Marginal Constraint

Marginal constraints, which restrict the distributions of certain variables in a problem, are a crucial aspect of various computational tasks, particularly in machine learning and optimal transport. Current research focuses on developing efficient algorithms, such as variations of Sinkhorn and flow-based methods, to handle these constraints, often within the context of weak supervision or optimal transport problems. This work aims to improve the accuracy and efficiency of solutions while providing theoretical guarantees on convergence and constraint satisfaction. The impact of this research extends to improving the reliability of machine learning models trained with limited or noisy data and advancing the field of optimal transport.