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Optimal Transport to a Variety

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Mathematical Aspects of Computer and Information Sciences (MACIS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11989))

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.

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Acknowledgments

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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Authors and Affiliations

  1. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

    Türkü Özlüm Çelik, Guido Montúfar, Bernd Sturmfels & Lorenzo Venturello

  2. University of California at Berkeley, Berkeley, USA

    Bernd Sturmfels

  3. University of California at Los Angeles, Los Angeles, USA

    Asgar Jamneshan & Guido Montúfar

Authors
  1. Türkü Özlüm Çelik
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  2. Asgar Jamneshan
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  3. Guido Montúfar
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  4. Bernd Sturmfels
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  5. Lorenzo Venturello
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Corresponding author

Correspondence to Türkü Özlüm Çelik .

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Editors and Affiliations

  1. AIT Austrian Institute of Technology, Vienna, Austria

    Daniel Slamanig

  2. IMJ-PRG, Sorbonne University, Paris, France

    Elias Tsigaridas

  3. Institute of Information Technologies, Gebze Technical University, Gebze, Turkey

    Zafeirakis Zafeirakopoulos

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Çelik, T.Ö., Jamneshan, A., Montúfar, G., Sturmfels, B., Venturello, L. (2020). Optimal Transport to a Variety. In: Slamanig, D., Tsigaridas, E., Zafeirakopoulos, Z. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science(), vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_29

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  • DOI: https://doi.org/10.1007/978-3-030-43120-4_29

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43119-8

  • Online ISBN: 978-3-030-43120-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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