Joint distribution optimal transportation for domain adaptation

This paper 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. Our work makes the following assumption: there exists a nonlinear transformation between the joint feature/label space distributions of the two domain P_s and P_t that can be estimated with optimal transport. We propose a solution of this problem that allows to recover an estimated target P_t^f = (X, f(X)) by optimizing simultaneously the optimal coupling and f. We show that our method corresponds to the minimization of a bound on the target error, and provide an efficient algorithmic solution, for which convergence is proved. The versatility of our approach, both in terms of class of hypothesis or loss functions is demonstrated with real world classification and regression problems, for which we reach or surpass state-of-the-art results.