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arXiv · 1712.07822

Geometrical Insights for Implicit Generative Modeling

Leon Bottou·Martin Arjovsky·David Lopez-Paz·Maxime Oquab
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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.

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Leon Bottou, Martin Arjovsky, David Lopez-Paz, Maxime Oquab. 2017-12-21. Geometrical Insights for Implicit Generative Modeling. https://arxiv.org/abs/1712.07822

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