  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}.
