Unbalanced Optimal Transport: Efficient solutions for outlier-robust machine learning (Laetitia Chapel)

Optimal transport (OT) has become a powerful tool for calculating distances (a.k.a. Wasserstein or earth mover's distances) between empirical distribution of data thanks to efficient computational schemes that make the transport computation tractable. The OT problem aims to find a transportation map that preserves the total mass between two probability distributions, requiring their mass to be equal. However, this requirement can be overly restrictive in certain applications such as color or shape matching, where distributions may have arbitrary masses and/or when only a fraction of the total mass has to be transported. This also happens when the source and/or target distributions are contaminated by outliers; in such cases, one might want to exclude these outliers from the transportation plan. Unbalanced Optimal Transport adresses the problem of removing some mass from the problem by relaxing marginal conditions (using weighted penalties in lieu of equality). In this talk, we will review efficient algorithms that can be devised in this context, particularly focusing on formulations where no additional regularization is imposed on the OT plan.