  As a vital problem in classification-oriented transfer, unsupervised domain
adaptation (UDA) has attracted widespread attention in recent years. Previous
UDA methods assume the marginal distributions of different domains are shifted
while ignoring the discriminant information in the label distributions. This
leads to classification performance degeneration in real applications. In this
work, we focus on the conditional distribution shift problem which is of great
concern to current conditional invariant models. We aim to seek a kernel
covariance embedding for conditional distribution which remains yet unexplored.
Theoretically, we propose the Conditional Kernel Bures (CKB) metric for
characterizing conditional distribution discrepancy, and derive an empirical
estimation for the CKB metric without introducing the implicit kernel feature
map. It provides an interpretable approach to understand the knowledge transfer
mechanism. The established consistency theory of the empirical estimation
provides a theoretical guarantee for convergence. A conditional distribution
matching network is proposed to learn the conditional invariant and
discriminative features for UDA. Extensive experiments and analysis show the
superiority of our proposed model.
