Skip to main content
eScholarship
Open Access Publications from the University of California

UCLA

UCLA Previously Published Works bannerUCLA

Optimal Transport to a Variety

  • Author(s): Çelik, TÖ
  • Jamneshan, A
  • Montúfar, G
  • Sturmfels, B
  • Venturello, L
  • Editor(s): Slamanig, Daniel
  • Tsigaridas, Elias P
  • Zafeirakopoulos, Zafeirakis
  • et al.

Published Web Location

http://doi.org/10.1007/978-3-030-43120-4_29
No data is associated with this publication.
Abstract

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.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Item not freely available? Link broken?
Report a problem accessing this item