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Geometrical Insights for Implicit Generative Modeling

  • Leon BottouEmail author
  • Martin Arjovsky
  • David Lopez-Paz
  • Maxime Oquab
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11100)

Abstract

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the Maximum Mean Discrepancy criterion. A careful look at the geometries induced by these distances on the space of probability measures reveals interesting differences. In particular, we can establish surprising approximate global convergence guarantees for the 1-Wasserstein distance, even when the parametric generator has a nonconvex parametrization.

Notes

Acknowledgements

We would like to thank Joan Bruna, Marco Cuturi, Arthur Gretton, Yann Ollivier, and Arthur Szlam for stimulating discussions and also for pointing out numerous related works.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Leon Bottou
    • 1
    Email author
  • Martin Arjovsky
    • 2
  • David Lopez-Paz
    • 3
  • Maxime Oquab
    • 4
  1. 1.Facebook AI ResearchNew YorkUSA
  2. 2.New York UniversityNew YorkUSA
  3. 3.Facebook AI ResearchParisFrance
  4. 4.InriaParisFrance

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