  The shift between the training and testing distributions is commonly due to
sample selection bias, a type of bias caused by non-random sampling of examples
to be included in the training set. Although there are many approaches proposed
to learn a classifier under sample selection bias, few address the case where a
subset of labels in the training set are missing-not-at-random (MNAR) as a
result of the selection process. In statistics, Greene's method formulates this
type of sample selection with logistic regression as the prediction model.
However, we find that simply integrating this method into a robust
classification framework is not effective for this bias setting. In this paper,
we propose BiasCorr, an algorithm that improves on Greene's method by modifying
the original training set in order for a classifier to learn under MNAR sample
selection bias. We provide theoretical guarantee for the improvement of
BiasCorr over Greene's method by analyzing its bias. Experimental results on
real-world datasets demonstrate that BiasCorr produces robust classifiers and
can be extended to outperform state-of-the-art classifiers that have been
proposed to train under sample selection bias.
