  Bottlenecks of binary classification from positive and unlabeled data (PU
classification) are the requirements that given unlabeled patterns are drawn
from the test marginal distribution, and the penalty of the false positive
error is identical to the false negative error. However, such requirements are
often not fulfilled in practice. In this paper, we generalize PU classification
to the class prior shift and asymmetric error scenarios. Based on the analysis
of the Bayes optimal classifier, we show that given a test class prior, PU
classification under class prior shift is equivalent to PU classification with
asymmetric error. Then, we propose two different frameworks to handle these
problems, namely, a risk minimization framework and density ratio estimation
framework. Finally, we demonstrate the effectiveness of the proposed frameworks
and compare both frameworks through experiments using benchmark datasets.
