*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.

Léon Bottou, Martin Arjovsky, David Lopez-Paz and Maxime Oquab: **Geometrical Insights for Implicit Generative Modeling**, *Braverman Readings in Machine Learning: Key Ideas from Inception to Current State*, 229–268, Edited by Ilya Muchnik Lev Rozonoer, Boris Mirkin, LNAI Vol. 11100, Springer, 2018.

@incollection{bottou-geometry-2018, author = {Bottou, L{\'e}on and Arjovsky, Martin and Lopez-Paz, David and Oquab, Maxime}, title = {Geometrical Insights for Implicit Generative Modeling}, booktitle = {Braverman Readings in Machine Learning: Key Ideas from Inception to Current State}, editor = {Lev Rozonoer, Boris Mirkin, Ilya Muchnik}, series = {LNAI Vol. 11100}, publisher = {Springer}, year = {2018}, pages = {229--268}, url = {http://leon.bottou.org/papers/bottou-geometry-2018}, }

papers/bottou-geometry-2018.txt · Last modified: 2018/09/07 12:36 by leonb