Geometrical Insights for Implicit Generative Modeling

By L. Eon Bottou, Martín Arjovsky, David Lopez-Paz, Maxime Oquab. 2017

52 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistics and Probability

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Citations in the corpus

Generalized Energy Based Models (2020, background): “When the latent spaceZ has a smaller dimension than the input spaceX , the IGM will be supported on a lower dimensional manifold of X , and thus will not possess a Lebesgue density on X (Bottou et al., 2017).”
Spurious Valleys in One-hidden-layer Neural Network Optimization Landscapes (2019, background): “, 2016) and implicit generative modeling (Bottou et al., 2017).”
KALE: When Energy-Based Learning Meets Adversarial Training (2020, methodology): “When the latent space Z has a smaller dimension than the input space X , the IGM will typically be supported on a lower dimensional manifold 1 of X and will thus not possess a Lebesgue density on X (Bottou et al., 2017).”