  We propose the discrepancy-based generalization theories for unsupervised
domain adaptation. Previous theories introduced distribution discrepancies
defined as the supremum over complete hypothesis space. The hypothesis space
may contain hypotheses that lead to unnecessary overestimation of the risk
bound. This paper studies the localized discrepancies defined on the hypothesis
space after localization. First, we show that these discrepancies have
desirable properties. They could be significantly smaller than the pervious
discrepancies. Their values will be different if we exchange the two domains,
thus can reveal asymmetric transfer difficulties. Next, we derive improved
generalization bounds with these discrepancies. We show that the discrepancies
could influence the rate of the sample complexity. Finally, we further extend
the localized discrepancies for achieving super transfer and derive
generalization bounds that could be even more sample-efficient on source
domain.
