Optimal Transport to a Variety

  • Türkü Özlüm ÇelikEmail author
  • Asgar Jamneshan
  • Guido Montúfar
  • Bernd Sturmfels
  • Lorenzo Venturello
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11989)


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 



GM has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant no 757983).


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Türkü Özlüm Çelik
    • 1
    Email author
  • Asgar Jamneshan
    • 3
  • Guido Montúfar
    • 1
    • 3
  • Bernd Sturmfels
    • 1
    • 2
  • Lorenzo Venturello
    • 1
  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.University of California at BerkeleyBerkeleyUSA
  3. 3.University of California at Los AngelesLos AngelesUSA

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