Entropic Optimal Transport

Entropic optimal transport (EOT) addresses the problem of efficiently comparing and aligning probability distributions, particularly in high-dimensional spaces, by incorporating entropic regularization into the classical optimal transport problem. Current research focuses on developing faster and more robust algorithms, such as variations of the Sinkhorn algorithm and novel approaches leveraging energy-based models and diffusion processes, to compute EOT distances and transport plans, often with a focus on handling constraints and unbalanced distributions. This field is significant due to its wide applicability in machine learning, including semi-supervised learning, data integration, and generative modeling, offering principled methods for tasks like data alignment, barycenter estimation, and transfer learning.