Geometrical Insights for Implicit Generative Modeling

21 Dec 2017  ·  Leon Bottou, Martin Arjovsky, David Lopez-Paz, Maxime Oquab ·

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. read more

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