Entropy Regularized Optimal Transport

Entropy-regularized optimal transport (EOT) addresses the problem of finding the most efficient way to transform one probability distribution into another, while incorporating an entropy term to encourage smoother, more robust solutions. Current research focuses on developing efficient algorithms like Sinkhorn iterations and Schrödinger bridges, improving robustness to noise and outliers, and extending EOT to handle various constraints (e.g., bounded domains, sparsity) and data types (e.g., time series, graphs). EOT's ability to compare and manipulate probability distributions has significant implications for diverse fields, including generative modeling, data analysis, and machine learning, offering improved methods for tasks like barycenter estimation, generative modeling within constraints, and independence testing.