Joint Distribution Optimal Transportation for Domain Adaptation
It addresses the problem of adapting models across domains without target labels, which is incremental as it builds on existing optimal transport approaches.
The paper tackles unsupervised domain adaptation by assuming a non-linear transformation between joint feature/label distributions of source and target domains, proposing an optimal transport method that jointly optimizes coupling and prediction functions, and achieves state-of-the-art results in classification and regression tasks.
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 non-linear transformation between the joint feature/label space distributions of the two domain $\mathcal{P}_s$ and $\mathcal{P}_t$. We propose a solution of this problem with optimal transport, that allows to recover an estimated target $\mathcal{P}^f_t=(X,f(X))$ 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.