We address the problem of unsupervised domain adaptation under the setting of generalized target shift (joint class-conditional and label shifts). For this framework, we theoretically show that, for good generalization, it is necessary to learn a latent representation in which both marginals and class-conditional distributions are aligned across domains. For this sake, we propose a learning problem that minimizes importance weighted loss in the source domain and a Wasserstein distance between weighted marginals. For a proper weighting, we provide an estimator of target label proportion by blending mixture estimation and optimal matching by optimal transport. This estimation comes with theoretical guarantees of correctness under mild assumptions. Our experimental results show that our method performs better on average than competitors across a range domain adaptation problems including emph{digits},emph{VisDA} and emph{Office}. Code for this paper is available at url{https://github.com/arakotom/mars_domain_adaptation}.
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