  We consider unsupervised domain adaptation (UDA) for classification problems
in the presence of missing data in the unlabelled target domain. More
precisely, motivated by practical applications, we analyze situations where
distribution shift exists between domains and where some components are
systematically absent on the target domain without available supervision for
imputing the missing target components. We propose a generative approach for
imputation. Imputation is performed in a domain-invariant latent space and
leverages indirect supervision from a complete source domain. We introduce a
single model performing joint adaptation, imputation and classification which,
under our assumptions, minimizes an upper bound of its target generalization
error and performs well under various representative divergence families
(H-divergence, Optimal Transport). Moreover, we compare the target error of our
Adaptation-imputation framework and the "ideal" target error of a UDA
classifier without missing target components. Our model is further improved
with self-training, to bring the learned source and target class posterior
distributions closer. We perform experiments on three families of datasets of
different modalities: a classical digit classification benchmark, the Amazon
product reviews dataset both commonly used in UDA and real-world digital
advertising datasets. We show the benefits of jointly performing adaptation,
classification and imputation on these datasets.
