  Importance weighting is a fundamental procedure in statistics and machine
learning that weights the objective function or probability distribution based
on the importance of the instance in some sense. The simplicity and usefulness
of the idea has led to many applications of importance weighting. For example,
it is known that supervised learning under an assumption about the difference
between the training and test distributions, called distribution shift, can
guarantee statistically desirable properties through importance weighting by
their density ratio. This survey summarizes the broad applications of
importance weighting in machine learning and related research.
