Generative Adversarial Networks based on optimal transport: a survey

Optimal transport theory provides a distance to find the cheapest way to convey an object from one place to another, based on a certain cost. Optimal transport thus defines a set of geometric tools with interesting properties in terms of coupling and correspondence between probability distributions. Recent theoretical and algorithmic advances in this theory generate interesting methods for data science. Bearing this in mind, Wasserstein Generative Adversarial Networks (WGAN) make it possible to generate complex data with a high degree of realism in addition to real data which may be limited in certain contexts where their accessibility is restricted. This paper presents a literature review of recent developments in optimal transport-based data science in some practical and theoretical contexts, for solving machine learning problems. In the theoretical developments, we will appreciate the extension of WGANs coupled with conditions, autoencoders, and transfer learning. We made a critical evaluation of prevalent WGANs by synthesizing and comparing information between them to improve understanding of their respective impact. The practical context shows prominent applications in the fields of industry, health, and safety. Finally, challenges are discussed, and the conclusion presents the benefits of WGAN and prospective analyses.