Joint distribution optimal transportation for domain adaptation

This paper deals with the unsupervised domain adaptation problem, where one wants to estimate aprediction function f in a given target domain without any labeled sample by exploiting the knowledgeavailable from a source domain where labels are known. Our work makes the following assumption: thereexists a non-linear transformation between the joint feature/label space distributions of the two domainPs andPt. We propose a solution of this problem with optimal transport, that allows to recover anestimated target Pt = (X, f(X)) by optimizing simultaneously the optimal coupling and f . We showthat our method corresponds to the minimization of a bound on the target error, and provide an efficientalgorithmic solution, for which convergence is proved. The versatility of our approach, both in terms ofclass 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.