  Learning from positive and unlabeled (PU) data is an important problem in
various applications. Most of the recent approaches for PU classification
assume that the class-prior (the ratio of positive samples) in the training
unlabeled dataset is identical to that of the test data, which does not hold in
many practical cases. In addition, we usually do not know the class-priors of
the training and test data, thus we have no clue on how to train a classifier
without them. To address these problems, we propose a novel PU classification
method based on density ratio estimation. A notable advantage of our proposed
method is that it does not require the class-priors in the training phase;
class-prior shift is incorporated only in the test phase. We theoretically
justify our proposed method and experimentally demonstrate its effectiveness.
