Wasserstein Barycenter

Wasserstein barycenters represent a powerful method for averaging probability distributions, finding a central distribution that minimizes the average Wasserstein distance to a set of input distributions. Current research focuses on improving the efficiency and robustness of barycenter computation, particularly for high-dimensional data and in the presence of outliers, employing techniques like coresets, entropic regularization, and neural networks (including transformers) to achieve scalability. These advancements are impacting diverse fields, including image processing, graph analysis, and fair machine learning, by enabling efficient aggregation of heterogeneous data and mitigating biases in data-driven decision-making.