This presentation deals with the unsupervised domain adaptation problem, where one wants to estimate a prediction function f in a given target domain without any labeled sample by exploiting the knowledge available from a source domain where labels are known. After a short introduction of recent developent in domain adaptation and their relation to optimal transport we will present a method that estimates a barycentric mapping between the feature distributions in order to adapt the training dataset prior to learning. Next we propose a novel method that model with optimal transport the transformation between the joint feature/labels space distributions of the two domains. We aim at recovering an estimated target distribution ptf=(X,f(X)) by optimizing simultaneously the optimal coupling and f. We discuss the generalization of the proposed method, and provide an efficient algorithmic solution. The versatility of the approach, both in terms of class of hypothesis or loss functions is demonstrated with real world classification, regression problems and large datasets where stochastic approaches become necessary.

Joint work with Nicolas COURTY, Devis TUIA, Amaury HABRARD, and Alain RAKOTOMAMONJY