  This paper presents a theoretical analysis of sample selection bias
correction. The sample bias correction technique commonly used in machine
learning consists of reweighting the cost of an error on each training point of
a biased sample to more closely reflect the unbiased distribution. This relies
on weights derived by various estimation techniques based on finite samples. We
analyze the effect of an error in that estimation on the accuracy of the
hypothesis returned by the learning algorithm for two estimation techniques: a
cluster-based estimation technique and kernel mean matching. We also report the
results of sample bias correction experiments with several data sets using
these techniques. Our analysis is based on the novel concept of distributional
stability which generalizes the existing concept of point-based stability. Much
of our work and proof techniques can be used to analyze other importance
weighting techniques and their effect on accuracy when using a distributionally
stable algorithm.
