  A key assumption in supervised learning is that training and test data follow
the same probability distribution. However, this fundamental assumption is not
always satisfied in practice, e.g., due to changing environments, sample
selection bias, privacy concerns, or high labeling costs. Transfer learning
(TL) relaxes this assumption and allows us to learn under distribution shift.
Classical TL methods typically rely on importance-weighting -- a predictor is
trained based on the training losses weighted according to the importance
(i.e., the test-over-training density ratio). However, as real-world machine
learning tasks are becoming increasingly complex, high-dimensional, and
dynamical, novel approaches are explored to cope with such challenges recently.
In this article, after introducing the foundation of TL based on
importance-weighting, we review recent advances based on joint and dynamic
importance-predictor estimation. Furthermore, we introduce a method of causal
mechanism transfer that incorporates causal structure in TL. Finally, we
discuss future perspectives of TL research.
