  Maximum mean discrepancy (MMD) has been widely adopted in domain adaptation
to measure the discrepancy between the source and target domain distributions.
Many existing domain adaptation approaches are based on the joint MMD, which is
computed as the (weighted) sum of the marginal distribution discrepancy and the
conditional distribution discrepancy; however, a more natural metric may be
their joint probability distribution discrepancy. Additionally, most metrics
only aim to increase the transferability between domains, but ignores the
discriminability between different classes, which may result in insufficient
classification performance. To address these issues, discriminative joint
probability MMD (DJP-MMD) is proposed in this paper to replace the
frequently-used joint MMD in domain adaptation. It has two desirable
properties: 1) it provides a new theoretical basis for computing the
distribution discrepancy, which is simpler and more accurate; 2) it increases
the transferability and discriminability simultaneously. We validate its
performance by embedding it into a joint probability domain adaptation
framework. Experiments on six image classification datasets demonstrated that
the proposed DJP-MMD can outperform traditional MMDs.
