  We present a 2-step optimal transport approach that performs a mapping from a
source distribution to a target distribution. Here, the target has the
particularity to present new classes not present in the source domain. The
first step of the approach aims at rejecting the samples issued from these new
classes using an optimal transport plan. The second step solves the target
(class ratio) shift still as an optimal transport problem. We develop a dual
approach to solve the optimization problem involved at each step and we prove
that our results outperform recent state-of-the-art performances. We further
apply the approach to the setting where the source and target distributions
present both a label-shift and an increasing covariate (features) shift to show
its robustness.
