  We study the label shift problem between the source and target domains in
general domain adaptation (DA) settings. We consider transformations
transporting the target to source domains, which enable us to align the source
and target examples. Through those transformations, we define the label shift
between two domains via optimal transport and develop theory to investigate the
properties of DA under various DA settings (e.g., closed-set, partial-set,
open-set, and universal settings). Inspired from the developed theory, we
propose Label and Data Shift Reduction via Optimal Transport (LDROT) which can
mitigate the data and label shifts simultaneously. Finally, we conduct
comprehensive experiments to verify our theoretical findings and compare LDROT
with state-of-the-art baselines.
