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

Positive-Unlabeled Classification under Class Prior Shift and Asymmetric Error