  Unsupervised Domain Adaptation aims to learn a model on a source domain with
labeled data in order to perform well on unlabeled data of a target domain.
Current approaches focus on learning \textit{Domain Invariant Representations}.
It relies on the assumption that such representations are well-suited for
learning the supervised task in the target domain. We rather believe that a
better and minimal assumption for performing Domain Adaptation is the
\textit{Hidden Covariate Shift} hypothesis. Such approach consists in learning
a representation of the data such that the label distribution conditioned on
this representation is domain invariant. From the Hidden Covariate Shift
assumption, we derive an optimization procedure which learns to match an
estimated joint distribution on the target domain and a re-weighted joint
distribution on the source domain. The re-weighting is done in the
representation space and is learned during the optimization procedure. We show
on synthetic data and real world data that our approach deals with both
\textit{Target Shift} and \textit{Concept Drift}. We report state-of-the-art
performances on Amazon Reviews dataset \cite{blitzer2007biographies}
demonstrating the viability of this approach.
