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Joint distribution optimal transportation for domain adaptation

Banff International Research Station for Mathematical Innovation and Discovery

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/labels space distributions of the two domain ${\mathrm{ps}}$ and ${\mathrm{pt}}$. We propose a solution of this problem with optimal transport, that allows to recover an estimated target ${\mathrm{pt}}^f=(X,f(X))$ by optimizing simultaneously the optimal coupling and $f$. We show that our method corresponds to the minimization of a generalization bound, 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. Joint work with Nicolas COURTY, Amaury Habrard, and Alain RAKOTOMAMONJY

Mathematics; Calculus of variations and optimal control; optimization; Statistics; Scientific computing

video/mp4

Author affiliation: Université de Nice Sophia Antipolis

2017-11-01

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/63506

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/