Quantitative Uniform Stability of the Iterative Proportional Fitting Procedure

OT provides a theoretical framework for analysis in the space of probability measures and has deep connections with many branches of mathematics including partial differential equations and probability. Beyond its intrinsic interest, OT has recently become an extremely important tool for data science and machine learning, finding numerous applications in fields as diverse as imaging, computer vision, natural language processing (Peyré and Cuturi, 2019).