Spun off from a reading group I ran
to the theme *what even is is the Wasserstein GAN?*
It’s a particular type of generative adversarial network.

The Wasserstein GAN paper (Arjovsky, Chintala, and Bottou 2017) made enough of a splash that it’s worth considering separately from the other GAN stuff. Is it even “adversarial”? That looks marginal to me.

Today I’m leading a reading group GANs are famous for generating images, but I am interested in their use in simulating from difficult distributions in general.

I will not summarize WGANs better than the following handy sources, so these are the basis for the tutorial until such time as I find myself actually using this stuff in my own work.

- Alexi Pan reads the WGAN paper.
- Mindcodec discusses Wasserstein-type metrics, i.e. optimal transport ones, with an eye to WGAN.
- Here is a deep learning course that culminates in WGAN with some involvement by the authors of the WGAN paper.
- Vincent Hermann presents the Kantorovich-Rubinstein duality trick intuitively.

Connection to other types of regularisation? (Gulrajani et al. 2017; Miyato et al. 2018)

Arjovsky, Martin, Soumith Chintala, and Léon Bottou. 2017. “Wasserstein Generative Adversarial Networks.” In *International Conference on Machine Learning*, 214–23. http://proceedings.mlr.press/v70/arjovsky17a.html.

Goodfellow, Ian, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. 2014. “Generative Adversarial Nets.” In *Advances in Neural Information Processing Systems 27*, edited by Z. Ghahramani, M. Welling, C. Cortes, N. D. Lawrence, and K. Q. Weinberger, 2672–80. NIPS’14. Cambridge, MA, USA: Curran Associates, Inc. http://papers.nips.cc/paper/5423-generative-adversarial-nets.pdf.

Gulrajani, Ishaan, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron Courville. 2017. “Improved Training of Wasserstein GANs,” March. http://arxiv.org/abs/1704.00028.

Lee, Hung-yi, and Yu Tsao. n.d. “Generative Adversarial Network.” In, 222.

Miyato, Takeru, Toshiki Kataoka, Masanori Koyama, and Yuichi Yoshida. 2018. “Spectral Normalization for Generative Adversarial Networks.” In *ICLR 2018*. http://arxiv.org/abs/1802.05957.

Panaretos, Victor M., and Yoav Zemel. 2019. “Statistical Aspects of Wasserstein Distances.” *Annual Review of Statistics and Its Application* 6 (1): 405–31. https://doi.org/10.1146/annurev-statistics-030718-104938.