü Özlüm Çelik, Asgar Jamneshan, Guido Montúfar, Bernd Sturmfels and Lorenzo Venturello


We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. We consider the setting of finite state spaces and describe the solution depending on the choice of the ground metric and the given distribution. The Wasserstein distance between the distribution and the variety is the minimum of a linear functional over a union of transportation polytopes. We obtain a description in terms of the solutions of a finite number of systems of polynomial equations. The case analysis is based on the ground metric. A detailed analysis is given for the two bit independence model.

algebraic statistics, Linear Programming, Optimal Transport Estimator, Polynomial Optimization, Transportation Polytope, Triangulation, Wasserstein distance

Related publications

2020 Repository Open Access
Türkü Özlüm Celik, Asgar Jamneshan, Guido Montúfar, Bernd Sturmfels and Lorenzo Venturello

Optimal transport to a variety

In: Mathematical aspects of computer and information sciences : 8th international conference, MACIS 2019, Gebze-Istanbul, Turkey, November 13-15, 2019 ; revised selected papers / Daniel Slamanig... (eds.)
Cham : Springer, 2020. - pp. 364-381
(Lecture notes in computer science ; 11989)