Unbalanced Optimal Transport

Unbalanced optimal transport (UOT) extends traditional optimal transport by relaxing the constraint of equal total mass between compared distributions, making it more robust to outliers and data imbalances. Current research focuses on developing efficient algorithms, such as improved Sinkhorn iterations and Frank-Wolfe methods, often incorporating entropic regularization or low-rank approximations to enhance scalability. These advancements are driving applications in diverse fields, including generative modeling, graph matching, and object detection, where UOT's ability to handle noisy or incomplete data offers significant advantages over traditional methods.