  The problem of domain adaptation on an unlabeled target dataset using
knowledge from multiple labelled source datasets is becoming increasingly
important. A key challenge is to design an approach that overcomes the
covariate and target shift both among the sources, and between the source and
target domains. In this paper, we address this problem from a new perspective:
instead of looking for a latent representation invariant between source and
target domains, we exploit the diversity of source distributions by tuning
their weights to the target task at hand. Our method, named Weighted Joint
Distribution Optimal Transport (WJDOT), aims at finding simultaneously an
Optimal Transport-based alignment between the source and target distributions
and a re-weighting of the sources distributions. We discuss the theoretical
aspects of the method and propose a conceptually simple algorithm. Numerical
experiments indicate that the proposed method achieves state-of-the-art
performance on simulated and real-life datasets.
