Understand
This short article revisits some of the ideas introduced in arXiv:1701.07875 and arXiv:1705.07642 in a simple setup.
- This sheds some lights on the connexions between Variational Autoencoders (VAE), Generative Adversarial Networks (GAN) and Minimum Kantorovitch Estimators (MKE).
Built on
On minimum Kantorovich distance estimators
Federico Bassetti, Antonella Bodini, and Eugenio Regazzini · 2006
Earlier work this paper cites.
Optimal transport: old and new
Cédric Villani · 2008
Earlier work this paper cites.
Auto-encoding variational bayes
Diederik P. Kingma and Max Welling · 2013
Earlier work this paper cites.
Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
Earlier work this paper cites.
Similar
Optimal transport for applied mathematicians
Filippo Santambrogio · 2015
Cited alongside, same era.
Scaling algorithms for unbalanced transport problems
Lenaic Chizat, Gabriel Peyré, Bernhard Schmitzer, and Fancois-Xavier Vialard · 2016
Cited alongside, same era.
Stochastic optimization for large-scale optimal transport
Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
Cited alongside, same era.
Wasserstein training of restricted Boltzmann machines
Grégoire Montavon, Klaus-Robert Müller, and Marco Cuturi · 2016
Cited alongside, same era.
Mémoire sur la théorie des déblais et des remblais
Gaspard Monge
Cited in the paper.
Then
Wasserstein GAN
Martin Arjovsky, Soumith Chintala, and Léon Bottou · 2017
Closest in time.
Inference in generative models using the Wasserstein distance
Espen Bernton, Pierre E Jacob, Mathieu Gerber, and Christian P Robert · 2017
Closest in time.
From optimal transport to generative modeling: the VEGAN cookbook
Olivier Bousquet, Sylvain Gelly, Ilya Tolstikhin, Carl-Johann Simon-Gabriel, and Bernhard Schoelkopf · 2017
Closest in time.
Sinkhorn-autodiff: Tractable Wasserstein learning of generative models
Aude Genevay, Gabriel Peyré, and Marco Cuturi · 2017
Closest in time.
Beyond the bibliography
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…