Wasserstein Distance

The Wasserstein distance, a metric from optimal transport theory, quantifies the similarity between probability distributions by measuring the minimum "work" needed to transform one distribution into another. Current research focuses on developing computationally efficient algorithms for calculating Wasserstein distances, particularly in high-dimensional spaces, with approaches including sliced Wasserstein distances, Sinkhorn algorithms, and embedding techniques using neural networks (e.g., transformers). These advancements are impacting diverse fields, enabling improved performance in tasks such as domain adaptation, data valuation, robust statistics, and generative modeling, by providing a robust and informative measure of distributional similarity.