  In unsupervised domain adaptation, it is widely known that the target domain
error can be provably reduced by having a shared input representation that
makes the source and target domains indistinguishable from each other. Very
recently it has been studied that not just matching the marginal input
distributions, but the alignment of output (class) distributions is also
critical. The latter can be achieved by minimizing the maximum discrepancy of
predictors (classifiers). In this paper, we adopt this principle, but propose a
more systematic and effective way to achieve hypothesis consistency via
Gaussian processes (GP). The GP allows us to define/induce a hypothesis space
of the classifiers from the posterior distribution of the latent random
functions, turning the learning into a simple large-margin posterior separation
problem, far easier to solve than previous approaches based on adversarial
minimax optimization. We formulate a learning objective that effectively pushes
the posterior to minimize the maximum discrepancy. This is further shown to be
equivalent to maximizing margins and minimizing uncertainty of the class
predictions in the target domain, a well-established principle in classical
(semi-)supervised learning. Empirical results demonstrate that our approach is
comparable or superior to the existing methods on several benchmark domain
adaptation datasets.
