  All famous machine learning algorithms that comprise both supervised and
semi-supervised learning work well only under a common assumption: the training
and test data follow the same distribution. When the distribution changes, most
statistical models must be reconstructed from newly collected data, which for
some applications can be costly or impossible to obtain. Therefore, it has
become necessary to develop approaches that reduce the need and the effort to
obtain new labeled samples by exploiting data that are available in related
areas, and using these further across similar fields. This has given rise to a
new machine learning framework known as transfer learning: a learning setting
inspired by the capability of a human being to extrapolate knowledge across
tasks to learn more efficiently. Despite a large amount of different transfer
learning scenarios, the main objective of this survey is to provide an overview
of the state-of-the-art theoretical results in a specific, and arguably the
most popular, sub-field of transfer learning, called domain adaptation. In this
sub-field, the data distribution is assumed to change across the training and
the test data, while the learning task remains the same. We provide a first
up-to-date description of existing results related to domain adaptation problem
that cover learning bounds based on different statistical learning frameworks.
