Wasserstein Space
Wasserstein space, the space of probability measures equipped with the Wasserstein distance (a metric based on optimal transport), is a powerful framework for analyzing and manipulating probability distributions. Current research focuses on developing efficient algorithms for optimization and inference within this space, including gradient descent methods, variational inference techniques, and dictionary learning approaches leveraging Wasserstein barycenters. These advancements are driving progress in diverse fields such as generative modeling, domain adaptation, and trajectory inference, offering improved robustness and scalability for handling complex data distributions. The ability to perform computations directly on probability measures rather than point estimates promises significant impact across machine learning and related disciplines.
Papers
Global Optimisation of Black-Box Functions with Generative Models in the Wasserstein Space
Tigran Ramazyan, Mikhail Hushchyn, Denis Derkach
Dataset Dictionary Learning in a Wasserstein Space for Federated Domain Adaptation
Eduardo Fernandes Montesuma, Fabiola Espinoza Castellon, Fred Ngolè Mboula, Aurélien Mayoue, Antoine Souloumiac, Cédric Gouy-Pailler