  Unsupervised domain adaptation studies how to transfer a learner from a
labeled source domain to an unlabeled target domain with different
distributions. Existing methods mainly focus on matching the marginal
distributions of the source and target domains, which probably lead a
misalignment of samples from the same class but different domains. In this
paper, we deal with this misalignment by achieving the class-conditioned
transferring from a new perspective. We aim to maximize the conditional
independence of feature and domain given class in the reproducing kernel
Hilbert space. The optimization of the conditional independence measure can be
viewed as minimizing a surrogate of a certain mutual information between
feature and domain. An interpretable empirical estimation of the conditional
dependence is deduced and connected with the unconditional case. Besides, we
provide an upper bound on the target error by taking the class-conditional
distribution into account, which provides a new theoretical insight for most
class-conditioned transferring methods. In addition to unsupervised domain
adaptation, we extend our method to the multi-source scenario in a natural and
elegant way. Extensive experiments on four benchmarks validate the
effectiveness of the proposed models in both unsupervised domain adaptation and
multiple source domain adaptation.
